Nearly-optimal simple explicit MPC regulators with recursive feasibility guarantees

Explicit Model Predictive Control (MPC) is an attractive control strategy, especially when one aims at a fast, computationally less demanding implementation of MPC. Although leading to a fast implementation of optimization-based control, the main downside of explicit MPC is its high complexity in terms of memory occupancy, which often limits practical applicability of such a control methodology. Therefore in this paper we propose to obtain simple explicit MPC controllers that provide guarantees of recursive satisfaction of input and state constraints. The task is accomplished by optimizing, off-line, the parameters of the feedback law such that an integrated square error between the optimal, but complex controller and its simpler replacement is minimized. We show that the task can be formulated as a quadratic optimization problem which always yields an admissible solution. In this way, suboptimality of simple feedbacks with respect to their complex optimal counterparts is significantly mitigated.