A Few Class Of Stochastic Nonlinear Systems Adaptive Neural Network Control

In the actual engineering problems, the control plants often present to be intrinsically nonlinear, uncertain and time-varying, and is often affected by stochastic perturbations. Therefore, study on the control problem for uncertain stochastic nonlinear system has great significance in theory and practical applications. Adaptive neural network control has been shown to be one of the most effective methods for controlling complex nonlinear systems. Based on the current research findings on the control of stochastic nonlinear systems, this thesis will utilize neural network control theory, adaptive backstepping technology, robust control theory and mathematical inequality to systematically investigate the control problem of stochastic nonlinear systems and develop new adaptive neural control methods. The compendious frame and description of this thesis are shown as follows:1. The problem of adaptive tracking control is considered for a class of single-input-single-output (SISO) strict-feedback stochastic nonlinear systems. In the control design, radial basis function (RBF) neural network is used to approximate the packaged unknown nonlinear functions, and backstepping technique is applied to design adaptive neural control scheme. The proposed control scheme guarantees that all the signals in the closed-loop systems are bounded in probability, and the desired output tracking performance is achieved. By estimating the maximum of the norm of neural network weight vectors, only one online updating equation is required for n-order nonlinear systems, which makes the computational burden alleviated. Simulation results demonstrate the effectiveness of the proposed scheme.2. An adaptive stabilization control problem is investigated for a class of SISO strict-feedback stochastic nonlinear time-delay systems. In the control design, suitable Lyapunov-Krasovskii functional is constructed to compensate nonlinear time-delay functions and RBF neural network is employed to model the packaged unknown nonlinear functions, then an adaptive neural stabilization controller is developed by combining backstepping approach and the property of the hyperbolic tangent function. It is shown that the proposed control scheme can ensure all the signals in the closed-loop systems are bounded in probability. Simulation studies further illustrate the feasibility of the developed controller.3. For a class of multiple-input-multiple-output (MIMO) large-scale stochastic nonlinear systems, RBF neural network and backstepping are combined to present an adaptive neural decentralized control scheme. The proposed control scheme guarantees the boundedness of all the signals in the resulting closed-loop system in probability. It is worth to point out that the presented control scheme requires only one adaptive parameter for each subsystem, which makes the control scheme more suitable in practical applications. Simulation results are given to illustrate the effectiveness of the proposed scheme.4. A direct adaptive neural tracking control is developed for a class of completely non-affine pure-feedback stochastic nonlinear systems. In the process of controller design, implicit function theorem and mean value theorem are combined to transform the non-affine function into affine form, RBF neural network is employed to model the virtual control signals and the actual control input, and backstepping technique and stochastic Lyapunov functional are combined to design a direct adaptive neural tracking control scheme. The proposed control scheme not only guarantees the boundedness of all the signals in the closed-loop system and the good tracking performance, but also overcomes the problem of controller circulation design. Simulation" results are shown to demonstrate the effectiveness of the developed scheme.5. An adaptive neural tracking control is presented for a class of pure-feedback stochastic nonlinear systems with unsmooth input dead zone and input saturation, respectively. In the control design, mean value theorem is first used to transform the non-affine function into affine form; for the dead-zone nonlinearity, equivalent decomposition method is used to divide the dead-zone into the linear part of dead-zone input and a bounded perturbed part, and a smooth function is introduced to compensated for the saturation nonlinearity; then a novel adaptive neural control scheme without depending on the information of unsmooth nonlinear parameters is proposed by using backstepping technique and the inequality of hyperbolic tangent function. It is proven that the proposed control scheme can guarantee that all the signals in the closed-loop systems are bounded in probability and the system output tracking error eventually convergences to a small neighborhood around the origin in the sense of mean quartic value. Simulation results are used to further demonstrate the effectiveness of the proposed control scheme.6. The problem of adaptive neural tracking control is investigated for a class of non-strict-feedback stochastic nonlinear systems. In the control design, the function separation technique is introduced to decompose the nonlinear function of all state variables, and RBF neural networks are used to approximate the packaged unknown nonlinear function. Then, an adaptive neural tracking control scheme is developed based on backstepping. The proposed control scheme guarantees that all the signals in the closed-loop systems are bounded in probability, and the tracking error eventually converges to a small neighborhood around the origin. Simulation studies further illustrate the effectiveness of the proposed control scheme...