A Set-Theoretic Robust Control Approach for Linear Quadratic Games with Unknown Counterparts

Abstract

Ensuring robust decision-making in multi-agent systems is challenging when agents have distinct, possibly conflicting objectives and lack full knowledge of each other's strategies. This is apparent in safety-critical applications such as human-robot interaction and assisted driving, where uncertainty arises not only from unknown adversary strategies but also from external disturbances. To address this, the paper proposes a robust adaptive control approach based on linear quadratic differential games. Our method allows a controlled agent to iteratively refine its belief about the adversary strategy and disturbances using a set-membership approach, while simultaneously adapting its policy to guarantee robustness against the uncertain adversary policy and improve performance over time. We formally derive theoretical guarantees on the robustness of the proposed control scheme and its convergence to $ε$-Nash strategies. The effectiveness of our approach is demonstrated in a numerical simulation.