非线性系统神经网络L_2增益控制

Neural networks L_2-gain controller design for nonlinear system

针对很难求解HJ偏微分不等式解析解的问题,采取一种新的思想,给出了利用神经网络构造HJ不等式解的一种方法,并利用遗传算法进行神经网络权值的优化,使得Lyapunov函数满足HJ不等式,避免了求解HJ偏微分不等式。并在此基础上,给出基于HJ不等式的仿射非线性系统神经网络L2增益抗干扰控制器设计方法,以神经网络的形式给出L2增益控制器的一般结构。仿真结果表明,提出的控制器设计方法是可行的,实现了闭环系统为从外界干扰到系统输出是有限增益L2稳定的。

Owing to the nonlinear and partial differential nature of the Hamiltion-Jacobi inequality （HJ）, it is very difficult to obtain an analytical solution. This paper employs a neural network to obtain a solution of the HJ which lead to the design of a nonlinear state feedback L2-gain disturbance rejection controller. The simulation demonstrates the design of controller is feasible and the closed-loop system ensures a finite gain between the disturbance and the output.