This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

Autonomous vehicles need to be able to plan trajectories to a specified goal that avoid obstacles, and are robust to the inherent uncertainty in the problem. This uncertainty arises due to uncertain state estimation, disturbances and modeling errors. Previous solutions to the robust path planning problem solved this problem using a finite horizon optimal stochastic control approach. This approa...

The probability of conflict between two aircraft is calculated by modeling aircraft motion as a deterministic trajectory plus a (scaled) Brownian motion perturbation. In this formalism, the probability of conflict becomes the probability that a Brownian motion escapes from a time-varying safe region. Approximate expressions for the probability of conflict are obtained in closed form for both th...

Recently, Chan et al. (2000) proposed an efficient heuristic for a class of finite time planning horizon single-warehouse multi-retailer system with complex (nonlinear) transportation cost structures. Their heuristic is based on solving a large LP relaxation of the underlying problem. In this paper, we analyze the strength of the proposed LP relaxation and show that it attains the best theoreti...

In the domain of decentralized Markov decision processes, we develop the first complete and optimal algorithm that is able to extract deterministic policy vectors based on finite state controllers for a cooperative team of agents. Our algorithm applies to the discounted infinite horizon case and extends best-first search methods to the domain of decentralized control theory. We prove the optima...

Two different methods are proposed to optimize the operations of the electricity transmission and distribution systems. In the first method new criticality importance measures are developed in order to determine the relative importance of each individual component within the system. The second method is a combined dynamic programming and integer programming replacement analysis method to obtain...

Planning problems that involve learning a policy from a single training set of finite horizon trajectories arise in both social science and medical fields. We consider Q-learning with function approximation for this setting and derive an upper bound on the generalization error. This upper bound is in terms of quantities minimized by a Q-learning algorithm, the complexity of the approximation sp...

Providing safety guarantees for autonomous robots operating in environments with moving obstacles is a difficult problem, particularly for underactuated systems or systems with drift due to momentum. The conventional approach to replanning in dynamic environments typically computes partial plans within the allotted CPU time and validates explored states through robot-obstacle collision checks. ...

This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective f...

A new replacement analysis methodology is developed to determine system-level component replacement schedules for radial electricity distribution configurations composed of sets of heterogeneous assets. The proposed model is an iterative combined dynamic programming and integer programming approach to obtain cost-efficient system-level component replacement schedules with the objective of minim...