A New Dissipativity Condition for Asymptotic Stability of Discounted Economic MPC

TL;DR

This paper introduces a new dissipativity condition that ensures asymptotic stability for discounted economic MPC, extending stability analysis to cases with a discount factor in the cost function.

Contribution

It proposes a novel dissipativity condition for discounted economic MPC and links it with existing stability results, enhancing theoretical understanding.

Findings

New dissipativity condition guarantees stability

Theoretical results validated with numerical examples

Connects discounted and undiscounted stability theories

Abstract

Economic Model Predictive Control has recently gained popularity due to its ability to directly optimize a given performance criterion, while enforcing constraint satisfaction for nonlinear systems. Recent research has developed both numerical algorithms and stability analysis for the undiscounted case. The introduction of a discount factor in the cost, however, can be desirable in some cases of interest, e.g., economics, stochastically terminating processes, Markov decision processes, etc. Unfortunately, the stability theory in this case is still not fully developed. In this paper we propose a new dissipativity condition to prove asymptotic stability in the infinite horizon case and we connect our results with existing ones in the literature on discounted economic optimal control. Numerical examples are provided to illustrate the theoretical results.