Abstract
Physical human--machine interaction and other multi-agent control settings require decision-making policies that adapt online. Differential games provide a principled framework where each agent optimizes an individual objective while anticipating the other's response. The relevant solution concept in many applications is the feedback Nash equilibrium (FNE), which yields time-consistent state-feedback strategies. However, computing the FNE is demanding and becomes intractable when state and input constraints must be enforced, motivating the need for approximate methods. This paper presents a Model Predictive Control (MPC) approach that approximates infinite-horizon FNE trajectories through repeated solution of finite-horizon open-loop games. An auxiliary-game formulation is introduced that selects prediction horizons and terminal costs to approximate the feedback-game optimality conditions. The approach is extended to incorporate hard constraints via a constrained open-loop game formulation. For the unconstrained setting, an analytic upper bound on the state-trajectory deviation between the MPC-induced and FNE trajectories is derived, enabling quantitative performance certification. Numerical examples illustrate the effectiveness of the proposed method compared with baseline approaches from the literature.
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Cite this article
APA 7
Varga, B., Handwerker, K., Rudas, I., & Galambos, P. (2026). Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees. https://omanscience.com/en/articles/approximate-feedback-nash-equilibria-in-constrained-differential-games-via-model-predictive-control-with-upper-bound-guarantees
MLA 9
Varga, Balint, et al. "Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees." https://omanscience.com/en/articles/approximate-feedback-nash-equilibria-in-constrained-differential-games-via-model-predictive-control-with-upper-bound-guarantees.
Chicago (author–date)
Varga, Balint, Karl Handwerker, Imre Rudas, and Peter Galambos. 2026. "Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees." https://omanscience.com/en/articles/approximate-feedback-nash-equilibria-in-constrained-differential-games-via-model-predictive-control-with-upper-bound-guarantees.
Harvard
Varga, B., Handwerker, K., Rudas, I. and Galambos, P. (2026) 'Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees', Available at: https://omanscience.com/en/articles/approximate-feedback-nash-equilibria-in-constrained-differential-games-via-model-predictive-control-with-upper-bound-guarantees.
Vancouver
Varga B, Handwerker K, Rudas I, Galambos P. Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees. https://omanscience.com/en/articles/approximate-feedback-nash-equilibria-in-constrained-differential-games-via-model-predictive-control-with-upper-bound-guarantees
IEEE
B. Varga, K. Handwerker, I. Rudas, and P. Galambos, "Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees," https://omanscience.com/en/articles/approximate-feedback-nash-equilibria-in-constrained-differential-games-via-model-predictive-control-with-upper-bound-guarantees.