Certifying Optimality in Hybrid Control Systems Via Lyapunov-Like Conditions

Francesco Ferrante1, Ricardo G. Sanfelice2

  • 1GIPSA-lab and Université Grenoble Alpes
  • 2University of California

Details

14:50 - 15:10 | Wed 4 Sep | Room FH 4 | WeD4.2

Session: Set-Valued and Nonsmooth Analysis in Systems and Control: Generalized Lyapunov Methods and Beyond I

Abstract

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 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.