Nonlinear MPC for Tracking for a Class of Non-Convex Admissible Output Sets

TL;DR

This paper extends nonlinear MPC for tracking to handle non-convex output sets by using a convexifying homeomorphism, enabling convergence guarantees and practical implementation for a new class of non-convex sets.

Contribution

Introduces a systematic method to incorporate convexifying homeomorphisms into nonlinear MPC for non-convex output sets, including a new class of such sets.

Findings

Guarantees convergence for non-convex output sets

Provides a systematic construction of convexifying homeomorphisms

Demonstrates effectiveness through an illustrative example

Abstract

This paper presents an extension to the nonlinear Model Predictive Control for Tracking scheme able to guarantee convergence even in cases of non-convex output admissible sets. This is achieved by incorporating a convexifying homeomorphism in the optimization problem, allowing it to be solved in the convex space. A novel class of non-convex sets is also defined for which a systematic procedure to construct a convexifying homeomorphism is provided. This homeomorphism is then embedded in the Model Predictive Control optimization problem in such a way that the homeomorphism is no longer required in closed form. Finally, the effectiveness of the proposed method is showcased through an illustrative example.