Synchronization Control Of Fractional Order Systems Based On State Estimation

Compared with traditional calculus,fractional calculus can often get more accurate results when modeling actual systems.Therefore,the control problem of fractional order systems has also become a research hotspot.However,in relevant literature,the order of fractional order systems is often between(0,1).In this thesis,the synchronization control of fractional order linear system,fractional order neural network systems and fractional order nonlinear systems whose order is between(1,2)and whose partial states are unmeasurable is mainly studied.This thesis uses the variable substitution method to transform the state observation and synchronization control problem of fractional order systems with orders between(1,2)into the state observation and synchronization control problem of fractional order systems with orders between(0,1).Moreover,in order to analyze the stability of observation error systems and synchronous control systems,relevant stability theorems have been proposed.The full text is divided into five parts.The first part introduces the research background and current situation of fractional order systems at home and abroad.The second part introduces some basic concepts,symbolic descriptions,and descriptions of fuzzy logic systems.In the third part,the synchronization control of fractional order linear system is introduced.In this part,because the system state is unknown,a suitable observer is designed to observe the system state.Then,in order to make the response system better track the linear system,a synchronization controller is designed,and the stability theorem and proof of the synchronization system are given.Afterwards,in order to verify the design effectiveness of the observer and controller,simulations are conducted on the example.Due to the simple structure and form of the linear system introduced in the previous part,further,in the fourth part,the fractional order neural network system synchronization control is studied.Because the given fractional order neural network system has unknown nonlinear function and unknown disturbance.Therefore,the fuzzy logic system is used to approximate the unknown nonlinear function.Then provide the assumption that the unknown disturbance is bounded and bounded by an unknown constant.Subsequently,in order to enable the slave neural network system to effectively track the main neural network system,suitable adjustable parameters and synchronization controllers are designed,and stability analysis of the synchronization error system is conducted.Finally,the effectiveness of the control algorithm is verified through simulation.Since the neural network is a special nonlinear system that can be linearized in time delay,in the fifth part,the synchronization control problem of the more general nonlinear system with part of the state unmeasurable is studied.Since the given fractional order nonlinear system has unknown disturbance and unknown state,it is assumed that the disturbance is bounded and the bound is a known constant.Afterwards,suitable observers are designed to observe the system state.Then,in order to make the response system track the fractional order nonlinear system more effectively,a suitable synchronization controller is designed,and the stability theorem and proof of the synchronization system are given.Finally,in order to verify the design effectiveness of the observer and controller,an example is simulated.