Piecewise linear optimal controllers for hybrid systems

In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for discrete-time hybrid systems. A stabilizing controller is obtained by designing a model predictive controller (MPC), which is based on the minimization of a weighted l(1)/infinity -norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a multiparametric mixed-integer linear program (mp-MILP), which avoids solving mixed-integer programs on-line [6]. As the resulting control law is piecewise affine, on-line computation is drastically reduced to a simple linear function evaluation.