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Certifying Optimality in Hybrid Control Systems via Lyapunov-like Conditions ⁎ ⁎ Research by R. G. Sanfelice has been partially supported by the National Science Foundation under Grant no. ECS-1710621 and Grant no. CNS-1544396, by the Air Force Office of Scientific Research under Grant no. FA9550-16-1-0015, Grant no. FA9550-19-1-0053, and Grant no. FA9550-19-1-0169, and by CITRIS and the Banatao Institute at the University of California. Research by Francesco Ferrante is funded in part by ANR via project HANDY, number ANR-18-CE40-0010.


We formulate an optimal control problem for hybrid systems with inputs and propose conditions for the design of state-feedback laws solving the optimal control problem. The optimal control problem has the flavor of an infinite horizon problem, but it also allows solutions to have a bounded domain of definition, which is possible in hybrid systems with deadlocks. Design conditions for optimal feedback laws are obtained by relating a quite general hybrid cost functional to a Lyapunov like function. These conditions guarantee closed-loop optimality and are given by constrained steady-state-like Hamilton-Jacobi-Bellman-type equations. Applications and examples of the proposed results are presented.

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