Research On Chaotic Time Series Predictive Control Based On State Space Model

Chaotic time series predictive control is very important in many fields now.With the continuous development of chaotic time series theory and application,the model predictive control of chaotic systems has become a hot topic in contemporary research.Since the state space model can effectively describe the dynamic response characteristics of nonlinear complex systems,the state equations are simple and easy to understand,so it is easily applied to prediction and control of financial,automation,and aerospace.In this paper,the identification method of state space model,state estimation and feedback control proposed for chaotic time series are studied.The main research work includesFor the lack of control problem of Volterra chaotic time series prediction model,firstly,the phase space is constructed to judge the chaotic characteristics,and the Volterra chaotic time series predictive control model is constructed.the Volterra chaotic time series prediction model is transformed into the state space model with the control quantity based on the theory of generalized predictive control.Secondly,the controller is designed by using the Riccati matrix and the minimum variance respectively.Simulation experiments show that the Riccati matrix method avoids a lot of complex calculations and is more accurate than the minimum variance method,so it is more suitable for the feedback controller design of the state space model.Aiming at the problem of poor accuracy of parameter identification in traditional identification methods,the parameters of state space model are estimated by EM(Expectation Maximization Algorithm,EM)algorithm.In the EM algorithm,the Kalman filtering algorithm is used to estimate the state expectation,It is iterated by maximizing the expected implementation of the log likelihood function and estimating the noise covariance until the optimal estimation parameters are obtained.For the state estimation problem of chaotic time series,the Kalman filter state estimation and particle filter state estimation are studied.The extended Kalman particle filter state estimation method is improved.In the resampling stage,the particles are selected according to the ratio of particle weight and error.The survival of the fittest is achieved,and the particle diversity is preserved.The experimental results show that the chaotic time series prediction method based on state space model can make highly accurate prediction.