一类纯反馈非线性系统的简化自适应神经网络动态面控制

Simplified adaptive neural dynamic surface control for a class of nonlinear systems in pure feedback form

针对一类完全非仿射纯反馈非线性系统,提出一种简化的自适应神经网络动态面控制方法.基于隐函数定理和中值定理将未知非仿射输入函数进行分解,使其含有显式的控制输入;利用简化的神经网络逼近未知非线性函数,对于阶SISO纯反馈系统,仅一个参数需要更新;动态面控制可消除反推设计中由于对虚拟控制反复求导而导致的复杂性问题.通过Lyapunov稳定性定理证明了闭环系统的半全局稳定性,数值仿真验证了方法的有效性.

A simplified adaptive neural dynamic surface control approach is proposed for a class of completely non-affine pure-feedback nonlinear systems.By using implicit function theorem and mean value theorem,unknown non-affine input functions can be transformed to partially affine forms.The simplified neural networks are used to approximate the unknown nonlinearities in systems,and for a-th order strict feedback nonlinear system,only one parameter is needed to be estimated on-line.The problem of explosion of terms in traditional backstepping design is eliminated by utilizing dynamic surface control.It is proved that the developed method can guarantee the semi-global stability of the close-loop system.Simulation results show the effectiveness of the proposed approach.