Certifying Optimality in Hybrid Control Systems via Lyapunov-like Conditions

Francesco Ferrante (1) , Ricardo Sanfelice (2)

1 GIPSA-SYSCO - GIPSA - Systèmes non linéaires et complexité
2 UCSC Department of Computer Engineering - Computer Engineering Department

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.

Domaines: Automatique

Francesco Ferrante, Ricardo Sanfelice. Certifying Optimality in Hybrid Control Systems via Lyapunov-like Conditions. MECHATRONICS 2019 - NOLCOS 2019 - 8th IFAC Symposium on Mechatronic Systems - 11th IFAC Symposium on Nonlinear Control Systems, Sep 2019, Vienne, Austria. pp.245-250, ⟨10.1016/j.ifacol.2019.11.786⟩. ⟨hal-02137357⟩