Adaptive Neural Network Control For Stochastic Nonlinear Systems

Recently, the investigation of stochastic nonlinear system has received a wide range of concern and become one of the hot topics on the research of nonlinear control theory. The adaptive neural network control problems of several classes of stochastic nonlinear systems have been investigated in this dissertation. The main contents are as follows:1. The problem of adaptive neural network tracking control is considered for a class of stochastic nonlinear strict-feedback system. The adaptive neural network control scheme which is based on the technique of dynamic surface control (DSC) is proposed. In the control design, the radial basis function (RBF) neural network is use to approximate the packaged unknown nonlinear functions. The dynamic surface control technique is applied to filter the virtual control law, which can solve the problem of circular construction of the controller. Since the adaptive law proposed in this paper contains only one adaptive parameter, the computational burden can be significantly alleviated and the control scheme is more implementable in practical applications. The proposed control scheme guarantees that all the signals in the closed-loop systems are bounded in probability, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness of the proposed approaches.2. The problem of adaptive neural network output-feedback tracking control is investigated for a class of stochastic nonlinear systems with unmodeled dynamics and unmeasured states. In the control design, the reduced-order observer is designed for the part of unmeasured states. Then, the actual control law is constructed by approximating unknown nonlinear functions of the system with only one RBF neural network, so that the computational loads can be significantly alleviated. At each intermediate step, a dynamic surface control technique is used to eliminate the problem of "explosion of complexity". Stability analysis based on the stochastic small-gain theorem and the stochastic stability theorem showsthat all the closed-loop system signals are bounded in probability, and the output of the system converges to a small neighborhood of the origin via choosing suitable design parameters. The simulation results demonstrate the performance of the proposed scheme.3. An output-feedback control problem is investigated for a class of stochastic nonlinear time-varying delay systems with unknown control directions. Firstly, in the process of controller design, to make the controller design more feasible, the original system is transformed into a new system which does not contain unknown control directions by using a linear state transformation technique. Secondly, the full-order state obsever of new system is given, and the mean value theorem is used to deal with the problem of time-varying delay. Finally, All the unknown output-dependent functions are grouped into a suitable unknown function that is compensated only by one neural network, and the parameters of neural network to be estimated online are greatly decreased by estimating the maximum of neural network parameters instead of the parameters themselves, which reduce the online learning time of neural network and the computation loads dramatically. The Nussbaum-type gain function is used to deal with the unknown parameters caused by the unknown control directions in the new system. It is shown that the proposed control scheme can guarantee that all the signals of the closed-loop system are bounded in probability. The effectiveness of the proposed scheme is demonstrated by the results of numerical simulation and the practical engineering systems simulation.4. An adaptive neural network tracking control is presented for a class of stochastic time-delay system with unknown dead-zone. Firstly, in the process of controller design, the nonlinear time-delay function is compensated by combining the Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions. Secondly, the parameters of neural network to be estimated online are greatly decreased by estimating the maximum of neural network parameters instead of the parameters themselves, which can efficiently solve the explosion of learning parameters, so the computation burden can be significantly alleviated. Finally, the unknown dead-zone of the system is compensated. Furthermore, the DSC technique is used to overcome the problem of "explosion of complexity" inherently in the conventional backstepping design, which reduces the complexity of controller design. The developed design approach does not need to either construct the dead-zone inverse or require the knowledge of the bounds of dead-zone slopes and can avoid the over-parameterization problem, guarantees that all the signals of the closed-loop system are bounded in probability, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. The numerical simulation example is provided to illustrate the effectiveness of the proposed control scheme.5. A single neural network adaptive controller is designed for a class of stochastic nonlinear time-delay system with unknown dead-zone. There is only one adaptive law and one actual control law in the control scheme by using the single neural network approach. Moreover, the virtual control law needs not to be implemented in the controller realization, which dramatically reduces the complexity of control design and the computation loads. The same as the former method, the unknown dead-zone input and the time-delay of system are compensated. The proposed control scheme does not only guarantees the boundedness of all signals in the closed-loop system, but also makes the steady state tracking error arbitrarily small by appropriately choosing control parameters. The effectiveness of the proposed approach is illustrated by using the numerical simulation example.6. An adaptive neural backstepping dynamic surface control approach is developed for a class of pure-feedback stochastic nonlinear systems with multiple unknown time-varying delays and unknown dead-zone input. Firstly, mean-value theorem is used to transform the non-affine function of the stochastic nonlinear pure-feedback,system to affine form. Secondly, multiple unknown time-varying delays and unknown dead-zone input of the system are compensated. Finally, by estimating the norm of the weight vector of RBF neural network which is used to approximate the unknown function rather than each element of the weight vector, the number of online adaptive parameters are no more than the order of the original system, which alleviate the computational burden significantly. Furthermore, the DSC technique is used to overcome the problem of "explosion of complexity" inherently in the backstepping technique in the process of control design. The proposed control scheme guarantees that all the signals of the closed-loop system are bounded in probability, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. An illustrative numerical simulation example is provided to demonstrate the effectiveness of the proposed control scheme.