动态规划最优控制在非线性系统中的应用

摘要

应用一种新的自适应动态最优化方法(ADP),在线实现对非线性连续系统的最优控制。首先应用汉密尔顿函数(Hamilton-Jacobi-Bellman,HJB)求解系统的最优控制,并应用神经网络 BP 算法对汉密尔顿函数中的性能指标进行估计,进而得到非线性连续系统的最优控制。同时引进一种新的自适应算法,基于参数误差,在线实现对系统进行动态最优求解,而且通过李亚普诺夫方法对参数收敛情况也进行详细的分析。最后,用仿真结果来验证所提出的方法的可行性。%This paper proposed a novel adaptive dynamic program (ADP)algorithm to online obtain the optimal control for nonlinear systems.Firstly,the optimal control of system was obtained by using HJB equation,and an NN algorithm was used to approximate the value function of HJB.In particular,this paper introduced a novel adaptive algorithm to online up-date critic NN weights based on the parameter error estimation.The closed-loop system stability was proved based on the Lyapunov theory.Finally,the simulation results were provided to verify the effectiveness of the proposed methods.