Research On Adaptive Control Of Discrete-time Nonlinear System

In recent decades, the neural network (NN) control of nonlinear system has been extensively researched, but the main application has been centered on the control problem. Because the Neural network has powerful approximation performance, so it becomes an effective tool on identification and control of the nonlinear system. Because neural network can approximate nonlinear function with any accuracy in certain conditions, so the neural network control got a wide range of development. At the same time, the neural network also revealed stability and efficiency in online control. The fuzzy modeling and adaptive control have important theoretical and practical significance.Adaptive control is based on the basic principle of adaptive, and using the characteristics of neural network designed. It played respective strengths of adaptive and neural network and it offers a new method for the research of nonlinear control. In this paper, we based on the Lyapunov stability theory, designed the controller by using the thoughts of direct adaptive neural network control, and research the control problem for a class of uncertain nonlinear system. By the realization of the adaptive neural network control, we can reduce the calculation. Finally stability and convergence of the system can be guaranteed in the hypothesis conditions. In this paper, we mainly research several following contents:For a class of uncertain single-input-single-output (SISO) discrete-time nonlinear system with the strict-feedback form, we put forward the algorithm of the direct adaptive neural network control. We use the neural networks to approximate unknown function, and synthesis of a stable adaptive neural network controller. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared to the previous discrete system research, this algorithm improved the robustness of the system. Simulation example shows the feasibility of this method.For a class of uncertain multiple-input-multiple-output (MIMO) discrete-time nonlinear system, we use a robust adaptive neural network control method, in the controller design, at first we take the multiple-input-multiple-output system converted into input/output system through the mapping, and get the ideal controller by the high-order neural network approximation conversion system, the system is stable by using Lyapunov stability theorem, by choosing the design parameters appropriately, the tracking error can converge to a small neighborhood of zero. Compared with the previous multi-input-multi-output (MIMO) discrete-time system, robust adaptive algorithm is significantly improved. Simulation example shows the feasibility of this method.