Finite-horizon distributionally robust framework for unknown-dynamic equilibrium seeking

This paper proposes a novel finite-horizon distributionally robust approximate (FH-DRA) framework for equilibrium-seeking problems (ESPs) under unknown coupled dynamical systems. The finite-horizon ESP under unknown dynamics poses significant challenges, as players struggle to handle the uncertainty in coupled dynamical systems and make long-term and reliable decisions. Leveraging recursive Gaussian process regression (GPR), the proposed FH-DRA achieves multi-step state prediction and constructs temporal dynamic ambiguity sets that guarantee containment of the actual state trajectory within a probabilistic confidence region over finite horizons. The ESP is effectively approximated through a distributionally robust optimization problem, for which FH-DRA provides a computationally tractable single-layer optimization formulation. As agents’ dynamical systems are inherently coupled, direct handling of interconnected dynamics becomes intractable. The FH-DRA framework circumvents this limitation by decoupling the system dynamics and reformulating the coupling relationships as composite objective functions in the optimization problem. Furthermore, the proposed FH-DRA framework guarantees recursive feasibility, stability, and computational tractability.