Neural control design of nonlinear composite systems using Lyapunov function derivative estimation

A new approach to the tracking problem, for the nonlinear composite systems, whose nonlinearities are assumed to be unknown, is presented in the paper. The philosophy of the developed technique is based on estimating the derivative of an unknown Lyapunov function by using the approximation capabilities of neural networks. A novel resetting strategy guarantees the boundedness away from zero of certain signals. The uniform ultimate boundedness of the tracking error to an arbitrarily small set, plus the boundedness of all other signals in the closed loop is guaranteed. Numerical simulation studies are used to illustrate and clarify the approach.