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Koopman-based Policy Iteration for Robust Optimal Control

Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the Hamilton-Jacobi-Issac equation (HJIE). We provide a novel Koopman-based expression of the HJIE, where the solutions can be obtained through the approximation of the Koopman operator itself. In particular, we developed a data-driven and model based policy iteration algorithm for approximating the optimal value function using a finite-dimensional approximation of the Koopman operator and generator.