基于S类函数的严格反馈非线性周期系统的自适应控制

S-class Functions Based Adaptive Controller Design for a Class of Periodically Time-varying Nonlinear Systems

针对一类严格反馈非线性周期系统,在周期非线性可时变参数化的条件下设计自适应控制器.通过将周期时变参数展开成傅里叶级数,并采用微分自适应律估计未知系数,进行控制器反推设计.引入S类函数,并在控制器设计中应用S类函数处理截断误差项对系统跟踪性能的影响,同时,S类函数能确保虚拟控制的可微.给出几种不同的S类函数设计,分析比较将其应用于控制器设计时产生的不同效果.理论分析与仿真结果表明,提出的控制方法能够实现系统输出跟踪期望轨迹,且闭环系统所有信号有界.

In this paper,an adaptive controller is designed for a class of strict-feedback nonlinear systems with periodically time-varying parametric uncertainties.The unknown periodic parameters are expanded into Fourier series and the coefficients are estimated by using a differential learning algorithm,and the backstepping design technique is applied to the controller design.S-class functions are introduced for eliminating the influence of truncation error and ensuring the tracking performance.In particular,the virtue control variables are differentiable due to the adoption of the S-class functions.Several different S-class functions are given and different control effects are produced by using them in the controller design.The theoretical analysis and numerical results show that the tracking of the system output is bounded to the desired one,while all the signals in the closed-loop system remain bounded.