Stability of Constrained Adaptive Model Predictive Control Algorithms

TL;DR

This paper develops stability guarantees for adaptive MPC algorithms that automatically adjust their optimization horizon, ensuring stability and a specified suboptimality level in closed-loop control.

Contribution

It provides a stability proof for arbitrary horizon adaptation schemes and introduces a simple strategy for horizon adjustment in adaptive MPC.

Findings

Stability can be maintained with horizon adaptation.

A simple horizon shortening and prolongation strategy is effective.

Suboptimality estimates can be evaluated at runtime.

Abstract

Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function type endpoint weight. The proposed methods yield a posteriori and a priori estimates of the degree of suboptimality with respect to the infinite horizon optimal control and can be evaluated at runtime of the MPC algorithm. Our aim is to design automatic adaptation strategies of the optimization horizon in order to guarantee stability and a predefined degree of suboptimality for the closed loop solution. Here, we present a stability proof for an arbitrary adaptation scheme and state a simple shortening and prolongation strategy which can be used for adapting the optimization horizon.