Adaptive Neural Network Control Of Stochastic Strict Feedback Nonlinear Systems

Due to its wide practical background, controller design of nonlinear systems has always been the focuses in automatic control community during the last two decades. Especially the adaptive backstepping neural network control, encompounded by backstepping technique and neural network approximation theory, has attracted much attention of many researchers. As an important part of nonlinear systems, stochastic nonlinear systems take into account the factors such as exogenous stochastic disturbances, and thus, are more applicable, but whose controller design and performance analysis are more complicated compared with the deterministic cases, considering the uncertainties and the increase of model complexity. For stochastic strict-feedback nonlinear systems, based on backstepping technique and integral-type Lyapunov function, a adaptive neural network control scheme is proposed. The main contributions are as follows:Firstly, Firstly, the Lyapunov function of integral type is introduced into a class of special stochastic strict-feedback nonlinear systems. By utilizing the approximation capability of neural networks, backstepping technique and Young’s inequality, a simple and effective adaptive neural network state feedback controller is constructed. The existing literature has studied the nonlinear canonical form, the control gain function contains only part of the state variables, now extends to the strict feedback nonlinear systems, cancels the restriction of the control gain function contains only part of the state variables. Based on the above system, considering the case with the perturbation, by giving the corresponding assumptions, an adaptive control scheme is proposed. By Lyapunov method, it is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment, and the tracking errors converge to a small neighborhood of the origin. Simulation results are given to illustrate the effectiveness of the proposed control scheme.Secondly, based on the backstepping technique, introducing the integral-type Lyapunov function and utilizing the approximation capability of neural networks, an adaptive neural network control scheme is proposed for a class of general stochastic strict-feedback nonlinear systems. Compared with the existing literature, the proposed approach relaxes the requirements of the system and cancels the restriction of the unknown function. By Lyapunov method, it is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment, and the tracking errors converge to a small neighborhood of the origin. Simulation results are given to illustrate the effectiveness of the proposed control scheme.Thirdly, using the technique of neural network parameterization and the backsteeping method, a novel adaptive neural network control scheme is proposed for a class of stochastic strict-feedback nonlinear systems. Compared with the existing literature, the proposed approach not only overcomes the defect that the number of adaptive parameters depend on the neural network nodes, but for an n-th order strict feedback nonlinear systems, only one parameter is needed to be estimated online. The computation burden is significantly reduced and the algorithm is easily realized in practice. By Lyapunov method, it is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment, and the tracking errors converge to a small neighborhood of the origin. Simulation results are given to illustrate the effectiveness of the proposed control scheme.