This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network with different time-scales. By means of a Lyapunov-like analysis we determine stability conditions for the identification. Based on the identification results, we design a sliding mode controller for the nonlinear system to track the trajectory of a reference model. The main contributions of the paper are: First, we extend our prior results of single-layer dynamic neural networks with multi-time scales to the multilayer case. Second, the e-modification in standard use in adaptive control is introduced in the on-line update laws to guarantee bounded weights, bounded identification and tracking errors. Simulation results are presented confirming the validity of the above approach.
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