Adaptive Neural Network Dynamic Surface Control for Nonlinear Stochastic Systems in The Strict-Feedback Form with Prandtl-Ishlinskii Hysteresis in The Actuator

Using the adaptive radial basis function (RBF) neural network dynamic surface control design method, a controller design approach is presented in order to the stabilization of strict-feedback nonlinear stochastic systems subjected to Prandtl-Ishlinskii nonlinearity in the actuator. This method is capable to be applied to nonlinear stochastic systems with any unknown dynamics. According to the universal approximation capability the RBF neural networks make it possible to approximate the unknown dynamics of the nonlinear stochastic systems. Using the minimal-learning-parameters algorithm the approximation procedure is done with a minimum complexity and required calculations. The stability of the proposed control system is proven analytically and its results are demonstrated using a simulation example. It is shown that the proposed design approach guarantees the boundedness in probability for adaptive control system, and in turn the uniformly ultimately boundedness of all closed-loop signals. It is also shown, that using this method the tracking error can be made arbitrarily small.