Continuation Method for Nonsmooth Model Predictive Control Using Proximal Technique

TL;DR

This paper introduces a continuation method for nonsmooth model predictive control that leverages proximal operators to reformulate optimality conditions, ensuring well-posedness and demonstrating effectiveness through numerical examples.

Contribution

It develops a novel continuation framework for nonsmooth MPC using proximal techniques, with new constraint qualifications for well-posedness.

Findings

Effective reformulation of nonsmooth optimality conditions

Ensures well-posedness with new constraint qualifications

Numerical example demonstrates approach's effectiveness

Abstract

This paper presents a novel framework for the continuation method of model predictive control based on optimal control problem with a nonsmooth regularizer. Via the proximal operator, the first-order optimality inclusion relation is reformulated into an equation system, to which the continuation method is applicable. In addition, we present constraint qualifications that ensure the well-posedness of the proposed equation system. A numerical example is also presented that demonstrates the effectiveness of our approach.