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 feed-backs 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 con-straints can be included as a set of linear constraints. Efficiency of the method is demonstrated on two examples