Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

TL;DR

This paper introduces a simplified multiobjective MPC algorithm that relaxes traditional dissipativity assumptions, providing stability guarantees and performance estimates for systems with multiple competing costs.

Contribution

It significantly simplifies existing assumptions by requiring dissipativity and terminal costs for only one objective, and offers a new algorithm with performance guarantees.

Findings

The algorithm ensures asymptotic stability under relaxed conditions.

Performance estimates are provided for all cost criteria.

Numerical simulations validate the theoretical results.

Abstract

We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an algorithm and give performance guarantees for the resulting MPC closed loop system. Thereby, we significantly simplify the assumptions made in the literature so far by assuming strict dissipativity and the existence of a compatible terminal cost for one of the competing objective functions only. We give conditions which ensure asymptotic stability of the closed loop and, what is more, obtain performance estimates for all cost criteria. Numerical simulations on various instances illustrate our findings. The proposed algorithm requires the selection of an efficient solution in each iteration, thus we examine several selection rules and their impact on the results.