This article studies the infinite-horizon adaptive optimal control of continuous-time linear periodic (CTLP) systems. A novel value iteration (VI) based off-policy adaptive dynamic programming (ADP) algorithm is proposed for a general class of CTLP systems, so that approximate optimal solutions can be obtained directly from the collected data, without the exact knowledge of system dynamics. Under mild conditions, the proofs on uniform convergence of the proposed algorithm to the optimal solutions are given for both the model-based and model-free cases. The VI-based ADP algorithm is able to find suboptimal controllers without assuming the knowledge of an initial stabilizing controller. Application to the optimal control of a triple inverted pendulum subjected to a periodically varying load demonstrates the feasibility and effectiveness of the proposed method.

中文翻译：

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线性周期系统的自适应最优控制：一种离策略值迭代方法


本文研究连续时间线性周期（CTLP）系统的无限范围自适应最优控制。针对一般类别的 CTLP 系统，提出了一种基于离策略自适应动态规划（ADP）的新型值迭代（VI）算法，以便可以直接从收集的数据中获得近似最优解，而无需了解系统动力学的确切知识。在温和的条件下，针对基于模型和无模型的情况，给出了所提出的算法一致收敛到最优解的证明。基于 VI 的 ADP 算法能够在不知道初始稳定控制器的情况下找到次优控制器。在周期性变化载荷作用下的三重倒立摆最优控制中的应用证明了该方法的可行性和有效性。