误差约束严格反馈系统的迭代学习控制

Iterative learning control of error-constrained strict-feedback systems

中文关键词  约束状态  迭代学习控制  反推设计  微分–差分学习律

英文关键词  constrained state  iterative learning control  backstepping design  differential-difference learning law

中文摘要

      针对一类严格反馈非线性系统, 本文提出误差跟踪学习控制算法, 旨在解决状态约束问题和系统的初值问 题. 文中构造了二次分式型对称障碍Lyapunov函数以及二次分式型非对称障碍Lyapunov函数, 并结合反推技术来分 别设计学习控制器. 两种控制方案里分别采用积分学习律和微分–差分学习律估计未知系数. 系统跟踪误差在控制 器作用下囿于预设的界内, 从而实现迭代过程中对状态的约束; 引入期望误差轨迹, 经迭代学习后, 两种控制方案均 能够实现状态误差在整个作业区间上对期望误差轨迹的完全跟踪, 并且实现系统输出在预指定作业区间上精确跟 踪参考信号. 数值仿真结果表明了控制方案的有效性.

英文摘要

      This paper presents an error-tracking iterative learning control approach for a class of strict-feedback nonlinear systems, which solves both the state-constrained problem and the initial-condition problem. The learning controllers are designed by using two types of quadratic-fraction barrier Lyapunov functions, and the backstepping technique is also applied. Integral learning law and differential-difference learning law are respectively used in the estimation of coefficients in the two control schemes. The system tracking error is enforced to stay in the pre-specified range by the controller, so as to realize the state constraint in the iterative process. A kind of desired error trajectory is constructed in this paper. After iterative learning, the two proposed control schemes can achieve the complete tracking of the desired error trajectory by the state error over the entire time interval, and the system output can accurately track the reference signal on the specified interval. Numerical results are presented to demonstrate the effectiveness of the control schemes.