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

Koopman-based Policy Iteration for Robust Optimal Control