Adaptive Observer Design Of Uncertain Nonlinear Systems

The kinds of factors such as uncertainty and external disturbance are widely exists in many practical control systems, and these factors is the important reason that lead to system instability. Therefore, when the controlled object using the intelligent control, the impact of these factors on the control effort should be taken into considered. And the adaptive algorithm is more superior than other intelligent control methods in dealing with system uncertainties. On the other hand, state estimation and parameter estimation have been widely used in many fields such as adaptive control, fault tolerant control, fault diagnosis. So this article combined with the adaptive algorithm to construct the adaptive observer, by using joint estimation of states and parameters to form a class of recursive algorithm. In this dissertation the design problem of adaptive observer is discussed, according to several classes of uncertain nonlinear systems adaptive observers are designed. This paper research content is as follows:First of all, aiming at a class of nonlinear uncertain systems, where both the nonlinear term and the nonlinear uncertainty are mismatched and subject to time-varying delay. Under certain assumptions, we designed the robust adaptive observers. The adaptive observer only has one adaptive parameter no matter how high the order of the system is. And the proposed adaptive observer guarantees that the state estimation errors are uniformly bounded, moreover, the state estimation error can be made arbitrarily small by choosing some design parameters appropriately. And the simulation experiments further demonstrate the feasibility and effectiveness of the observers through the application of LMI and MATLAB.Secondly, the paper focused on a class of parameter uncertain neutral-type systems with time-varying delays. The design of the adaptive observer adopted in the proportional item and integral item. By using the Lyapunov candidate function with integral items and the advanced theory of linear matrix inequality(LMI) to put forward a new stability criterion for the neutral delay systems. At last, through numerical example and using MATLAB M files, and from the simulation curves, we obtained the effectiveness of the design of the observer.In the end, under certain conditions, for a class of uncertain nonlinear Lur’e differential inclusion system, we designed the adaptive full order observers and the reduced order observers respectively. And through theoretical proof and simulation examples, we concluded that the designed observer is feasible and effective. Compared with previous research results, this article’s innovations are embodied in the following aspects: first, the system of nonlinear function is more universal, the condition of nonlinear function is assumed as Lipschitz function in the previous articles, and in this article the conditions relaxed to be unilateral Lipschitz functions; Second, in previous articles, the research on Lur’e differential inclusion systems with an uncertainties the uncertainties is only unknown parameter, but in this article the uncertainties is an unknown function, so it increased the difficulty of the observer design; Three, this paper reduced the amount of calculation of observer, you can directly check via linear matrix inequality(LMI) toolkit.