基于自适应动态规划的随机时滞线性二次型最优跟踪控制  

Stochastic Linear Quadratic Optimal Tracking Control with Time-Delays Based on Adaptive Dynamic Programming

作　　者：谭旭峰 李媛[1] 刘洋[1] TAN Xufeng;LI Yuan;LIU Yang(School of Science,Shenyang University of Technology,Shenyang 110870)

机构地区：[1]沈阳工业大学理学院,沈阳110870

出　　处：《系统科学与数学》2024年第1期17-30,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(62103289)资助课题.

摘　　要：针对模型未知且带有时滞的随机线性二次型(SLQ)最优跟踪控制问题,提出了一种自适应动态规划(ADP)算法.首先,利用双因果坐标变换导出原时滞系统的等效系统,构造一个新的由等效系统和命令生成器组成的增广系统,并给出该增广系统的随机代数方程.其次,为了解决随机线性二次最优跟踪控制问题,将随机问题转化为确定性问题.然后提出ADP算法,并给出该算法的收敛性分析.为了实现ADP算法,设计了三种神经网络,分别近似最优性能指标函数,最优控制增益矩阵和系统模型.最后,通过一个数值算例验证算法的有效性.An adaptive dynamic programming(ADP)algorithm is proposed for a class of model-free stochastic linear quadratic(SLQ)optimal tracking problem with time-delay.Firstly,the equivalent system of the original time-delay system is derived using the double causal coordinate transformation.A new augmented system consisting of the equivalent system and the command generator is constructed,and then the stochastic algebraic equations of the augmented system are given.Secondly,in order to solve the SLQ tracking control problem,the stochastic problem is transformed into deterministic problem.Then the ADP algorithm is proposed and its convergence analysis is given.For the purpose of realizing the ADP algorithm,three neural networks are designed,which approximate the optimal cost function,the optimal control gain matrix and the system model respectively.Finally,the effectiveness of the algorithm is verified by a numeric example.

关 键 词：随机线性系统 时滞 自适应动态规划 神经网络 

分 类 号：O232[理学—运筹学与控制论]