Research On Prediction Control Strategy For Discrete-time Nonlinear Systems

Predictive control is a new class of computer control algorithms based on discrete-time system. Predictive control received widespread attention in the field of control for its characteristics of adaptability to the complex production process control. To improve the performance of the discrete-time nonlinear systems, the analysis and control problems of discrete-time nonlinear systems with constraints, uncertainty, time-delay and disturbance are discussed based on predictive control theory. The application of the predictive control in the autonomous underwater vehicle (AUV) control system was discussed. The research enriched and developed the theory of predictive control. The main contributions of this paper as follows:Firstly, based on the linear matrix inequality theory, a robust model predictive control method is proposed for a class of discrete-time nonlinear systems with interval time-delay, perturbation, input constraint and polytopic-type uncertainties. The contributions are list bellow. In order to get the way to obtain the robust model predictive controller, the linear matrix inequality technology and the min-max model predictive control method are used. They make the min-max optimization problem converted to the convex optimization problem with linear matrix inequality constraints. Besides, the information of the upper and lower bounds of delay are applied to construct Lyapunov functional for obtain the sufficient condition of controller. The feasibility of the proposed control algorithm and the asymptotic stability of close-looped system are proved.Secondly, a sliding mode predictive control algorithm is proposed for a class of discrete-time uncertain nonlinear systems with internal dynamics. The contributions are list bellow. By the feedback correction and receding horizon optimization, the effects of uncertainties can be compensated in time, and the robustness to matched or unmatched uncertainties has been improved. The control penalty term in the quadratic form performance index can adjust the influence of control input and the sliding mode predictive tracking error. Especially, the chattering of sliding mode control can be eliminated by feedback correction technique. The stability of internal dynamics was ensured by the theory of input-to-state stability in discrete-time. It is shown that the tracking error is robustly stable and all the signals in the closed-loop systems are bounded, without requiring the boundary knowledge of the uncertainty. The proposed algorithm has stronger robustness compared with the conventional reaching law method. Thirdly, based on the predictive control and the neural-network, an adaptive output feedback controller is proposed for a class of the uncertain nonaffine discrete-time nonlinear systems with dynamic compensator. The contributions are list bellow. For solve the problem of nonaffine, the fixed point theorem is first employed to ensure the existence of the feedback control input and reduce the constraints. For realize the stability of tracking error system, a dynamic compensator is introduced to stabilize the linear portion of the tracking error system and a neural network approximation mechanism is introduced to cancel the uncertainties resulting from the nonaffine function. It reduced the computational complexity effectively by divide the error system into linear and nonlinear parts. Since the output feedback induced the state in tracking error system are unmeasurable, a predictor is given to predictive its state. Finally, ultimate boundedness of the error signals is shown through Lyapunov’s direct method.Fourthly, a predictive control method is proposed based on the recurrent neural network for a class of input delay strict-feedback discrete-time nonlinear systems. The contributions are list bellow. By differential homeomorphism transformation, the strict-feedback discrete-time nonlinear systems transform into the triangular ones for simplicity. Based on this system, a neural network adaptive predictive controller is given for deal with nonlinear uncertain and input delay. The controller utilizes the idea of predictive design of predictive control and transforms the problem of input delay into the stabilized of the predictive control systems. Then the effect of delay cancelled and the systems achieve tracking objective in the same instant. The proposed method provides a new control design idea. Besides, the recurrent neural network is used to identify the triangular system uncertain nonlinear systems and makes the identify nonlinear function easily.Finally, a predictive control algorithm is addressed for the horizonal path following predictive control of autonomous underwater vehicle with time-delay. The contributions are list bellow. For compensate the time-delay in control systems and realize path following, a predictive control algorithm is proposed based on predictive control theory. The locally controller is given that contains neural network signal, dynamic compensator and robust controller. The neural network is used to estimate the nonlinear uncertainty of the AUV induced by hydrodynamic coefficients and the surge, sway and yaw angular velocity coupling. The dynamic compensator is introduced to improve the performance of considered systems. The robust law is used to compensate the reconstructive error of neural network and environmental disturbances. The proposed algorithm overcomes the measurement error and measurement noise induced by excessive device, does not need the accurate model of system and have strong robustness for changing the internal parameters, uncertainty and external disturbance.