论文标题
连续时间线性二次法规的强大政策迭代
Robust Policy Iteration for Continuous-time Linear Quadratic Regulation
论文作者
论文摘要
本文研究了连续时间无限 - 马线性二次调节（LQR）问题的稳健性。结果表明，Kleinman的政策迭代算法本质上是对小型干扰的坚固性，并且在Sontag的意义上享有本地输入到国家的稳定性。更确切地说，每次迭代中的干扰诱导的输入项都有界限且小时，策略迭代算法的解决方案也会界定并进入LQR问题最佳解决方案的一个小社区。基于此结果，当系统动力学受到小型添加剂未知的有界干扰时，证明LQR问题的单个数据驱动的策略迭代算法被证明是可靠的。理论结果通过数值示例验证。
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.
