Model predictive control approximates feedback Nash equilibria with constraints
Approximate Feedback Nash Equilibria in Constrained Differential Games via Model Predictive Control with Upper Bound Guarantees
Computer Science and Game Theory
Summary
Making decisions in situations where multiple players interact and react to each other can be very complicated, especially when rules limit what each can do. The authors propose a way to simplify these problems by solving shorter, easier steps repeatedly, instead of tackling the whole problem at once. Their method can handle strict limits on actions and provides a way to measure how close the solution is to the ideal strategy. They also tested their approach and found it performs well compared to other methods.
What this means in practice
- •For robotics control teams: Design control policies for robots interacting with humans while respecting safety constraints using repeated finite-horizon planning.
- •For autonomous vehicle developers: Develop adaptive control strategies for multiple vehicles that optimize performance while considering interaction and physical constraints.
Authors
Balint Varga, Karl Handwerker, Imre Rudas, Peter Galambos
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.