Regional predictive control with suboptimally extended regions of validity

Abstract: Model predictive control (MPC) is based on perpetually solving optimization problems. The solution of the optimization is usually interpreted as the optimal input for the current state. However, the solution of the optimization does not just provide an optimal input, but an entire optimal affine feedback law and a polytope on which this law is optimal. We recently proposed to use this feedback law as long as the system remains in its polytope. This can be interpreted as an event-based approach, where leaving the current polytope is the event that triggers the next optimization. This approach is especially appropriate for a networked control setting since the feedback laws and their polytopes can be evaluated with a low computational effort on lean local nodes. In this article the region of validity for a feedback law is extended. More precisely, the optimal polytopes are extended to nonlinearly bounded regions of validity resulting from the intersection of a feasibility and stability region. As a result, fewer quadratic programs need to be solved compared to the optimal approach. The new validity regions are still suitable for the evaluation on a lean local node. Moreover, the regions can be adjusted for a desired closed-loop performance.