An observer-based neural adaptive control for rolling cart systems

Abstract

Rolling cart system is a highly nonlinear phenomenon in which links undergo tipping and rolling with no fixed base. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the rolling cart states by applying observer-based adaptive wavelet neural network (OBAWNN) tracking sliding mode control scheme with system uncertainties, multiple time-delayed state uncertainties, and external disturbances. Based on a recurrent adaptive wavelet neural network model for approximating the dynamics of the rolling cart, an observer-based adaptive control scheme is developed to override the nonlinearities, time delays, and external disturbances such that the uniform ultimate boundedness of all signals in the closed loop and the H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> tracking performance are achieved. The advantage of employing adaptive wavelet neural dynamics is that we can utilize the neuron information by activation functions to on-line tune the parameters of dilation and translation of wavelet basis functions and hidden-to-output weights, and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. Based on Lyapunov criterion and Riccati-inequality, some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbance on the tracking error can be attenuated to any prescribed level and consequently an H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> tracking control is achieved. Finally, a numerical example of a rolling cart is given to illustrate the effectiveness of the proposed control scheme.