On Adaptive Dynamics Surface Control Of Nonlinear Systems

In recent years, with the development of control systems and revelant theories, the studying on the problem of nonlinear system control was given more and more attentions. Backstepping technology has been widely applied to the design of nonlinear system controller, which combined the traditional backstepping technology and the adaptive control method, and made the control system become more perfect. Dynamic surface method is developed on the traditional backstepping control technology, and which is an effective way of studying the non-linear system problems, it can effectively reduce the number of the parameters, and lower the complexity of the design. The approximation ability of nonlinear uncertain systems by using neural network method make the design of system control become more simple, the related studies have already made lots of aehijevements.This paper based on the aspects above, analysed adaptive dynamic surface control method of nonlinear Systems, it mainly involves the following several contents:nonlinear system; dynamic surface control; adaptive control; neural network control; unmodeled dynamics. The specific work of this paper is as follows:Firstly, introducing a scheme about adaptive dynamic surface control, in allusion to a class of pure nonlinear feedback systems with uncertain disturbances, and easing the restrictions for control system by expanding the controlled gain as unknown system functions with uncertain disturbances nonlinear pure feedback system; The estimation for the parameters mainly use two methods, the estimation of the Euclidean normal square of weight vectors and weight vectors direct estimation, and also compared the effective and the quality of the two methods. Canceled the partial derivative assumptions about control gain, reduced the complexity of the design, combined the design methods of general dynamic surface control method and integral type Lyapunov function, and then presented a scheme of adaptive dynamic surface control method, proved the stability of the whole closed-loop system, with the tracking error converging to a small neighborhood of the origin.Secondly, adaptive dynamic surface control for a class of nonlinear system in strict feedback form with unmodeled dynamics is presented. By incorporating the approximation capability of neural networks, the design makes the approach of dynamic surface control be extended to the nonlinear system with unmodeled dynamics, and relaxes the extent of application of the approach of dynamic surface control. Discussed the situation of unknown gain, and the estimation for the parameters use the estimation of the Euclidean normal square of weight vectors, which reduces the number of adjustable parameters. Compared with the existing research, the proposed approach does not require the derivative of the virtual control coefficients, and reduces the complexity of the design. Taked advantage of the compact set to overcome the effects of unmodeled dynamics. By theoretical analysis, the stability of close-loop system is proved by using the Lyapunov method.Thirdly, adaptive dynamic surface control for a class of nonlinear system in pure feedback form with unmodeled dynamics is presented. The estimation for the parameters mainly use two methods, the estimation of the Euclidean normal square of weight vectors and weight vectors direct estimation. The paper discussed the controller design with dead-zone input system, and compared it with the original control effect. At last, by theoretical analysis, the stability of close-loop system is proved by using the Lyapunov method.By the studying of this paper, the problems about the design and control tracking of several nonlinear control systems have got a very good solution, and all the results above have passed the simulation validation, it can be know from the simulation results that all the methods which proposed in this paper are effective and feasible.