Contraction Analysis of Continuation Method for Suboptimal Model Predictive Control

TL;DR

This paper investigates the contraction properties of nonlinear systems under suboptimal MPC using continuation methods, introducing a contraction metric and matrix inequalities to analyze stability and suboptimality effects.

Contribution

It introduces a contraction metric and matrix inequalities to analyze the stability of suboptimal MPC with continuation methods, extending understanding beyond stabilization.

Findings

Contraction metric effectively captures hierarchical dynamics.

Matrix inequalities relate suboptimality to contraction properties.

Numerical example verifies the theoretical analysis.

Abstract

This letter analyzes the contraction property of the nonlinear systems controlled by suboptimal model predictive control (MPC) using the continuation method. We propose a contraction metric that reflects the hierarchical dynamics inherent in the continuation method. We derive a pair of matrix inequalities that elucidate the impact of suboptimality on the contraction of the optimally controlled closed-loop system. A numerical example is presented to verify our contraction analysis. Our results are applicable to other MPCs than stabilization, including economic MPC.