Nearly optimal simple explicit MPC controllers with stability and feasibility guarantees

We consider the problem of synthesizing simple explicit model predictive control feedback laws that provide closed-loop stability and recursive satisfaction of state and input constraints. The approach is based on replacing a complex optimal feedback law by a simpler controller whose parameters are tuned, off-line, to minimize the reduction of the performance. The tuning consists of two steps. In the first step, we devise a simpler polyhedral partition by solving a parametric optimization problem. In the second step, we then optimize parameters of local affine feedbacks by minimizing the integrated squared error between the original controller and its simpler counterpart. We show that such a problem can be formulated as a convex optimization problem. Moreover, we illustrate that conditions of closed-loop stability and recursive satisfaction of constraints can be included as a set of linear constraints. Efficiency of the method is demonstrated on two examples.