Research On Design For One-sided Lipschitz Nonlinear Systems

With the rapid development of social productivity,people have put forward higher requirements for the improvement of the level of science and technology and the depth of theoretical research,which also make the considered actual control systems more and more complex.Among them,the complexity of nonlinear systems and the difficulty in constructing mathematical models have brought challenges to the related research work.However,nonlinear systems are still the main research directions and hotspots of control theory and further research on nonlinear systems is of background and significance.This paper investigates one-sided Lipschitz nonlinear systems primarily.Under the practical background of single-link flexible manipulator system,the paper also simulates the numerical examples to show the effectiveness of all presented design methods.This paper includes the following mainly:Quadratically inner-bounded condition and S-procedure are used to study one-sided Lipschitz nonlinear systems,and a full-order observer design method is put forward.Based on the designed full-order observer,a reduced-order observer is constructed by using the structure decomposition method,the existence condition of the reduced-order observer is given.The above conclusion is extended to the nonlinear system with both one-sided Lipschitz function and unknown parameter.Based on the nonlinear system,an adaptive full-order observer and a reduced-order observer are constructed.The one-sided Lipschitz condition is extended to a more general form,and a non-fragile controller design method is given on the basis of the observer design theory.The main contribution of this paper can be summarized as follows:Under the observer design for one-sided Lipschitz nonlinear systems,the quadratically inner-bounded condition and S-procedure are applied to the full-order and reduced-order observer design.The observer design method and theory is greatly simplified and enriched,respectively.The design of an adaptive full-order and reduced-order observer for the one-sided Lipschitz nonlinear system with unknown parameter is studied.Besides,the one-sided Lipschitz nonlinear system is further generalized,which makes it has important theoretical significance.For synchronizationproblem of the one-sided Lipschitz nonlinear system,the more general one-sided Lipschitz condition is proposed and a non-fragile controller is applied.It is greatof theoretical significance for the controller design of the nonlinear systems.