Data-Driven Single-Loop Policy Iteration Control of Uncertain Singularly Perturbed Systems

Two-player zero-sum games often rely on solving the game algebraic Riccati equation (GARE) in the linear case. However, existing approaches for solving the GARE typically require stringent initial conditions, which pose challenges for practical implementation. Although the double-loop iterative scheme is commonly used to learn the GARE solution, the single-loop iterative method is more time-efficient during computation. Therefore, we develop a novel data-driven single-loop iterative method to address the guaranteed cost control (GCC) problem for uncertain singularly perturbed systems (USPSs). Unlike existing GCC methods, this scheme incorporates data from both fast and slow subsystems for GCC design, removing the need for precise system dynamics and effectively handling ill-conditioned numerical problems. Moreover, this algorithm alleviates the necessity for initial stabilizing control policies and is easier to execute. This superiority is illustrated in Table 1 through the comparison of error propagation. Finally, we rigorously establish the convergence of both the proposed model-based and model-free algorithms through mathematical derivations and validate their effectiveness with a simulated example.