论文标题
基于库普曼的政策迭代，用于强大的最佳控制
Koopman-based Policy Iteration for Robust Optimal Control
论文作者
论文摘要
从经典上讲，在对手存在下的最佳控制问题被公式为两人零和差异游戏或$ h_ \ infty $控制问题。解决这些问题的解决方案可以通过解决汉密尔顿 - 雅各布 - ISSAC方程（HJIE）来获得。我们提供了基于Koopman的新型HJIE表达，可以通过近似Koopman操作员本身获得解决方案。特别是，我们开发了一种基于数据驱动和模型的策略迭代算法，用于使用Koopman操作员和生成器的有限维近似来近似最佳值函数。
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.
