Research On Observer Design For Some Classes Of Nonlinear Systems

The present paper focuses on the investigation of the observer design for nonlinear systems. For several different classes of nonlinear systems, we consider the designs of full-order adaptive observer, reduced-order robust observer and finite time functional observer respectively. The main contents of this paper are composed of the following three parts:(I). Study on nonlinear adaptive observer design without a priori knowledge on the unknown parametersIn this part, the adaptive observer design is investigated for a class of nonlinear systems with unknown parameters. Different from the existing results, the nonlinear system studied here is more general and possesses less a priori knowledge: (1) the upper bound of the (Euclidean) norm of the system unknown parameters is unknown; (2) there exist nonlinear dynamics which are not Lipschitz continuous with respect to the measurable output; (3) the system output explicitly depends upon the control input. By adding an adaptive regulator to estimate the norm of the unknown parameters, a novel approach is developed under some conditions to design the nonlinear adaptive observer. The observer designed is globally asymptotically convergent, i.e., it not only gives the convergent reconstruction of the system states, but also guarantees the uniform boundedness of the estimations of the unknown parameters.(II). Study on the reduced-order robust nonlinear observer design for a class of nonlinear systems with unknown parametersIn this part, we consider the problem of the reduced-order robust nonlinear observer design for a class of nonlinear systems with unknown parameters. Different from the above part, the unknown parameters of the nonlinear system studied here are no longer only constants, and the system output is independent of the control input. By the coordinate transformations of the system stales, a new approach is presented to design the reduced-order robust observer. Compared with the full-order adaptive observer, the observer designed in this part needn't give any estimation of the unknown parameters. Consequently. 1 ho observer design not only makes the structure of the whole feedback system simple, but also real- izes the exponential reconstruction of the unknown system states rather than the asmplotical reconstruction.(III). An approach to design the finite time functional observer for a class of nonlinear systemsIn this part, the problem of the finite time functional observer design is investigated for a class of nonlinear systems, and the related results existing in the literature are generalized: (1) An approach to design the asymptotic convergent functional observer is proposed for the nonlinear system; (2) based on the asymptotic convergent functional observer designed, and combined with the theory of finite time observer, a new approach to design the finite time functional observer for the nonlinear systems is presented. It has been shown that, within any given lime interval, the finite time functional observer designed realizes the accurate reconstruction of the function of the nonlinear system states.The above three parts give the corresponding simulation examples which illustrate the effectiveness and feasibility of three types of observer design methods.