一类非线性系统的神经网络L_2鲁棒自适应控制

The Neural Networks L_2 Robust Adaptive Control for a Class of Nonlinear Systems

对于一类具有三角结构的单输入单输出不确定非线性系统的跟踪控制问题,用反步法和动态面控制方法设计了一种神经网络L_2鲁棒自适应控制器.控制器设计中没有直接解HJI(Hamilton-Jacobi-Isaac)不等式,而是合理地选择了L_2增益性能指标,将被控系统各个状态变量的跟踪误差和神经网络各权值的跟踪误差看作整个控制系统的各个状态变量,并用李亚普诺夫定理和HJI不等式证明了使用提出的控制器后,这些状态变量具有小于等于事先规定的正实数γ的L_2增益,并且当所考虑的干扰向量为零向量时,提出的控制器在原点大范围渐近稳定.仿真研究结果表明所提出的控制器具有很好的跟踪性能和很强的鲁棒性.

For the tracking control of a class of uncertain SISO（single input single output） nonlinear systems with triangle structure,the neural network L2 robust adaptive controllers are designed using backstepping and dynamic surface control technique.The controllers are designed without solving the HJI inequality directly.The right L2-gain performance index is chosen reasonably.The tracking errors of the states of the controlled system and the weights of the neural networks are taken as the state variables of the whole control system.The Lyapunov theorem and HJI（Hamilton-Jacobi-Isaac） inequality are adopted to prove that the whole control system has the L2-gain which is less than or equal to the prescribed positive constγ, and when the considered disturbance vector is a zero vector,the whole control system are large-scale asymptotically stable at origin.The simulation results indicate that the proposed approach has high tracking performance and strong robustness.