具有初始状态不确定性的非线性系统脉冲补偿迭代学习控制(英文)  

Pulse compensated iterative learning control to nonlinear systems with initial state uncertainty

作　　者：阮小娥[1] 赵建永[1] 

机构地区：[1]西安交通大学数学与统计学院,陕西西安710049

出　　处：《控制理论与应用》2012年第8期993-1000,共8页Control Theory & Applications

基　　金：supported by the National Natural Science Foundation of China(No.F030114-60974140)

摘　　要：针对于具有初始状态不确定性的非线性时不变系统,采用矩形脉冲信号补偿传统的比例微分型一阶和二阶迭代学习控制律.在Lebesgue-p范数度量跟踪误差意义下,利用卷积的推广的Young不等式分析学习控制律的跟踪性能.分析表明,在适当选取比例学习增益,微分学习增益和非线性状态函数的Lipschitz常数以保证收敛因子小于1的前提下,渐近跟踪误差是由初始状态不确定性引起的,而且可通过调节补偿因子予以消减.数值仿真验证了补偿策略的有效性和理论分析的正确性.A type of rectangular pulse is adopted to compensate for conventional proportional-derivative-type firstorder and second-order iterative learning controllers of nonlinear time-invariant systems with initial state uncertainty.The tracking error is measured in the form of Lebesgue-p norm and the tracking performance is analyzed by the technique of generalized Young inequality of convolution integral.The analysis shows that the asymptotical tracking error is incurred by the initial state uncertainty and can be eliminated by tuning the compensation gain in the presuppose that the proportional and derivative learning gains together with the Lipschitz constant of the nonlinear state function are properly chosen to guarantee that convergence factor is less than one.Numerical simulations exhibit the validity of the theoretical derivation and the effectiveness of the compensation strategy.

关 键 词：迭代学习控制 非线性系统 脉冲补偿 初始状态不确定性 Lebesgue-p范数 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]