This paper studies the robustness of policy iteration in the context of continuous-time infinite-horizon linear quadratic regulation (LQR) problem. It is shown that Kleinman's policy iteration algorithm is inherently robust to small disturbances and enjoys local input-to-state stability in the sense of Sontag. More precisely, whenever the disturbance-induced input term in each iteration is bounded and small, the solutions of the policy iteration algorithm are also bounded and enter a small neighborhood of the optimal solution of the LQR problem. Based on this result, an off-policy data-driven policy iteration algorithm for the LQR problem is shown to be robust when the system dynamics are subjected to small additive unknown bounded disturbances. The theoretical results are validated by a numerical example.

中文翻译：

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连续时间线性二次调节的稳健策略迭代

本文研究了连续时间无限范围线性二次调节 (LQR) 问题背景下策略迭代的鲁棒性。结果表明，Kleinman 的策略迭代算法对小扰动具有内在的鲁棒性，并且在 Sontag 的意义上享有局部输入到状态的稳定性。更准确地说，每当每次迭代中扰动引起的输入项是有界且很小的时候，策略迭代算法的解也有界并进入 LQR 问题最优解的一个小邻域。基于此结果，当系统动力学受到小的附加未知有界干扰时，LQR 问题的离策略数据驱动策略迭代算法被证明是稳健的。通过数值例子验证了理论结果。