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摘要: 针对具有输入时滞的非线性系统直接自适应最优控制问题, 提出了一种新的数据驱动输出反馈控制方法. 该方法通过融合Q学习与值迭代和策略迭代, 在学习过程中无需依赖系统动力学知识. 在系统满足一致可观性的条件下, 提出了一种基于输出数据和带有时滞的输入数据的系统状态重构方法, 基于值迭代和策略迭代来学习自适应最优控制策略. 将该方法应用于范德波尔振荡器这一经典非线性系统的控制, 并通过仿真结果充分验证了该方法的有效性.Abstract: This paper proposes a new data-driven output-feedback control method to address the direct adaptive optimal control problem for nonlinear systems with input time-delay. The combination of $ Q$-learning with value iteration (VI) and policy iteration (PI) enables the learning process to be conducted without any knowledge of the system dynamics. Under the condition that the system is uniformly observable, we propose a novel method to reconstruct the state of the system based on output data and input data with time-delay. We then present two iterative methods, VI and PI, to learn the adaptive optimal control policy. Finally, the proposed methods are applied to the classical nonlinear system——Van der Pol oscillator. The simulation results demonstrate the effectiveness of the proposed methods.
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Key words:
- Optimal control /
- output-feedback /
- time-delay /
- adaptive dynamic programming
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图 1 时滞系统的输出反馈控制器设计思路
Fig. 1 Design approach for output feedback controllers with time delay
图 3 考虑时滞的输出反馈下闭环系统的输入输出轨迹
Fig. 3 The input-output trajectories of the closed-loop system under output feedback with time delay
图 4 不考虑时滞后闭环系统的输入输出轨迹)
Fig. 4 The input-output trajectories of the closed-loop system under output feedback without time delay
图 5 $Q$函数迭代前后对对比(除$u_k,\;u_{k-1}$外其他参数为0)
Fig. 5 Comparison of the $Q$ function before and after iteration (with other parameters set to 0 except for $u_k$ and $u_{k-1}$)
图 8 $Q$函数迭代前后对比(除$u_{k-2},\;u_{k-3}$外其他参数为0)
Fig. 8 Comparison of the $Q$ function before and after iteration (with other parameters set to 0 except for $u_{k-2}$ and $u_{k-3}$
图 6 $Q$函数迭代前后对比(除$u_k,\;u_{k-3}$外其他参数为0)
Fig. 6 Comparison of the $Q$ function before and after iteration (with other parameters set to 0 except for $u_k$ and $u_{k-3}$)
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