WCGT 2014 – The 3 rd Midwest Workshop on Control and Game Theory

Inference (prediction) is believed to be a fundamentally important computational function for biological sensory systems. For example, the Bayesian model of sensory (e.g., visual) signal processing postulates that the cortical networks in the brain encode a probabilistic belief about reality. The belief state (modeled as a posterior distribution in the Bayes’ formalism) is updated based on comparison between the novel stimuli (from senses) and the internal prediction. A natural question to ask then is whether there is a rigorous methodology (and algorithms) to implement complex forms of prediction (via Bayes theorem) at the level of neurons the computing elements of the brain? In this talk I will provide a qualified answer to this question based on a coupled oscillator feedback particle filter model. A single oscillator is a simplified model of a single spiking neuron, and the coupled oscillator model solves an inference problem. The methodology will be described with the aid of an activity recognition demonstration. Time permitting, some applications to robotic locomotion will also be discussed. This work is the result of collaboration with Professor Sean Meyn, and with several students at the University of Illinois. Title: A Distributed Algorithm for Network Localization Using AngleOf-Arrival Information Author: Jianghai Hu (Purdue University, [email protected]) Abstract: The focus of this talk is the AOA network localization problem, namely, localizing network nodes based on the angles-of-arrival measurements between certain neighboring network nodes together with the absolute locations of some anchor nodes. We propose the concepts of stiffness matrix and fixability for the anchored formation graphs modeling the networks and show that they provide a complete characterization of the AOA localizability as well as an explicit formula for the localization result. Moreover, a distributed continuous-time algorithm is proposed that converges globally to the correct localization result on fixable formation graphs. Performances of the proposed algorithm, e.g., convergence rate and robustness to comThe focus of this talk is the AOA network localization problem, namely, localizing network nodes based on the angles-of-arrival measurements between certain neighboring network nodes together with the absolute locations of some anchor nodes. We propose the concepts of stiffness matrix and fixability for the anchored formation graphs modeling the networks and show that they provide a complete characterization of the AOA localizability as well as an explicit formula for the localization result. Moreover, a distributed continuous-time algorithm is proposed that converges globally to the correct localization result on fixable formation graphs. Performances of the proposed algorithm, e.g., convergence rate and robustness to comWCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 7 munication delay, are characterized. Sensitivities of the localization results with respect to errors in AOA measurements and anchor nodes positions will also be discussed. Title: Resilience in Networked Cyber-Robotic Systems Author: Sourabh Bhattacharya (Iowa State University, [email protected]) Abstract: Robots play an important role in tasks related to surveillance. Teams of mobile robots and autonomous vehicles are often deployed in civil as well as military scenarios for intrusion detection and monitoring purposes. In this talk, I will present scenarios of adversarial intrusion and persistent surveillance in teams of autonomous vehicles. I will present some recent results in persistent visual tracking for mobile robots based on pursuit and evasion games. Robots play an important role in tasks related to surveillance. Teams of mobile robots and autonomous vehicles are often deployed in civil as well as military scenarios for intrusion detection and monitoring purposes. In this talk, I will present scenarios of adversarial intrusion and persistent surveillance in teams of autonomous vehicles. I will present some recent results in persistent visual tracking for mobile robots based on pursuit and evasion games. Title: Cooperative Aircraft Defense from an Attacking Missile Author: Eloy Garcia (Air Force Research Laboratory, [email protected]) Abstract: A three-body pursuit-evasion scenario will be addressed. In this scenario an Attacker missile using Command to Line of Sight guidance pursues a Target aircraft and a Defender missile launched by a wingman aims at intercepting the Attacker before it reaches the aircraft. A cooperative optimal control problem is posed which captures the goal of the Target-Defender team, namely, to maximize the separation between Target and Attacker at the instant of capture of the Attacker by the Defender. The optimal control law provides the heading angles for the Target and the Defender team. Similar scenarios are explored, using a game theoretical approach, which characterize different objectives and capabilities of the Attacker and the Target-Defender team. A three-body pursuit-evasion scenario will be addressed. In this scenario an Attacker missile using Command to Line of Sight guidance pursues a Target aircraft and a Defender missile launched by a wingman aims at intercepting the Attacker before it reaches the aircraft. A cooperative optimal control problem is posed which captures the goal of the Target-Defender team, namely, to maximize the separation between Target and Attacker at the instant of capture of the Attacker by the Defender. The optimal control law provides the heading angles for the Target and the Defender team. Similar scenarios are explored, using a game theoretical approach, which characterize different objectives and capabilities of the Attacker and the Target-Defender team. 8 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory Session II: Energy Systems (Saturday, April 26, 10:35 12:00) Title: Generation Investment Equilibria with Strategic Producers Author: Antonio J. Conejo (Ohio State University, [email protected]) Abstract: This presentation describes a methodology to characterize generation investment equilibria in an electricity market with strategic producers. To this end, the investment problem of each producer is represented using a Stackelberg game, whose upper-level problem determines the optimal investment and offers of the producer to maximize its profit, and whose lower-level problems represent different market clearing conditions. This model can be transformed into a mathematical program with equilibrium constraint, MPEC. The joint consideration of all producer MPECs, one per producer, which constitutes a set to interdependent Stackelberg games, is an equilibrium problem with equilibrium constraints. To identify the solutions of this equilibrium problem, each MPEC is replaced by its KKT conditions. The resulting mixed-integer system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem. This presentation describes a methodology to characterize generation investment equilibria in an electricity market with strategic producers. To this end, the investment problem of each producer is represented using a Stackelberg game, whose upper-level problem determines the optimal investment and offers of the producer to maximize its profit, and whose lower-level problems represent different market clearing conditions. This model can be transformed into a mathematical program with equilibrium constraint, MPEC. The joint consideration of all producer MPECs, one per producer, which constitutes a set to interdependent Stackelberg games, is an equilibrium problem with equilibrium constraints. To identify the solutions of this equilibrium problem, each MPEC is replaced by its KKT conditions. The resulting mixed-integer system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem. Title: Modelling and Control of Highly Distributed Loads Author: Ian Hiskens (University of Michigan, [email protected]) Abstract: Responsive load control offers a particularly effective approach to compensating for the variability inherent in large-scale renewable generation, and mitigating the effects of generation and transmission outages. Furthermore, as plug-in electric vehicles grow in popularity, scheduling their charging load will become vitally important to prevent local overloads, and to ensure optimal use of generation resources. The presentation will discuss various control strategies that achieve coordinated response of large numbers of highly distributed and diverse loads. Designing and analysing the dynamic behaviour of load control schemes is reliant upon models that capture both the inherent characteristics of loads together with their response to control signals. The presentation will consider load models which fulfill these requirements. Responsive load control offers a particularly effective approach to compensating for the variability inherent in large-scale renewable generation, and mitigating the effects of generation and transmission outages. Furthermore, as plug-in electric vehicles grow in popularity, scheduling their charging load will become vitally important to prevent local overloads, and to ensure optimal use of generation resources. The presentation will discuss various control strategies that achieve coordinated response of large numbers of highly distributed and diverse loads. Designing and analysing the dynamic behaviour of load control schemes is reliant upon models that capture both the inherent characteristics of loads together with their response to control signals. The presentation will consider load models which fulfill these requirements. Title: Control of Thermostatic Loads Using Moving Horizon Estimation of Individual Load States Author: Johanna Mathieu (University of Michigan, [email protected]) Abstract: Electric power systems with high penetrations of intermittent and uncertain renewable energy sources will require additional reserve capacity. Recent research has shown that thermostatically controlled loads (TCLs) can Electric power systems with high penetrations of intermittent and uncertain renewable energy sources will require additional reserve capacity. Recent research has shown that thermostatically controlled loads (TCLs) can WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 9 provide reserves to power systems. However, a key challenge is to achieve coordinated control of large populations of resources using existing communication and control infrastructure or with minimal addition of new infrastructure. In this talk, I will describe how we can use state estimation to improve our ability to control an aggregation of TCLs to track power system signals. Past work has focused on estimating the states of aggregate system models, such as Markov models and PDE models. Our new work investigates the possibility of estimating the states of individual TCLs, modeled as stochastic hybrid systems, using measurements/estimates obtained from existing equipment, for example, data transmitted from residential smart meters at low frequency (e.g., every 15 minutes) and real-time estimates of the aggregate power consumption of an aggregation of TCLs computed from distribution substation power measurements. We develop a moving horizon state estimator (MHSE) and benchmark it against a simpler modelbased predictor. We also propose a scalable closed-loop control structure that uses the MHSE to provide frequency control with TCL populations. We demonstrate our results via a number of case studies with different TCL aggregations, process and measurement noise characteristics, and controller forcing levels. Our simulations show that the MHSE usually provides accurate state estimates and improves the controller tracking performance, but the results are dependent upon the noise and forcing levels. Lunch/Poster Session (Saturday, April 26, 12:00 13:30) Title: Real-Time Energy Market Price Volatility Analysis and Control Author: Zhao Wang (University of Notre Dame, [email protected]) Abstract: Real-time dispatching operations, among other operations in different time scales, are organized in deregulated energy markets. Besides traditional generators, novel service providers, such as renewable energy resources, provide services responding to real-time dispatching signals. Uncertain outputs of these novel service providers may influence the underlying realtime energy market, in particular resulting in price volatility. Outputs of uncertain service providers are modeled as Markov processes whose transitions depend on external conditions. We then build market dynamic models to analyze the impacts of unfulfilled services with realistic marginal cost curves. Furthermore, we propose a bidding strategy for uncertain service providers to reduce the impact of uncertainty on market price volatility and improve their expected profits. Real-time dispatching operations, among other operations in different time scales, are organized in deregulated energy markets. Besides traditional generators, novel service providers, such as renewable energy resources, provide services responding to real-time dispatching signals. Uncertain outputs of these novel service providers may influence the underlying realtime energy market, in particular resulting in price volatility. Outputs of uncertain service providers are modeled as Markov processes whose transitions depend on external conditions. We then build market dynamic models to analyze the impacts of unfulfilled services with realistic marginal cost curves. Furthermore, we propose a bidding strategy for uncertain service providers to reduce the impact of uncertainty on market price volatility and improve their expected profits. Title: On Passivity Analysis and Passivation of Feedback Interconnected Systems Using Passivity Indices Author: Feng Zhu (University of Notre Dame, [email protected]) 10 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory Abstract: Passivity indices (levels) are used to measure the excess or shortage of passivity. While most of the work in the literature focuses on stability conditions for interconnected systems using passivity indices (levels), here we focus on passivity and passivation of the feedback interconnection of two input feed-forward output-feedback (IF-OF) passive systems. Passivity indices (levels) are used to measure the excess or shortage of passivity. While most of the work in the literature focuses on stability conditions for interconnected systems using passivity indices (levels), here we focus on passivity and passivation of the feedback interconnection of two input feed-forward output-feedback (IF-OF) passive systems. Although it is well known that the negative feedback interconnection of two passive systems is still passive, the quantitative characterization of passivity for the closed-loop system has not been addressed previously. In our work, the conditions are given to determine passivity indices (levels) in feedback interconnected systems. The results can be viewed as the extension of the well-known compositional property of passivity. We also consider the passivation problem which can be used to render a non-passive plant passive using a feedback interconnected passive controller. The passivity indices (levels) of the passivated system are also determined. The results derived do not require linearity of the systems as it is commonly assumed in the literature. Moreover, passivity and passivation problems for event-triggered feedback interconnected systems are also addressed. The results are extensions of the previous results by considering, in addition, the effect of event-triggered samplers in the feedback path. In this work, we consider passivity in two event-triggered control schemes based on the location of the event-triggered samplers: sampler at plant output and sampler at controller output. For both schemes, we first derive the conditions to characterize passivity indices (levels) for the interconnected systems. The event-triggering condition proposed guarantees that these indices (levels) can be achieved. Then the passivation problem is considered and passivation conditions are provided. The passivation conditions depend on the passivity indices (levels) of the plant and controller and also the event-triggering condition, which reveals the trade off between desired passivity levels and communication resource utilization. Title: Linear-Quadratic Risk-Sensitive Mean Field Games Author: Jun Moon (University of Illinois at Urbana Champaign, [email protected]) Abstract: In this paper, we consider linear-quadratic risk-sensitive mean field games (LQRSMFGs). Each agent strives to minimize an exponentiated integral quadratic cost or risk-sensitive cost function, which is coupled with other agents via a mean field term. By invoking the Nash certainty equivalence principle, we first obtain a robust decentralized control law for each agent to construct a mean field system. We then provide appropriate conditions under which the mean field system admits a unique deterministic function In this paper, we consider linear-quadratic risk-sensitive mean field games (LQRSMFGs). Each agent strives to minimize an exponentiated integral quadratic cost or risk-sensitive cost function, which is coupled with other agents via a mean field term. By invoking the Nash certainty equivalence principle, we first obtain a robust decentralized control law for each agent to construct a mean field system. We then provide appropriate conditions under which the mean field system admits a unique deterministic function WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 11 that approximates the mean field term with arbitrarily small error when the number of agents, say N, goes to infinity. We also show the closed-loop system stability, and prove that the set of N robust decentralized control laws possesses an epsilon-Nash equilibrium property. Moreover, it is shown that epsilon can be taken to be arbitrarily close to zero as N goes to infinity, but our epsilon bound is weaker than its linear-quadratic mean field game (LQMFG) counterpart due to risk-sensitivity in the present case. We also discuss the partial equivalence between the LQRSMFG and the LQ robust mean field game. Finally, we discuss two different limiting cases, and show that one of these is equivalent to the corresponding LQMFG. Title: Electricity Pooling Markets with Strategic Producers Possessing Asymmetric Information Author: Mohammad Rasouli (University of Michigan, [email protected]) Abstract: In the restructured electricity industry, electricity pooling markets are an oligopoly with strategic producers possessing private information (private production cost function). We focus on pooling markets where aggregate demand is represented by a non-strategic agent. We consider demand to be elastic. In the restructured electricity industry, electricity pooling markets are an oligopoly with strategic producers possessing private information (private production cost function). We focus on pooling markets where aggregate demand is represented by a non-strategic agent. We consider demand to be elastic. We propose a market mechanism that has the following features. • It is individually rational. • It is budget balanced. • It is price efficient, that is, at equilibrium the price of electricity is equal to the marginal cost of production. • The energy production profile corresponding to every non-zero Nash equilibrium of the game induced by the mechanism is a solution of the corresponding centralized problem where the objective is the maximization of the sum of the producers’ and consumers’ utilities. We identify some open problems associated with our approach to electricity pooling markets. Title: Sliding Mode Boundary Control of Uncertain Distributed Parameter Dynamic Systems Author: Meng-Bi Cheng (Ohio Stste University, [email protected]) Abstract: This talk considers the boundary stabilization problems of distributed parameter systems subjected to boundary disturbance. These systems including heat systems, wave systems, delay systems, Burgers equations, and This talk considers the boundary stabilization problems of distributed parameter systems subjected to boundary disturbance. These systems including heat systems, wave systems, delay systems, Burgers equations, and 12 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory Schrodinger equations, which are particularly utilized to describe the dynamic behavior of these engineering process: heat conduction processes, mechanical vibrations, time-delay plants, traffic dynamics, and quantum control, respectively. Their system dynamic are governed by partial differential equation (PDE) with different forms or even with complex values. To deal with the system instability, we apply the integral transformation to convert the original PDE system into a target PDE when an appropriate backstopping boundary control input is applied. The associated Lyapunov function can then be used for designing an infinite-dimensional sliding surface for each plant, on which the system exhibits exponential stability, invariant of the bounded matched disturbance. This sliding surface holds the property of one relative order with respect to the control input, such that the conventional or continuous sliding-mode control can be directly applied to achieve the control goal. Simulation results are provided to demonstrate the feasibility of the proposed control scheme. Title: Optimal Velocity Profile using Model Predictive Control Based on V2V Technology Author: Junbo Jing (Ohio Stste University, [email protected]) Abstract: Vehicles’ fuel economy is strongly influenced by the drivers driving habits and judgments. Properly planned velocity profile can effectively reduce the vehicles fuel consumption in various scenarios. However, restricted by the drivers experience and limited traffic information obtained, the drivers can hardly plan precisely for the aim of saving energy. Our research focuses on minimizing the vehicles fuel consumption in the car-following scenario on highways by providing optimal velocity profiles. The system obtains the traffic information needed from on-board sensors and V2V Technology. The on-board sensors measure the positions of the front vehicle, and V2V communications provide over-thehorizon awareness of the changes in traffic flow. Based on the information obtained, Gibbs model is adopted to fit the parameters of the front vehicles driving style using genetic optimization, and the front vehicles future velocity profile is predicted for a horizon of seconds. Intelligent Driver Model and Markov Model is deployed to further increase the prediction horizon. With the predicted velocities of the front vehicle, the ego vehicles velocity is determined by using model predictive control. Apart from the aim of optimized fuel economy, driving safety is enforced and ride comfort is cared. Results show that this algorithm can save up to 9% of fuel, and can help to form traffic platoons if widely adopted. Vehicles’ fuel economy is strongly influenced by the drivers driving habits and judgments. Properly planned velocity profile can effectively reduce the vehicles fuel consumption in various scenarios. However, restricted by the drivers experience and limited traffic information obtained, the drivers can hardly plan precisely for the aim of saving energy. Our research focuses on minimizing the vehicles fuel consumption in the car-following scenario on highways by providing optimal velocity profiles. The system obtains the traffic information needed from on-board sensors and V2V Technology. The on-board sensors measure the positions of the front vehicle, and V2V communications provide over-thehorizon awareness of the changes in traffic flow. Based on the information obtained, Gibbs model is adopted to fit the parameters of the front vehicles driving style using genetic optimization, and the front vehicles future velocity profile is predicted for a horizon of seconds. Intelligent Driver Model and Markov Model is deployed to further increase the prediction horizon. With the predicted velocities of the front vehicle, the ego vehicles velocity is determined by using model predictive control. Apart from the aim of optimized fuel economy, driving safety is enforced and ride comfort is cared. Results show that this algorithm can save up to 9% of fuel, and can help to form traffic platoons if widely adopted. Title: Scaled Down Testing and Autonomous Parking Author: Guchan Ozbilgin WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 13 (Ohio Stste University, [email protected]) Abstract: This study illustrates a methodology to reduce the time and effort spent on full-scale Intelligent Transportation System testing, through the use of smallscale testbeds. Scaled down testing platforms enable the researchers to implement, compare, and assess different architectures for intelligent transportation by deploying hardware-in-the-loop (HIL) simulation and testing, giving strong indications on the performance and high-level behavior of such systems at full scale. The performance of the scaled down testing is illustrated using a specific example based on an autonomous parking. The approach is demonstrated on intelligent transportation system testbed in The Ohio State University Control and Intelligent Transportation Research Laboratory. The detailed experimental results show the applicability and robustness of the proposed system. This study illustrates a methodology to reduce the time and effort spent on full-scale Intelligent Transportation System testing, through the use of smallscale testbeds. Scaled down testing platforms enable the researchers to implement, compare, and assess different architectures for intelligent transportation by deploying hardware-in-the-loop (HIL) simulation and testing, giving strong indications on the performance and high-level behavior of such systems at full scale. The performance of the scaled down testing is illustrated using a specific example based on an autonomous parking. The approach is demonstrated on intelligent transportation system testbed in The Ohio State University Control and Intelligent Transportation Research Laboratory. The detailed experimental results show the applicability and robustness of the proposed system. Title: On Market-Based Coordination of Thermostatically Controlled Loads With User Preference Author: Sen Li (Ohio Stste University, [email protected]) Abstract: We focus on the transactive control framework for a group of autonomous Thermostatically Controlled Loads (TCL) to achieve system-level objectives with price incentives. The problem is formulated as maximizing the social welfare subject to a feeder power constraint. It allows the coordinator to affect the aggregated power of a group of dynamical systems, and creates an interactive market where the users and the coordinator cooperatively determine the optimal energy allocation and energy price. The optimal pricing strategy is derived, which maximizes social welfare while respecting the feeder power constraint. The bidding strategy is also proposed, along with the estimation framework for the users to derive bidding in real time with unknown model parameters and partially measureable system state. The simulation results demonstrate that the proposed approach can effectively maximize the social welfare and reduce power congestion at key times. We focus on the transactive control framework for a group of autonomous Thermostatically Controlled Loads (TCL) to achieve system-level objectives with price incentives. The problem is formulated as maximizing the social welfare subject to a feeder power constraint. It allows the coordinator to affect the aggregated power of a group of dynamical systems, and creates an interactive market where the users and the coordinator cooperatively determine the optimal energy allocation and energy price. The optimal pricing strategy is derived, which maximizes social welfare while respecting the feeder power constraint. The bidding strategy is also proposed, along with the estimation framework for the users to derive bidding in real time with unknown model parameters and partially measureable system state. The simulation results demonstrate that the proposed approach can effectively maximize the social welfare and reduce power congestion at key times. Title: Hierarchical Design for Demand-Side Primary Frequency Control Author: Christian Moya (Ohio Stste University, [email protected]) Abstract: A novel hierarchical decentralized framework is proposed for demand-side primary frequency control based on the structure preserving power system model. The proposed framework involves two decision layers and enables the systematic design of load controllers that can effectively increase the system damping. At the supervisory layer, the control gain is determined to specify the desired aggregate load response if frequency deviates. This A novel hierarchical decentralized framework is proposed for demand-side primary frequency control based on the structure preserving power system model. The proposed framework involves two decision layers and enables the systematic design of load controllers that can effectively increase the system damping. At the supervisory layer, the control gain is determined to specify the desired aggregate load response if frequency deviates. This 14 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory gain is periodically updated by taking into account the time-varying availability of end-use responsive loads and the system oscillatory modes. At the device layer, each end-use load changes its operating mode independently with certain probability that is calculated based on a Markov-Chain model, the received control gain, and local frequency measurement. This probability is calculated such that the actual aggregate load response can match the desired one required by the supervisory layer. Simulation results demonstrate the efficacy of the proposed load control strategy. Title: Control of Over-Actuated Constrained Systems with Application to High-efficiency Internal Combustion Engines Author: Junqiang Zhou (Ohio Stste University, [email protected]) Abstract: Modern engines for passenger vehicles are characterized with various advanced technologies with an increased number of actuators, to improve the engine performance such as fuel economy, emission and drivability. However, an innovative control approach is not available to integrate the advanced technologies in its entirety to meet desired system-level performance. This research is motivated by the need to develop a systematic methodology to simultaneously control and optimize over-actuated engine systems. The proposed control methodology relies upon the characterization in geometric terms of the state-space redundancy, which is exploited based on inverse model allocation to shape transient response by optimizing on-line a given cost function. A case study on a Diesel engine shows the effectiveness of the proposed control strategy. Modern engines for passenger vehicles are characterized with various advanced technologies with an increased number of actuators, to improve the engine performance such as fuel economy, emission and drivability. However, an innovative control approach is not available to integrate the advanced technologies in its entirety to meet desired system-level performance. This research is motivated by the need to develop a systematic methodology to simultaneously control and optimize over-actuated engine systems. The proposed control methodology relies upon the characterization in geometric terms of the state-space redundancy, which is exploited based on inverse model allocation to shape transient response by optimizing on-line a given cost function. A case study on a Diesel engine shows the effectiveness of the proposed control strategy. WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 15 Session III: Nonlinear Control (Saturday, April 26, 13:30 15:00) Title: The Geometry of Over-Actuated Systems: Application to Dynamic Control Allocation Author: Andrea Serrani (Ohio State University, [email protected]) Abstract: Input redundancy in a control system is typically resolved by means of (static) control allocation strategies, where the standing assumption prescribes that a virtual control input can be defined, which has the same dimensionality of the regulated output. A control strategy designed on the basis of this virtual input is then “distributed” across the redundant set of actuators via on-line optimization. Essentially, this implies that the redundancy is confined to the null-space of the input operator, which can be factored out by projection. On the other hand, the elusive case of input redundancy with full-rank input operators constitutes an “intrinsic” redundancy in the system, as multiple independently controllable statetrajectories exist that are compatible with a given reference output. In this talk, we give a geometric characterization of intrinsically redundant linear systems, in the context of the full-information output regulation problem. It is shown that intrinsic input redundancy can be exploited in the inverse system towards the definition of novel dynamic control allocation strategies. In the proposed scheme, the steady-state behavior of the system is shaped through dynamic optimization of selected performance criteria penalizing both the control input and the state trajectory, while maintaining invariance of the error-zeroing subspace. An illustrative example on a low-order model of a fighter jet is presented to elucidate the applicability of the method. Input redundancy in a control system is typically resolved by means of (static) control allocation strategies, where the standing assumption prescribes that a virtual control input can be defined, which has the same dimensionality of the regulated output. A control strategy designed on the basis of this virtual input is then “distributed” across the redundant set of actuators via on-line optimization. Essentially, this implies that the redundancy is confined to the null-space of the input operator, which can be factored out by projection. On the other hand, the elusive case of input redundancy with full-rank input operators constitutes an “intrinsic” redundancy in the system, as multiple independently controllable statetrajectories exist that are compatible with a given reference output. In this talk, we give a geometric characterization of intrinsically redundant linear systems, in the context of the full-information output regulation problem. It is shown that intrinsic input redundancy can be exploited in the inverse system towards the definition of novel dynamic control allocation strategies. In the proposed scheme, the steady-state behavior of the system is shaped through dynamic optimization of selected performance criteria penalizing both the control input and the state trajectory, while maintaining invariance of the error-zeroing subspace. An illustrative example on a low-order model of a fighter jet is presented to elucidate the applicability of the method. Title: New Results on Global Stabilization of a Class of NonminimumPhase Nonlinear Systems by Output Feedback Author: Wei Lin (Case Western Reserve University, [email protected]) Abstract: This talk will present some new results on global stabilization by output feedback for nonminimum-phase nonlinear systems. The class of nonlinear systems under consideration has a cascade configuration that consists of a driven system, also known as the inverse dynamics, and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonlinear system if both the driven and driving systems have a lower-triangular form and satisfy a global Lipschitz-like condition,and the inverse dynamics satisfy the inputto-state stabilizability condition. A design procedure is provided for the construction of an n-dimensional dynamic output feedback compensator. Two examples and simulations are also presented to validate the effectiveness of the proposed output feedback control scheme. This talk will present some new results on global stabilization by output feedback for nonminimum-phase nonlinear systems. The class of nonlinear systems under consideration has a cascade configuration that consists of a driven system, also known as the inverse dynamics, and a driving system. It is proved that although the zero dynamics may be unstable, there is an output feedback controller, globally stabilizing the nonlinear system if both the driven and driving systems have a lower-triangular form and satisfy a global Lipschitz-like condition,and the inverse dynamics satisfy the inputto-state stabilizability condition. A design procedure is provided for the construction of an n-dimensional dynamic output feedback compensator. Two examples and simulations are also presented to validate the effectiveness of the proposed output feedback control scheme. 16 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory Title: Stability of Sparse Systems: Theory and Algorithms Author: Mohamed Ali Belabbas (University of Illinois at Urbana-Champaign, [email protected]) Abstract: Many problems of practical and theoretical nature in control, biology and communications are described by an underlying graph encoding which interactions between a group of agents are allowed. It is thus interest to know whether this underlying graph is such that systems defined over it are stabilizable. In this lecture, we present results characterizing such graphs and algorithms to create them in polynomial time. Many problems of practical and theoretical nature in control, biology and communications are described by an underlying graph encoding which interactions between a group of agents are allowed. It is thus interest to know whether this underlying graph is such that systems defined over it are stabilizable. In this lecture, we present results characterizing such graphs and algorithms to create them in polynomial time. Student Session I: Economics and Game Theory (Saturday, April 26, 15:15 16:15) Title: Complexity of Equilibrium for Diffusion Game Over Social Networks Author: Seyed Rasoul Etesami (University of Illinois at Urbana-Champaign, [email protected]) Abstract: We revisit the competitive diffusion game on undirected connected graphs and study the complexity of the existence of pure Nash equilibrium for such game. We first characterize the utility of each player based on the location of its initial seed placements. Using this characterization, we show that the utility of the each player is a sub modular function of its initial seed set. Following this, a simple greedy algorithm provides an initial seed placement within a constant factor of optimal solution. We show the NPhardness of the decision about existence of the pure Nash equilibrium for general networks. Finally we provide some necessary conditions for a given profile to be a Nash equilibrium and prove a lower bound for the maximum social welfare of the game with two players. We revisit the competitive diffusion game on undirected connected graphs and study the complexity of the existence of pure Nash equilibrium for such game. We first characterize the utility of each player based on the location of its initial seed placements. Using this characterization, we show that the utility of the each player is a sub modular function of its initial seed set. Following this, a simple greedy algorithm provides an initial seed placement within a constant factor of optimal solution. We show the NPhardness of the decision about existence of the pure Nash equilibrium for general networks. Finally we provide some necessary conditions for a given profile to be a Nash equilibrium and prove a lower bound for the maximum social welfare of the game with two players. Title: Can Carriers Make More Profit While Users Save Money Author: John Tadrous (Ohio State University, [email protected]) Abstract: In this work, we investigate the profit maximization problem for wireless network carriers and payment minimization for end users. Motivated by our recent findings on proactive resource allocation, we focus on the scenario whereby end users harness predictable demand and WiFi connectivity in proactive data downloads, to minimize their expected payments. Carriers, on the other hand, utilize smart pricing schemes to differentiate between the off-peak and peak hour prices so as to reduce peak costs and maximize their profit. We formulate the tension between the carrier and end user as a In this work, we investigate the profit maximization problem for wireless network carriers and payment minimization for end users. Motivated by our recent findings on proactive resource allocation, we focus on the scenario whereby end users harness predictable demand and WiFi connectivity in proactive data downloads, to minimize their expected payments. Carriers, on the other hand, utilize smart pricing schemes to differentiate between the off-peak and peak hour prices so as to reduce peak costs and maximize their profit. We formulate the tension between the carrier and end user as a WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 17 two-player Stackelberg game in which the carrier assigns prices first, then the end user responds with optimized proactive downloads. We explore the equilibrium points under maximum and average price constraints, and study the impact of WiFi availability on the system’s performance. In particular, we compare the new equilibria with the baseline scenario of flat pricing and no proactive downloads. Despite the potential uncertainty about future demand, and the freshness of proactively downloaded content, we characterize new equilibria points that yield win-win situation with respect to the baseline equilibrium. Title: Robust Toll Design: Influencing Selfish Behavior in Congestion Games with Unknown Price-Sensitive Users Author: Philip Brown (University of Colorado at Boulder, [email protected]) Abstract: We focus on the derivation of taxation mechanisms for improving systemlevel behavior in congestion games with unknown price-sensitive users. Here, a taxation mechanism represents a general rule for assigning local taxation functions to edges in a given network, e.g., Pigovian taxes or marginal-cost taxes. Recent results have identified taxation mechanisms that lead to optimal system-level behavior for the considered class of games; however, these mechanisms require that a system-designer has a complete characterization of network structure and the users’ sensitivities. Furthermore, the robustness of these mechanisms to mis-characterization in this information is unknown. With these issues in mind, we focus on the derivation of robust taxation mechanisms that is, taxation mechanisms that provide strong efficiency guarantees irrespective of the underlying network or user characteristics. With this goal in mind, we define a scaled marginalcost taxation mechanism in which the edge taxation functions are derived without explicit knowledge of the network structure or the users’ sensitivities. We then derive the optimal scaled marginal-cost taxation mechanism that limits worst-case inefficiencies over these uncertainties for the class of parallel-network congestion games with affine latency functions. In other words, we derive the scaled marginal-cost taxation mechanism that optimizes the price of anarchy. Note that viewing the price of anarchy as a design objective represents a significant departure from traditional price of anarchy results in the existing literature. We focus on the derivation of taxation mechanisms for improving systemlevel behavior in congestion games with unknown price-sensitive users. Here, a taxation mechanism represents a general rule for assigning local taxation functions to edges in a given network, e.g., Pigovian taxes or marginal-cost taxes. Recent results have identified taxation mechanisms that lead to optimal system-level behavior for the considered class of games; however, these mechanisms require that a system-designer has a complete characterization of network structure and the users’ sensitivities. Furthermore, the robustness of these mechanisms to mis-characterization in this information is unknown. With these issues in mind, we focus on the derivation of robust taxation mechanisms that is, taxation mechanisms that provide strong efficiency guarantees irrespective of the underlying network or user characteristics. With this goal in mind, we define a scaled marginalcost taxation mechanism in which the edge taxation functions are derived without explicit knowledge of the network structure or the users’ sensitivities. We then derive the optimal scaled marginal-cost taxation mechanism that limits worst-case inefficiencies over these uncertainties for the class of parallel-network congestion games with affine latency functions. In other words, we derive the scaled marginal-cost taxation mechanism that optimizes the price of anarchy. Note that viewing the price of anarchy as a design objective represents a significant departure from traditional price of anarchy results in the existing literature. Title: User Participation in Monopolistic Cyber-Insurance Markets Author: Parinaz Naghizadeh (University of Michigan, [email protected]) Abstract: A user’s investment in security in an interdependent system affects the security standing of other entities interacting with it as well, by reducing the probability of an indirect attack initiated from the protected user. A user’s investment in security in an interdependent system affects the security standing of other entities interacting with it as well, by reducing the probability of an indirect attack initiated from the protected user. 18 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory The interactions of strategic users in such setting is often modeled as an interdependent security (IDS) game. The Nash equilibria of these game are in general inefficient, as users ignore the externality of their actions on others, and may in addition free-ride on other users’ efforts. To improve the overall security at the equilibrium state of these games, the literature has proposed cyber-insurance as a potential mechanism, using which users are incentivized to improve their investments in security. In particular, existing work has shown that, under a binary investment model, a monopolist insurer can design cyber-insurance contracts so as to induce socially optimal security investments. In this talk, we first present a new insurance design mechanism by a monopolist insurer for a continuous investment decision model, which implements the socially optimal equilibrium of the corresponding IDS game. We then study users’ participation incentives in this monopolistic market. These constraints have not been specifically addressed in the literature on monopolistic cyber-insurance, as the existing works have assumed mandatory insurance. We show that due to the non-excludable nature of security, there may exist scenarios in which it is impossible to guarantee that users voluntarily purchase insurance from the market, irrespective of how the insurer designs the contracts. We discuss the implication of this impossibility and possible ways to circumvent it. Student Session II: Nonlinear and Stochastic Systems (Saturday, April 26, 16:25 17:25) Title: Stability and Control of Infection Diffusion Dynamics Over Arbitrary Networks Author: Ali Khanafer (University of Illinois at Urbana-Champaign, [email protected]) Abstract: In this work, we analyze the stability properties of a susceptible-infectedsusceptible (SIS) diffusion model over arbitrary networks. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high enough, the allhealthy state is globally asymptotically stable. Otherwise, a strictly positive endemic state arises and the entire network could become infected. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. Using notions from positive systems theory, we prove that the endemic state is globally asymptotically stable in connected undirected graphs as well as strongly connected digraphs. We also show that for these networks, the endemic state is locally exponentially stable. For a weakly connected digraph, we In this work, we analyze the stability properties of a susceptible-infectedsusceptible (SIS) diffusion model over arbitrary networks. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high enough, the allhealthy state is globally asymptotically stable. Otherwise, a strictly positive endemic state arises and the entire network could become infected. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. Using notions from positive systems theory, we prove that the endemic state is globally asymptotically stable in connected undirected graphs as well as strongly connected digraphs. We also show that for these networks, the endemic state is locally exponentially stable. For a weakly connected digraph, we WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 19 provide conditions for the existence, uniqueness, and global stability of a strictly positive endemic state. Further, we identify scenarios in which only a strongly connected component can be infected, while the remaining nodes in the network remain healthy. Finally, when the curing rates are viewed as controllers, we propose a framework for reducing the residual infection in arbitrary networks using a limited number of control nodes. Several simulations illustrate our results.This work is in collaboration with Tamer Basar and Bahman Gharesifard. Title: Passivity and Dissipativity Analysis of a System and its Approximation Author: Meng Xia (University of Notre Dame, [email protected]) Abstract: We consider the following problem: what passivity properties can be inferred for a system by studying only an approximate mathematical model for it. Our results show that an excess of passivity (whether in the form of input strictly passive, output strictly passive or very strictly passive) in the approximate model guarantees a certain passivity index for the system, provided that the norm of the error between the approximate and the true models is sufficiently small in a suitably defined sense. Further, we consider (Q;S;R)-dissipative systems and show that (Q;S;R)-dissipativity has a similar robustness property, even though the supply rates for the system and its approximation may be different. These results may be particularly useful if either the approximate model is much easier to analyze, or if the accurate system model is unknown precisely. We consider the following problem: what passivity properties can be inferred for a system by studying only an approximate mathematical model for it. Our results show that an excess of passivity (whether in the form of input strictly passive, output strictly passive or very strictly passive) in the approximate model guarantees a certain passivity index for the system, provided that the norm of the error between the approximate and the true models is sufficiently small in a suitably defined sense. Further, we consider (Q;S;R)-dissipative systems and show that (Q;S;R)-dissipativity has a similar robustness property, even though the supply rates for the system and its approximation may be different. These results may be particularly useful if either the approximate model is much easier to analyze, or if the accurate system model is unknown precisely. Title: Bayesian Traffic Light Parameter Tracking Based on Semi Hidden Markov Models Author: Engin Ozatay (Ohio State University, [email protected]) Abstract: The previous studies have shown that the optimization of the driving velocity profiles and route selection based on the availability of the traffic lights’ operation information in a traffic network can significantly reduce the individual and cumulative energy consumption of the on road vehicles for the urban drivings. In this work we propose an accurate and precise stochastic online estimation method of the parameters of the traffic lights operating at a piece-wise constant period. In our work we first model the traffic lights with a Semi Hidden Markov Model (SHMM) and then develop the period measurement model governed by an unique noise model specific to the indirect traffic light period measurements. The proposed method solves the estimation problem in two stages: in the first stage we determine the sequence of Markovian States maximizing the probability given the measurements and the SHMM parameters, the in the second stage we update The previous studies have shown that the optimization of the driving velocity profiles and route selection based on the availability of the traffic lights’ operation information in a traffic network can significantly reduce the individual and cumulative energy consumption of the on road vehicles for the urban drivings. In this work we propose an accurate and precise stochastic online estimation method of the parameters of the traffic lights operating at a piece-wise constant period. In our work we first model the traffic lights with a Semi Hidden Markov Model (SHMM) and then develop the period measurement model governed by an unique noise model specific to the indirect traffic light period measurements. The proposed method solves the estimation problem in two stages: in the first stage we determine the sequence of Markovian States maximizing the probability given the measurements and the SHMM parameters, the in the second stage we update 20 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory the period and state duration estimates based on the Bayesian Tracking given the corresponding latest measurements. The simulation and real vehicle data results prove that the proposed method can accurately estimate the switching times and the period of the piece-wise fixed period traffic lights. Title: Large-Scale Dissipative and Passive Control Systems and the Role of Symmetry Author: Vahideh Ghanbari (University of Notre Dame, [email protected]) Abstract: In this study, stability conditions for large-scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors. Stability for dissipative and passive systems is considered and conditions are derived for the maximum number of subsystems that may be added while preserving stability. There may exist an upper bound on the number of subsystems so to guarantee stability, depending on the structure of symmetric interconnection. Three kinds of symmetries are studied: star-shaped symmetry, cyclic symmetry and chain symmetry. Also, approximate symmetry with respect to interconnections are represented. In this study, stability conditions for large-scale systems are derived by categorizing agents into symmetry groups and applying local control laws under limited interconnections with neighbors. Stability for dissipative and passive systems is considered and conditions are derived for the maximum number of subsystems that may be added while preserving stability. There may exist an upper bound on the number of subsystems so to guarantee stability, depending on the structure of symmetric interconnection. Three kinds of symmetries are studied: star-shaped symmetry, cyclic symmetry and chain symmetry. Also, approximate symmetry with respect to interconnections are represented. Session IV: Networked Control Systems (Sunday, April 27,8:30 9:50) Title: Forecasting Regime Shifts in Networked Dynamical Systems with Applications to the Development of Sustainable Infrastructure Author: Michael Lemmon (University of Notre Dame, [email protected]) Abstract: A regime shift occurs when a dynamical system “flips” from a nominal operating state to an alternative operating state. Regime shifts can be catastrophic for users who have grown accustomed to the quality of services provided by the system prior to this shift. This talk will discuss methods for assessing a dynamical system’s susceptibility to catastrophic regime shifts using sum-of-squares relaxations to bound the system’s socalled “distance to bifurcation” and “first passage time” probabilities. The methods will be used to assess the susceptibility of aquatic ecosystems to regime shifts. A regime shift occurs when a dynamical system “flips” from a nominal operating state to an alternative operating state. Regime shifts can be catastrophic for users who have grown accustomed to the quality of services provided by the system prior to this shift. This talk will discuss methods for assessing a dynamical system’s susceptibility to catastrophic regime shifts using sum-of-squares relaxations to bound the system’s socalled “distance to bifurcation” and “first passage time” probabilities. The methods will be used to assess the susceptibility of aquatic ecosystems to regime shifts. Title: On the Security of Cyber-Physical Systems Author: Bruno Sinopoli (Carnegie Mellon University, [email protected]) Abstract: Cyber Physical Systems (CPS) refer to the embedding of widespread sensing, computation, communication, and control into physical spaces. AppliCyber Physical Systems (CPS) refer to the embedding of widespread sensing, computation, communication, and control into physical spaces. AppliWCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 21 cation areas are as diverse as aerospace, chemical processes, civil infrastructure, energy, manufacturing and transportation, most of which are safetycritical. The availability of cheap communication technologies such as the internet makes such infrastructures susceptible to cyber security threats, which may affect national security as some of them, such as the power grid, are vital to the normal operation of our society. Any successful attack may significantly hamper the economy, the environment or may even lead to loss of human life. As a result, security is of primary importance to guarantee safe operation of CPS. In an offensive perspective, attacks of this sort can be carried out to disrupt the functionality of the enemy’s critical infrastructures without destroying it or even be directly identified. Stuxnet, the malware at the root of the destruction of centrifuges employed to enrich uranium in Iran’s nuclear facilities, is a clear example of how strategically important is to gain a deep understanding of CPS security. In this talk I will provide an introduction to CPS security, give an overview of recent results from our research group as well as directions for future work. Title: Networked Control over Non-Deterministic Channels Author: Vincenzo Liberatore (Case Western Reserve University, [email protected]) Abstract: Networked Control Systems (NCSs) involve the remote control of a plant that is connected to a controller via a communication network. In this talk, we will start by reviewing established research results in Distributed Algorithms and Internet Measurement: for example, clocks can be synchronized only to within a round-trip time, and packet losses must be assumed to follow an arbitrary non-deterministic pattern. These facts imply a novel approach for the analysis of NCSs, which will be exemplified by playback buffers. Playback buffers turn network delays into time-invariant quantities, but at the potential expense of increased packet losses and delays. We will describe a class of controllers for buffered NCS that is stable under arbitrary packet losses. Networked Control Systems (NCSs) involve the remote control of a plant that is connected to a controller via a communication network. In this talk, we will start by reviewing established research results in Distributed Algorithms and Internet Measurement: for example, clocks can be synchronized only to within a round-trip time, and packet losses must be assumed to follow an arbitrary non-deterministic pattern. These facts imply a novel approach for the analysis of NCSs, which will be exemplified by playback buffers. Playback buffers turn network delays into time-invariant quantities, but at the potential expense of increased packet losses and delays. We will describe a class of controllers for buffered NCS that is stable under arbitrary packet losses. Session V: Optimization and Optimal Control (Sunday, April 27, 10:00 11:10) Title: Distributed Optimization over Directed Graphs Author: Angelia Nedich (University of Illinois at Urbana-Champaign, [email protected]) Abstract: Recent advances in wired and wireless technology necessitate the development of theory, models and tools to cope with new challenges posed by large-scale networks and various problems arising in current and anticipated applications over such networks. In this talk, optimization problems Recent advances in wired and wireless technology necessitate the development of theory, models and tools to cope with new challenges posed by large-scale networks and various problems arising in current and anticipated applications over such networks. In this talk, optimization problems 22 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory and algorithms for distributed multi-agent networked systems will be discussed. The distributed nature of the problem is reflected in agents having their own local (private) information while they have a common goal to optimize the sum of their objectives through some limited information exchange. The inherent lack of a central coordinator is compensated through the use of network to communicate certain estimates and the use of appropriate local-aggregation schemes. The overall approach allows agents to achieve the desired optimization goal without sharing the explicit form of their locally known objective functions. However, the agents are willing to cooperate with each other locally to solve the problem by exchanging some estimates of relevant information. Distributed algorithms will be discussed for directed graphs with their basic convergence properties. Title: Decision Making Algorithms for Unmanned Vehicles with Resource Constraints Author: Sivakumar Rathinam (Texas A&M University, [email protected]) Abstract: Small, heterogeneous, unmanned vehicles are being used increasingly in civil and military applications for monitoring a group of targets. In this work, I consider a path planning problem involving multiple, heterogeneous vehicles starting from distinct depots. The objective of the path planning problem is to find a path for each vehicle so that each of the targets is visited at least once by a vehicle, the motion constraints of the vehicles are satisfied, and the sum of the travel times of all the vehicles is minimized. By exploiting the structure of the problem, I will present the algorithms developed by our research group, which are currently the best known for this path planning problem. Small, heterogeneous, unmanned vehicles are being used increasingly in civil and military applications for monitoring a group of targets. In this work, I consider a path planning problem involving multiple, heterogeneous vehicles starting from distinct depots. The objective of the path planning problem is to find a path for each vehicle so that each of the targets is visited at least once by a vehicle, the motion constraints of the vehicles are satisfied, and the sum of the travel times of all the vehicles is minimized. By exploiting the structure of the problem, I will present the algorithms developed by our research group, which are currently the best known for this path planning problem. Joint work with Dr. Swaroop Darbha and students at Texas A & M. Title: A Duality Framework for Stochastic Optimal Control of Complex Systems Author: Andreas Malikopoulos (Oak Ridge National Laboratory, [email protected]) Abstract: In this talk, we present a model for the analysis and stochastic optimization of a system consisting of interactive subsystems and address the problem of minimizing the system’s long-run expected average cost. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems and we develop a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For In this talk, we present a model for the analysis and stochastic optimization of a system consisting of interactive subsystems and address the problem of minimizing the system’s long-run expected average cost. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems and we develop a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 23 practical situations with constraints consistent to those studied here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems. Student Session III: Game Theory and Applications (Sunday, April 27, 11:10 11:55) Title: Common Information based Markov Perfect Equilibria for LinearQuadratic-Gaussian (LQG) Games with Asymmetric Information Author: Abhishek Gupta (University of Illinois at Urbana-Champaign, [email protected]) Abstract: We consider a class of two-player dynamic stochastic LQG nonzero-sum games. Each controller acquires possibly different dynamic information about the state process and the other controller’s past actions and observations. This leads to a dynamic LQG game of asymmetric information among the controllers. In this talk, we present a novel refinement concept for Nash equilibrium in dynamic LQG games with asymmetric information, called common information based Markov perfect equilibrium. We prove that in a dynamic LQG game, under certain conditions, a unique common information based Markov perfect equilibrium exists. Furthermore, this equilibrium can be computed by solving a sequence of linear equations. We consider a class of two-player dynamic stochastic LQG nonzero-sum games. Each controller acquires possibly different dynamic information about the state process and the other controller’s past actions and observations. This leads to a dynamic LQG game of asymmetric information among the controllers. In this talk, we present a novel refinement concept for Nash equilibrium in dynamic LQG games with asymmetric information, called common information based Markov perfect equilibrium. We prove that in a dynamic LQG game, under certain conditions, a unique common information based Markov perfect equilibrium exists. Furthermore, this equilibrium can be computed by solving a sequence of linear equations. Title: Learning Efficient Correlated Equilibria Author: Holly Borowski (University of Corolado at Boulder, [email protected] ) Abstract: The vast majority of the literature in distributed learning focuses on attaining convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize collective behavior that is far more efficient than even the best Nash equilibrium. However, there are no distributed learning algorithms in the existing literature that coverage to specific correlated equilibria. We provide one such algorithm. In particular, the proposed algorithm guarantees that the agents? collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior as the result of a distributed learning process is incorporating a common random signal into the learning environment. The vast majority of the literature in distributed learning focuses on attaining convergence to Nash equilibria. Correlated equilibria, on the other hand, can often characterize collective behavior that is far more efficient than even the best Nash equilibrium. However, there are no distributed learning algorithms in the existing literature that coverage to specific correlated equilibria. We provide one such algorithm. In particular, the proposed algorithm guarantees that the agents? collective joint strategy will constitute an efficient correlated equilibrium with high probability. The key to attaining efficient correlated behavior as the result of a distributed learning process is incorporating a common random signal into the learning environment. Title: Optimal Energy Procurement from a Strategic Seller with Private Renewable and Conventional Generation Author: Tavafoghi Hamidreza (University of Michigan, [email protected]) 24 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory Abstract: We consider a mechanism design problem for energy procurement, when there is one buyer and one seller, and the buyer is the mechanism designer. The seller can generate energy from conventional (deterministic) and renewable (random) plants, and has multi-dimensional private information which determines her production cost. The objective is to maximize the buyer’s utility under the constraint that the seller voluntarily participates in the energy procurement process. We show that the optimal mechanism is a menu of contracts (nonlinear pricing) that the buyer offers to the seller, and the seller chooses one based on her private information. We consider a mechanism design problem for energy procurement, when there is one buyer and one seller, and the buyer is the mechanism designer. The seller can generate energy from conventional (deterministic) and renewable (random) plants, and has multi-dimensional private information which determines her production cost. The objective is to maximize the buyer’s utility under the constraint that the seller voluntarily participates in the energy procurement process. We show that the optimal mechanism is a menu of contracts (nonlinear pricing) that the buyer offers to the seller, and the seller chooses one based on her private information. WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 25 5 Alphabetical List of Participants Last Name, First Name Affiliation Email Address Adamey, Emrah Ohio State University [email protected] Alshehri, Khaled University of Illinois at Urbana-Champaign [email protected] Antsaklis, Panos University of Notre Dame [email protected] Başar, Tamer University of Illinois at Urbana-Champaign [email protected] Belabbas, Mohamed University of Illinois at Urbana-Champaign [email protected] Bhattacharya, Sourabh Iowa State University [email protected] Borowski, Holly University of Colorado at Boulder [email protected] Brown, Philip University of Colorado at Boulder [email protected] Casbeer, David Air Force Research Lab [email protected] Chang, Chin-Yao Ohio State University [email protected] Chen, Hua Ohio State University [email protected] Cheng, Meng-Bi Ohio State University [email protected] Conejo, Antonio Ohio State University [email protected] Etesami, Seyed University of Illinois at Urbana-Champaign [email protected] Fredette, Danielle Ohio State University [email protected] Gao, Xiaobin University of Illinois at Urbana-Champaign [email protected] Garcia, Eloy Air Force Research Laboratory [email protected] Ghanbari, Vahideh University of Notre Dame [email protected] Gupta, Abhishek University of Illinois at Urbana-Champaign [email protected] Hamidreza, Tavafoghi University of Michigan [email protected] Hemami, Hooshang Ohio State University [email protected] Hiskens, Ian University of Michigan [email protected] Hu, Jianghai Purdue University [email protected] Jing, Junbo Ohio State University [email protected] Khanafer, Ali University of Illinois at Urbana-Champaign [email protected] Krishna, Kalyanam Air Force Research Lab [email protected] Kurt, Arda Ohio State University [email protected] LeBlanc, Heath Ohio Northern University [email protected] Lemmon, Michael University of Notre Dame [email protected] Liberatore, Vincenzo Case Western Reserve University [email protected] Li, Sen Ohio State University [email protected] Li, Xiaohui Ohio State University xiaohui [email protected] Lin, Wei Case Western Reserve University [email protected] Lin, Hai University of Notre Dame [email protected] 26 WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory Last Name, First Name Affiliation Email Address Liu, Jianzhe Ohio State University [email protected] Liu, Peng Ohio State University [email protected] Lu, Yueyun Ohio State University [email protected] Loparo, Kenneth Case Western Reserve University [email protected] Malikopoulos, Andreas Oak Ridge National Laboratory [email protected] Marx, Matthew Ohio State University [email protected] Mathieu, Johanna University of Michigan [email protected] Mehta, Prashant University of Illinois at Urbana-Champaign [email protected] Moon, Jun University of Illinois at Urbana-Champaign [email protected] Moya, Christian Ohio State University [email protected] Naghizadeh, Parinaz University of Michigan [email protected] Nedich, Angelia University of Illinois at Urbana-Champaign [email protected] Ozbilgin, Guchan Ohio State University [email protected] Ozatay, Engin Ohio State University [email protected] Özgüner, Ümit Ohio State University [email protected] Passino, Kevin Ohio State University [email protected] Rasouli, Mohammad University of Michigan [email protected] Rathinam, Sivakumar Texas A&M University [email protected] Serrani, Andrea Ohio State University [email protected] Shea, Timothy Ohio State University [email protected] Sinopoli, Bruno Carnegie Mellon [email protected] Sun, Dengfeng Purdue University [email protected] Tadrous, John The Ohio State University [email protected] Utkin, Vadim Ohio State University [email protected] Wang, Zhao University of Notre Dame [email protected] Xia, Meng University of Notre Dame [email protected] Zhao, Lin Ohio State University [email protected] Zhou, Junqiang Ohio State University [email protected] Zhu, Feng University of Notre Dame [email protected] Zhu, Quanyan New York University [email protected] Zhu, Yanzheng Ohio State University [email protected] Zhang, Wei Ohio State University [email protected] WCGT 2014–The 3rd Midwest Workshop on Control and Game Theory 27