We derive optimality conditions for the paths of a Dubins vehicle when the state space is partitioned into two patches with different vehicle’s forward velocity. We recast this problem as a hybrid optimal control problem and solve it using optimality principles for hybrid systems. Among the optimality conditions, we derive a “refraction” law at the boundary of the patches which generalizes the ...

A 3D biped with knees and a hip is naturally modeled as a nontrivial hybrid system; impacts occur when the knee strikes and when the foot impacts the ground causing a switch in the dynamics governing the system. Through a variant of geometric reduction—termed functional Routhian reduction—we can reduce the dynamics on each domain of this hybrid system to obtain a planar equivalent biped. Using ...

This paper presents a hierarchical control strategy for heat and electric power control of a building integrating hybrid renewable power sources including photovoltaic, fuel cell and battery energy storage with Plug-in Electric Vehicles (PEV) in smart distribution systems. Because of the controllability of fuel cell power, this power sources plays the main role for providing heat and electric p...

The optimal control problem for a class of hybrid systems (switched Lagrangian systems) is studied. Some necessary conditions of the optimal solutions of such a system are derived based on the assumption that there is a group of symmetries acting uniformly on the domains of different discrete modes, such that the Lagrangian functions, the guards, and the reset maps are all invariant under the a...

It is my great pleasure to welcome Daniel Liberzon, a professor at the University of Illinois Urbana-Champaign, as the next editor for the nonlinear systems and control area within Automatica. Daniel is well known in the nonlinear systems and control field for a vast array of contributions, including his pioneering work on switched nonlinear systems. I am especially pleased that Daniel’s resear...

The objective of this paper is to solve the controller synthesis problem for bisimulation equivalence in a wide variety of scenarios including discrete-event systems, nonlinear control systems, behavioral systems, hybrid systems and many others. This will be accomplished by showing that the arguments underlying proofs of existence and methods for the construction of controllers are extraneous t...

In this paper we study the solution to optimal control problems for discrete time linear hybrid systems. First, we prove that the closed form of the state-feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a time-varying piecewise affine feedback control law. Then, we give an insight into the structure of the optimal state-feedback soluti...

This work provides the full proofs of the properties of the tableaux calculus for hybrid logic with the global and converse modalities presented in [3], which focuses on the HL(@) fragment of the calculus. While such a fragment terminates without loop checks, when the converse and global modalities are added to the language, and the corresponding rules to the system, termination is achieved by ...

The paper presents a constructive control design for integrator backstepping in nonsmooth systems. The approach is based on non smooth analysis and Lyapunov stability for nonsmooth systems and is similar in spirit with the robust control designs that have appeared in literature, but is applicable to a larger class of systems. The backstepping controller is 1rst applied to the case of a unicycle...

This paper represents a continuation of a previous work, where a practical approach to the treatment of nominal equalities in tableaux for basic Hybrid Logic HL(@) was proposed. Its peculiarity is a substitution rule accompanied by nominal deletion. The main advantage of such a rule, compared with other approaches, is its efficiency, that has been experimentally verified for the HL(@) fragment....