Infinite time optimal control of hybrid systems with a linear performance index

We consider the constrained infinite time optimal control problem for the class of discrete time linear hybrid systems. When a linear performance index is used the infinite time optimal solution is a piecewise affine (PWA) state feedback control law. In this paper we present an algorithm that computes the optimal solution in a computationally efficient manner. It combines a dynamic programming exploration strategy with a multi-parametric linear programming solver and basic polyhedral manipulation.