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针对一类参数未知的周期非线性时滞系统的输出跟踪控制问题,设计了一种周期自适应迭代学习跟踪控制算法,该方法利用信号置换的思想重组系统,并在假设未知时变参数和参考输出的周期具有已知最小公倍数的情况下,将时滞以及其他不确定的时变项合并为一个周期性的辅助时变参数新变量,进而用周期自适应算法来估计该辅助量。通过构造一个Lyapunov-Krasovskii型复合能量函数,分析了系统的收敛性,证明了经过多次重复迭代学习,所有闭环信号有界且输出跟踪误差收敛,最后通过构造数值实例进行了仿真验证。理论分析和仿真结果表明,该算法简单有效,对于非线性时滞系统的跟踪问题具有很好的控制效果。
Aiming at the problem of output tracking control for a class of periodic nonlinear time-delay systems with unknown parameters, a periodic adaptive iterative learning tracking control algorithm is proposed. This method uses the idea of signal replacement and reorganizes the system. Output cycle with the least common multiple known, the time lag and other uncertain time-varying terms are merged into a periodic new variable of the auxiliary time-varying parameter, and then the periodic adaptive algorithm is used to estimate the auxiliary variable. By constructing a Lyapunov-Krasovskii composite energy function, the convergence of the system is analyzed. It is proved that all the closed-loop signals are bounded and the output tracking error converges after repeated iterative learning. Finally, numerical examples are given to verify the proposed method. Theoretical analysis and simulation results show that the proposed algorithm is simple and effective and has good control effect on the tracking problem of nonlinear time-delay system.