Research On Robust Control Of Complex Variable Nonlinear Systems

In 1963,Lorenz first proposed nonlinear theory,which became a popular research topic.In recent years,the study of nonlinear systems with unique properties has attracted extensive attention.Complex variable nonlinear systems usually contain real and imaginary numbers,which makes them perform well in maintaining information security.With the continuous change of complex variable nonlinear system,its dynamic characteristics far exceed its own,so it is extremely difficult to control it effectively.Physicists have proposed many effective schemes to solve the control problem of complex variable nonlinear systems.These schemes include both uncertainty control and disturbance estimation control.The UDE controller(Uncertain and Disturbance Estimator)is composed of multiple high bandwidth filters and is the core part of the entire system.By using appropriate filters,the influence of external factors on the system can be effectively suppressed,and the internal characteristics of nonlinear systems can be accurately predicted.By effectively controlling uncertainty and external factors,we can effectively eliminate these impacts and restore stability to the system.The full text will be expanded from the following four aspects:(1)Inspired by the UDE idea,filters were designed for two different cases of external disturbances by selecting appropriate functions.(2)The stabilization of a four dimensional complex variable nonlinear system with model uncertainties and external disturbances is studied.Firstly,by introducing a semi tensor product tool,the complex variable system is transformed into an equivalent six dimensional real system.Then the controller was designed in two steps.The first step is to construct a dynamic gain feedback controller that can adjust parameters to achieve the control problem of the nominal system.In the second step,based on the results of the filter in Chapter 2,a controller that can asymptotically estimate external disturbances is designed,and the required controller is obtained.Finally,the effectiveness and correctness of this method were verified through practical testing on an underwater robot model.(3)The synchronization problem of a four-dimensional complex variable nonlinear system with model uncertainty and external disturbances is studied.By transforming a four-dimensional complex variable nonlinear system with model uncertainty and external disturbance into a six dimensional real system,a dynamic gain feedback controller that can adjust parameters can be constructed,so that the system can reach a stable state;By using UDE technology to construct a variety of controllers,complex variable nonlinear systems can be effectively processed to achieve synchronous state;The effectiveness of this method was verified through practical testing of an underwater robot model.(4)The anti synchronization problem of a four-dimensional complex variable nonlinear system with model uncertainty and external disturbances is studied.On the basis of stabilization and synchronization problems,a new filter is introduced to achieve effective control of the system.