Minimum Time for a Hybrid System with Thermostatic Switchings [chapter]

Fabio Bagagiolo
Hybrid Systems: Computation and Control  
In this paper we study a minimum time problem for a hybrid system subject to thermostatic switchings. We apply the Dynamic Programming method and the viscosity solution theory of Hamilton-Jacobi equations. We regard the problem as a suitable coupling of two minimumtime/exit-time problems. Under some controllability conditions, we prove that the minimum time function is the unique bounded below continuous function which solves a system of two Hamilton-Jacobi equations coupled via the boundary conditions.
doi:10.1007/978-3-540-71493-4_6 dblp:conf/hybrid/Bagagiolo07 fatcat:aq43ev4f6jfazjh7ub7xi6gpoa