Indirect adaptive control of nonlinear system via dynamic multilayer neural networks with multi-time scales

This paper deals with adaptive nonlinear identification and trajectory tracking problem via dynamic multilayer neural network with different time scales. By means of a Lyapunov-like analysis, we determine stability conditions for the on-line identification. Then, a sliding mode controller is designed for trajectory tracking with consideration of the modeling error and disturbance. The main contributions of the paper lie in the following aspects. First, we extend our prior identification results of single-layer dynamic neural networks with multi-time scales to those of multilayer case. Second, the e-modification in standard use in adaptive control is introduced in the on-line update laws to guarantee bounded weights and bounded identification errors. Third, the potential singularity problem in controller design is solved by using new update laws for the NN weights so that the control signal is guaranteed bounded. The stability of proposed controller is proved by using Lyapunov function. Simulation results demonstrate the effectiveness of the proposed algorithm.