The Study On Control Of Nonlinear Systems With Uncertainty And Disturbance Estimation

In nonlinear dynamics,the synchronization of nonlinear systems has always been a hot research direction,and the model uncertainty and external disturbance are one of the main factors restricting the synchronization of nonlinear syste ms.In order to solve the synchronization problem of nonlinear systems with model uncertainty and external disturbance,the key problem is how to design the controller to meet the requirements.In this regard,although a single controller can achieve the control problem,the controller designed in the current results is often too complex.In view of this situation,the main contribution of this thesis is to give a kind of combined control method,that is,according to the advantages and disadvantages of different types of controllers,learn from each other and use them together.The main design idea of this thesis is step-by-step design,that is,a class of nonlinear system with uncertainty and disturbance is given.Firstly,the synchronization problem of the nominal system is considered,and then how to use the appropriate filter to realize the synchronization of the original system is considered.The design feature of the controller in this thesis is based on a control method of uncertainty and disturbance estimation,which mainly uses the characteristics of low-pass filter to accurately estimate the model uncertainty and external disturbance of the system and filter them out,Compared with other perturbation removal methods,UDE is less constrained and does not need to consider the upper and lower bounds of perturbation.The full thesis is divided into the following three aspects:(1)Synchronization problem: firstly,a class of nonlinear system with model uncertainty and external disturbance is given.Firstly,the nominal system is considered,and an adaptive feedback controller is designed to solve the synchronization problem of the system.Then,combined with the obtained adaptive feedback controller,a combined control method based on ude is designed to s olve the synchronization problem of a given nonlinear system.(2)Projective synchronization problem: Based on the extension of synchronization problem,the basic concept and research significance of projective synchronization for nonlinear systems are given,and a method to judge the existence of projective synchronization for nonlinear systems and an algorithm for solving projective synchronization are introduced.Then,the projective synchronization of a given nonlinear system is still implemented in two steps.The first step is to realize the projective synchronization of the nominal system,which is different from the adaptive feedback control method.The latter is better at solving the projective synchronization and other synchronization problems with more complex control mechanism.(3)Stabilization of complex variable nonlinear systems: the research significance of complex dynamics and system stabilization is expounded.Aiming at the stabilization control problem of a class of complex variable nonline ar systems with external disturbance and model uncertainty,the research work is carried out in three aspects.Firstly,the equivalent transformation method from complex variable system to real variable system is obtained by using matrix semi tensor product;Secondly,a dynamic gain feedback controller is designed to stabilize the nominal system;Thirdly,combined with the existing controllers,a combined controller based on UDE is designed to stabilize a class of complex variable nonlinear systems with disturbances and uncertainties.