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.
Related
- Receding Horizon Control and Dissipativity - Optimal Control, Games and Uncertainty
- Multi-Agent Receding Horizon Games Framework for Autonomous Market Participation
- Characterizing Identifiability and Generalization for Inverse Receding-Horizon Linear-Quadratic Regulator Problems
- Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games
- Multidimensional Infinite-Horizon Markovian Backward Stochastic Differential Equations with Continuous Coefficients and Nonzero-Sum Differential Games
BibTeX
@misc{tatarenko2026stability,
title = {{Stability Filters for Receding-Horizon Games}},
author = {Tatiana Tatarenko and Alberto Bemporad},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02953},
eprint = {2611.02953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02953},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability Filters for Receding-Horizon Games
AU - Tatiana Tatarenko
AU - Alberto Bemporad
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02953
UR - https://arxiv.org/abs/2611.02953
AB - 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.
ER -