Parameter Optimization Of Linear Disturbance Rejection Controller For A Class Of Fractional Order Chaotic Systems

Chaotic system widely existing in nature and society is a complex nonlinear system with seemingly random and irregular motion characteristics,whose behavior is uncertainty,non-repeatability and irregular.The study of chaotic system plays an important role in the research of scientific field such as digital signal processing,image encryption and secure communication.In recent years,fractional order calculus has gradually attracted more and more attention at home and abroad.Compared with the calculus with integer order,the calculus with fractional order is more widely used and can more accurately indicate and model the actual system.Therefore,based on the theory of three-dimensional fractional order chaotic system,this paper studies the control problem of three-dimensional fractional order chaotic system,and the specific research work is carried out in the following aspects:1.First of all,the development background and research status of chaotic system are briefly introduced.Then,the content of fractional order calculus are given and compared.Finally,the three-dimensional fractional order chaotic systems are numerically simulated by using MATLAB simulation software.2.The development and theoretical basis of linear active disturbance rejection control(ADRC)are introduced.The control structure,control law and parameters needed to be adjusted are given for the linear ADRC controller used in this paper.However,because there are lots of parameters of linear ADRC needed to be adjusted and all parameters are difficult to obtain better coordination setting.So in order to solve this problem,the author propos an improved quantum-behaved particle swarm optimization algorithm using the cosine decreasing function to control the scaling factor in the particle update formula that allows the algorithm to search carefully in the later of iterations and make the algorithm have good global search ability at the same time.In the end,the searching ability of improved algorithm was tested.3.The proposed improved quantum-behaved particle swarm optimization algorithm is applied to the linear ADRC for the three-dimensional fractional order chaotic systems,and the simulation process is realized by using MATLAB simulation software.The results show that the optimized linear ADRC controller can achieve good control effect and has strong anti-interference ability.