Broucke, Mireille; Di Benedetto, Maria Domenica; Di Gennaro, Stefano; Sangiovanni-Vincentelli, Alberto Efficient solution of optimal control problems using hybrid systems. (English) Zbl 1098.49027 SIAM J. Control Optimization 43, No. 6, 1923-1952 (2005). Summary: We consider the synthesis of optimal controls for continuous feedback systems by recasting the problem to a hybrid optimal control problem: synthesize optimal enabling conditions for switching between locations in which the control is constant. An algorithmic solution is obtained by translating the hybrid automaton to a finite automaton using a bisimulation and formulating a dynamic programming problem with extra conditions to ensure non-Zenoness of trajectories. We show that the discrete value function converges to the viscosity solution of the Hamilton–Jacobi–Bellman equation as a discretization parameter tends to zero. Cited in 1 Document MSC: 49M05 Numerical methods based on necessary conditions 49L20 Dynamic programming in optimal control and differential games 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 65N99 Numerical methods for partial differential equations, boundary value problems Keywords:optimal control; hybrid systems; bisimulation; feedback systems PDFBibTeX XMLCite \textit{M. Broucke} et al., SIAM J. Control Optim. 43, No. 6, 1923--1952 (2005; Zbl 1098.49027) Full Text: DOI