Constrained Optimal Control for Hybrid Systems

Abstract

In this chapter we study the solution to optimal control problems for discrete time linear hybrid systems. First, we show that the closed form of the state feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a time-varying piecewise affine state feedback control law. Then, we give insight into the structure of the optimal state feedback solution and of the value function. Finally, we describe how the optimal control law can be efficiently computed by means of multiparametric programming, for linear and quadratic performance criteria. For the linear performance criteria the piecewise affine feedback control law can be computed by means of multiparametric mixed integer linear programming. For quadratic performance criteria we present an algorithm to solve multiparametric mixed integer quadratic programs by means of dynamic programming and multiparametric quadratic programs.