Stability Filters for Receding-Horizon Games

Abstract

In receding-horizon games, self-interested players repeatedly solve a finite-horizon generalized Nash equilibrium problem (GNEP) and apply its first-stage actions. Ensuring stability of the resulting closed-loop system, however, is a challenging task that requires careful design of the players' strategies or additional constraints. We propose a stability filter that minimally modifies the variational equilibrium of the finite-horizon GNEP to enforce a prescribed decrease of a quadratic Lyapunov function. For receding-horizon games with linear dynamics, quadratic costs, and polyhedral coupling input constraints, whose associated GNEP is strongly monotone, we show that a filter always exists such that a closed-loop equilibrium exists, the filter is always feasible, does not intervene when the equilibrium already satisfies the decrease condition, and that renders the closed loop globally exponentially stable. Moreover, the filtered strategy is an $ε$-generalized Nash equilibrium, with $epsilon$ vanishing exponentially along closed-loop trajectories.