The Neural Networks L₂ Robust Adaptive Control for a Class of Nonlinear Systems

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.