On Control Design Algorithms And Its Applications For A Class Of Stochastic Nonlinear Systems

Because of the influence of environmental interference and the modeling error, thecompletely deterministic system is not exist in the real word. Hence, the researches on thecontrol of uncertain nonlinear systems have both theoretical and practical interests. Stochasticnonlinear systems are a class of nonlinear systems with stochastic dynamic characterstics, andthe one of the hot research direction of nonlinear control theory. In this paper, based on theadaptive robust nonlinear control theory, the neural network approximation theory, thestability of stochastic differential equation and the stability of delay differential equation, theproblems of control for a class of stochastic nonlinear systems are investigate. The maincontributions of are outlined as follows:Firstly, based on the high gain observer and neural-network(NN), an adaptiveoutput-feedback control is addressed for a class of nonaffine uncertain nonlinear systems withstochastic disturbance and internal dynamics. Under the assumption that zero dynamics of thesystem is stable, the obtained results extend the existing methodology from deterministicsystems to stochastic systems. Using the generalization learn ability of the neural network, anadaptive estimation and robust control law are addressed for the nonaffine nonlinear systems.Using Lyapunov theorem, it is shown that all the signals of the closed-loop system arebounded in probability, and the tracking error converges to an adjustable neighborhood of theorigin.Secondly, the problem of adaptive observer design is investigated for a class ofstochastic nonlinear systems with nonparametric uncertainties. Different from the existingresults, the uncertain parameters of the systems not only contain output variable. Through thedesign of a nonlinear observer with an adaptive law of parameters to reconstruct the systemstates, the adaptive observer can solve the state estimation problem of the uncertaintynonaffine stochastic nonlinear systems effectively. Application of Lyapunov theorem andIto stochastic differential theory show that the observation error convergences toneighborhood of the origin, whose size can be adjusted by observer parameters.Thirdly, the control design problem is studied for a class of uncertain stochasticnonlinear system with unknown time delays. For a class of uncertain stochastic nonlinearsystem with unknown time delays and uncertain nonlinear function, a delay-independentadaptive control is proposed. Furthermore, for a class of uncertain stochastic nonlinear system with unknown time delays, uncertain parameters and uncertain nonlinear functions, anadaptive filtered backstepping controller is designed based on neural network. Using thefiltered backstepping instead of the traditional backstepping to avoid the inherent problem of“explosion of complexity” in the traditional baskstepping design. It is proved that theproposed adaptive control is able to guarantee boundedness in probability of all the signals inthe closed-loop system and the tracking error is proven to converge to a small adjustableneighborhood.Fourthly, based on the adaptive Kalman filter (AKF), a nonlinear output-feedbackcontrol scheme is proposed for macro-micro dual-drive positioning stage with highacceleration and high precision. AKF is used to compensate VCM vibration and the externalnoise. For the inherent hysteresis of Piezoactuator-driven stage, an adaptive output-feedbackcontrol is proposed based on the high-gain observer. The control scheme uses a neuralnetwork to simulate the uncertain nonlinear hysteresis, and a robust control is designed tocompensate the neural network approximation error and observer error.Fifthly, for the problem of the inevitable stochastic communication packet dropouts in themulti-AUV cooperation, an optimal estimation is proposed based on a measurement predictor.The estimated measurement values for the lost information are obtained by using all theweighted known measurement values instead of the latest one, improved the traditionalmethods. Based on the estimated measurement values, the optimal estimators including filter,predictor and smoother are developed via an innovation analysis approach for multiple packetdropouts systems.