基于HDP的离散多时滞系统的优化控制

Heuristic Dynamic Planning Optimal Control of Discrete Multiple Time-Delay Systems

针对状态和控制都含有时滞的离散非线性系统提出求解其最优控制的方案,根据自适应动态规划和最优控制理论给出系统性能指标函数的HJB方程;在启发式动态规划方法的基础上引入一个时滞函数矩阵并利用自适应迭代算法对所给出的离散时滞系统的性能指标函数进行迭代求解,采用神经网络方法逼近性能指标函数,实现启发式动态规划的自适应迭代算法;通过迭代求解得出最优控制的表达式;最后通过两个仿真实例说明启发式动态规划最优控制方案的有效性。

In this paper, a heuristic dynamic programming （HDP） iterative algorithm is used to solve a class of discrete time nonlinear with multiple delays in the state and the control input. Then to obtain the optimal control expression it provides the performance index function of the Hamilton Jacobi Bellman equation （HJB） according the optimal theory. In order to facilitate the implementation of the iterative HDP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. The optimal control expression is obtained by using the iterative algorithm of the optimal control policy and the index function until the performance index function reach the saddle point. Finally, two simulation examples are provided to show the proposed optimal control scheme is valid.