Study On Stable Adaptive Neural Networks Control By Dynamic Surface Technology

As one of the major methods of the adaptive control of nonlinear systems, backstepping has been received more and more attention in recent years. In this paper, aclass of single-input single-output(SISO) & multiple-input multiple-output(MIMO)perturbed strict-feedback nonlinear systems with unknown constant/function gain, and aclass of nonlinear systems with saturation model input are studied in turn. Based on themethod of backstepping, the design and analysis procedures use a series of controltheories such as Lyapunov stability theory, adaptive control theory, neural networkcontrol theory, dynamic surface control, robust control theory and so on. The main work.of this paper is summarized as follows.Firstly, based on dynamic surface control, two novel design schemes of adaptiveneural network control are proposed for a class of strict-feedback nonlinear systemswith unknown constant gain. The two proposed schemes all eliminate the problem ofexplosion of complexity in traditional backstepping design, which is caused by repeateddifferentiations of certain nonlinear functions such as virtual control. In the case ofindirect control, the designed controller can completely overcome the. possiblesingularity problem. While in the direct case, the adaptive parameter is reduced.Naturally, the controller is simple. By using Lyapunov method, the closed-loop systemsare shown to be semi-globally uniformly ultimately bounded, with tracking errorconverging to a small neighborhood by appropriately choosing design constants in thetwo schemes.Secondly, the problem of adaptive neural network control is discussed for a class ofstrict-feedback nonlinear systems with perturbed and unknown function control gain.Two indirect design schemes are proposed by combining dynamic surface control andneural network control and adaptive control. In the first scheme, the projectionalgorithm is used to avoid the possible controller singularity in the indirect control.While the controller in the second scheme can completely overcome the possiblecontroller singularity in feedback linearization. Naturally, the constitution of thecontroller is simple without projection algorithm. In addition, the problem of explosioncomplexity in traditional backstepping design, which is caused by repeateddifferentiations of certain nonlinear functions such as virtual control, is eliminated byintroducing the first order filter in the two schemes. Moreover, the expressions offeedback gains, in the controller and the time constants in the filters are also presented.By using Lyapunov method, the closed-loop systems are shown to be semi-globallyuniformly ultimately bounded, with tracking error converging to a small neighborhoodof the origin.Thirdly, based on backstepping and dynamic surface control, two indirect designschemes of adaptive neural network control are proposed for two classes of MIMOnonlinear systems with different forms. It is no need to know the sign of control gain in the first scheme. In the second scheme, it is unnecessary for the gain matrix to bepositive or reversible.Lastly, the problem of adaptive neural network control is discussed for a class ofSISO nonlinear systems with unknown saturation model. Base on the principle ofsliding mode control and the approximation capability of neural network, a new designscheme of adaptive neural network controller is proposed. The approach removes thecondition of knowing the parameters by compensating saturation. Robust term is used toeliminate the approximating error and disturbance. By theoretical analysis, theclosed-loop systems are shown to be semi-globally uniformly ultimately bounded, withtracking error converging to zero. In addition, the region of the state is gained.Through the research in this paper, the design and analysis problems for theperturbed nonlinear control systems have been properly solved via the method ofbackstepping. Numerical simulation experiments of the control schemes demonstratetheir effectiveness and practicability.