Piecewise linear optimal controllers for hybrid systems

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, which is based on the minimization of a weighted l₁/∞-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, which avoids solving mixed-integer programs online. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation