一类不确定性非线性系统的神经网络稳定控制

A Stable Neural Network Control Scheme for CompanionType Nonlinear System

针对一类伴随型的ｎ阶非线性系统中存在不确定性，引入神经网络作为非线性系统的模型，基于Ｌｙａｐｕｎｏｖ稳定性理论，提出有效的控制律及参数自适应律，由全局不变集定理证明闭环系统是全局跟踪收敛的。仿真研究结果表明了本文方法的有效性。

Stability analysis of neuralnetworkbased nonlinear control system has presented great difficulties. For the companiontype neuralnetworkbased nonlinear control system whose nonlinearities are unknown, we succeeded in constructing a suitable Lyapunov function and then achieving global tracking convergence. Eq.(1) gives the companiontype nonlinear control system whose nonlinearities are unknown. Eq.(7) is its neuralnetwork model. The control law we designed for this neuralnetwork model is eq.(15). Eqs.(19), (20) and (21) were selected as a group. Drawing on our experience, after several trials, we constructed the Lyapunov function given by eq.(21). To go along well with eq.(21), we selected eqs.(19) and (20) as the adaptive laws of the parameters of eq.(15). Then, utilizing global invariant set theorem, we proved that the closedloop system possesses global tracking convergence. Simulation results (Figs. 1 and 2) show that the scheme we proposed is effective.