Stable adaptive neuro-control design via Lyapunov function derivative estimation

A new approach to the tracking problem, for affine in the control nonlinear dynamical systems, whose nonlinearities are assumed to be unknown, is presented in this paper. The philosophy of the developed technique is based on estimating the derivative of an unknown Lyapunov function, exploiting the approximation capabilities of the linear in the weights neural network structures. 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.

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