Regional predictive control with suboptimally extended regions of validity

TL;DR

This paper extends the regions of validity for model predictive control feedback laws, reducing computational effort and allowing for adjustable performance in networked control systems.

Contribution

It introduces a method to extend the polytopic regions of validity to nonlinear regions, decreasing the number of quadratic programs needed.

Findings

Fewer quadratic programs are required with the extended validity regions.

The regions can be tailored to achieve specific closed-loop performance.

The approach is suitable for low-computation local nodes in networked control.

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.