一种含噪声不确定多输入多输出非线性时变系统的最优跟踪控制  

An optimal tracking control for uncertain multiple-input multiple-output non-linear time-varying systems with noises

作　　者：张超 姜天华[2] 孙启鸣 ZHANG Chao;JIANG Tian-hua;SUN Qi-ming(School of Electrical Engineering and Automation,Henan Institute of Technology,Xinxiang Henan 453003,China;School of Transportation,Ludong University,Yantai Shangdong 264025,China;College of Information Science and Technology,Nanjing Forestry University,Nanjing Jiangsu 210037,China)

机构地区：[1]河南工学院电气工程与自动化学院,河南新乡453003 [2]鲁东大学交通学院,山东烟台264025 [3]南京林业大学信息科学技术学院,江苏南京210037

出　　处：《控制理论与应用》2020年第3期676-686,共11页Control Theory & Applications

基　　金：河南省重点研发与推广专项基金项目(182102210034,182102210258,192102210063,182102210261);河南省高等学校重点科研项目(16A120011);河南工学院高层次人才科研启动基金项目(KQ1863);山东省自然科学基金培养基金项目(ZR2016GP02)资助.

摘　　要：如何在确保实时性能的前提下,将系统耦合、随机因素、时变特性和不确定非线性的影响一同最小化具有重要意义.为此,本文提出了一种基于自适应多维泰勒网(MTN)的优化控制方案,包括MTN控制器(MTNC)和MTN滤波器(MTNF).首先,设计基于强化学习和自适应动量因子的改进梯度法来调节MTNC权值以快速响应被控对象的不确定性和时变特性,实现最优控制;证明闭环系统稳定性.而后,通过Lyapunov稳定性理论设计MTNF权值更新律,使动态误差指数收敛到零;恰当选择Lyapunov函数来构造具有全局最小值的能量空间并对MTNF的Lyapunov特性进行分析;证明MTNF误差的收敛速度和收敛区域,避免奇点问题.最后,仿真结果表明所提出的控制器和滤波器可在较短的时间内获得更高的精度.It is of great significance to minimize the effects of system coupling, stochastic factors, time-varying characteristics, and uncertain nonlinearity while ensuring real-time performance. Therefore, we propose an optimization control scheme based on adaptive multidimensional Taylor network(MTN), comprising a MTN controller(MTNC) and a MTN filter(MTNF). Firstly, an improved gradient method, which is based on reinforcement learning and adaptive momentum factor, is designed to adjust the MTNC weights to respond quickly to the uncertainty and time-varying characteristics of the controlled object to achieve the optimal control. The stability of the closed-loop system is proved. Then, the MTNF weight update law is designed by Lyapunov stability theory, and the dynamic errors exponentially converge to zero. The Lyapunov function is appropriately selected to construct the energy space with the global minimum value and the Lyapunov characteristics is analyzed. The convergence speed and convergence area of MTNF error are proved, and the singularity problem is avoid. Lastly, simulation results show that the proposed controller and filter can obtain higher precision in a short period of time.

关 键 词：多维泰勒网 跟踪控制 自适应动量因子 自适应滤波 量测噪声 

分 类 号：O232[理学—运筹学与控制论]