Towards Closed-loop Stability of Nonlinear Receding Horizon Games

TL;DR

This paper investigates the stability of nonlinear receding horizon games without terminal ingredients, establishing conditions for practical convergence and demonstrating exponential attraction region shrinkage.

Contribution

It provides new theoretical insights into stability conditions and introduces a linear end penalty to improve convergence in receding horizon games.

Findings

Closed-loop region of attraction shrinks exponentially with horizon length.

Linear end penalty suppresses leaving arcs and ensures convergence.

Practical asymptotic convergence can be achieved without MPC terminal ingredients.

Abstract

We analyze Receding Horizon Games without any MPC-like terminal ingredients. We show that recursive feasibility can be inferred from the turnpike phenomenon under mild assumptions. Moreover, we prove sufficient conditions for practical asymptotic convergence of the closed-loop trajectories, and we discuss how the gap towards practical asymptotic stability may be closed. We use numerical examples to show that the closed-loop region of attraction around the steady-state GNE shrinks exponentially with the horizon length, a behavior previously known only for model predictive control. Further, we apply a linear end penalty and demonstrate in numerical simulations that it suppresses the leaving arc and ensures asymptotic convergence to the steady-state GNE.