输入饱和非线性系统的周期自适应补偿学习控制

摘要

A periodic adaptive tracking compensating learning algorithm is proposed for a class of Brunovsky standard nonlinear uncertain systems with time delay and input saturation. By restructuring the system according to signal replace-ment theory and functional transformation with the lowest common cycle, the delay and other time-varying parameters are combined into an auxiliary time-varying parameter. Then a periodic adaptive learning algorithm is designed to es-timate the auxiliary parameter for approximating and compensating the section which exceeds the saturated limit by a compensator. Finally a comprehensive controller is constituted so that the system state can track the bounded expected value and the repeated iterative learning control problem based on periodic system with input saturation is solved. It is proved that the track error is convergent and all the closed-loop signals are bounded by the difference calculation of Lyapunov-Krasovskii composite energy function. The torque control simulation of common coupled nonlinear manipulator further confirms the effectiveness of the algorithm.%针对一类输入饱和不确定Brunovsky 标准型非线性时滞系统，提出一种周期自适应跟踪补偿学习算法。利用信号置换思想重组系统，基于最小公倍周期函数变换，将时滞时变项和不确定项合并为辅助参数，进而设计周期自适应学习律估计该辅助量，并利用饱和补偿器逼近和补偿超出饱和限的部分，由此构成综合控制器，以保证系统状态对有界期望值的跟踪，解决了饱和输入周期系统的重复迭代学习控制问题。最后通过构造Lyapunov-Krasovskii复合能量函数的差分，计算证明了系统跟踪误差的收敛性和闭环信号值的有界性。常见耦合非线性机械臂系统的力矩控制仿真，进一步验证了该算法的有效性。