Research On Subspace Identification For Continuous-Time Stochastic Systems

Continuous-time stochastic systems are dynamic systems in which each variable is a continuous function of time and the state and output vectors are disturbed by noise.Due to the existent phenomenon of continuous stochastic in biology,economics and physics,the identification of continuous-time stochastic systems has attracted much attention by experts and scholars in various fields.In addition,many industrial processes are of the continuous stochastic nature,especially in the blast furnace metallurgy and petrochemical industry.Most of their models axe the continuous-time stochastic systems described by differential equations.At present,there are still many problems to be solved in the identification of continuous-time stochastic systems,such as how to reduce the computational load of the identification method and improve the accuracy of the identification model.Obviously,how to solve the identification problem of the continuous-time stochastic systems is of theoretical and practical values.Based on the structure of the continuoustime stochastic systems,this dissertation deeply researches the implementation,the property analysis and the application of the subspace identification method,and provides lots of important theoretical results.The main work and research results of this dissertation are as follows:(1)In order to reduce the influence of system noise and optimize the system order,the nuclear norm subspace identification method based on the Kalman filter is studied.The biology of plague model is a typical continuous-time stochastic system.We take the continuous-time stochastic plague model as the research background.First of all,the Kalman filter of the continuous-time stochastic system is assumed with the undetermined matrices.The equivalent innovation form of the system is obtained on condition that mean square error is minimum.Secondly,the projection matrix is obtained by calculating the extended observability matrix.Constructing nuclear norm minimization with the projection matrix,the augmented Lagrangian of the problem is solved by alternating direction multiplier method,and the most optimal output sequences are obtained.Thirdly,substituting the output sequences into the projection matrix,the most optimal system order is given by singular value decomposition,and system matrices and noise intensity are obtained.Finally,the simulation experiment of the continuous-time stochastic model of plague is studied.(2)For the zeros of the identification process of the continuous-time stochastic system are not easily translatable to the poles,the nuclear norm subspace identification via distribution-based approach is proposed.Firstly,random distribution theory in the sense of Ito-Schwartz is introduced to differential and integral calculus of the output equation,and we have the input-output algebraic relationship.Secondly,the optimal state estimation is obtained by the Kalman filter,and an extended state space model and the projection matrix is given.Thirdly,the nuclear norm minimization is used to optimize the projection matrix.The augmented Lagrangian of the problem is solved by alternating direction multiplier method.System matrices and noise intensity are obtained by performing the singular value decomposition on the projection matrix.Finally,the numerical simulations of the scalar stochastic system and continuous-time stochastic systems are studied.(3)In view of the off-line model cannot effectively track the dynamic of the systems,the recursive subspace identification based on random distribution theory is researched.The Tennessee-Eastman process has the characteristic of continuity,randomness and dynamism.The data of the Tennessee-Eastman process is used as the research basis.Firstly,the time-derivative in sense of the distribution of the time-varying continuous stochastic process is calculated by using integration by parts.The input-output matrix equation is given in a small interval.By introducing a positive-definite the weight function,we have the weighted input-output algebraic equation.Secondly,performing the QR decomposition on the equivalent equation composed by input-output data and fixing the size of the "R" data matrices,the system matrices are obtained by performing the eigenvalue decomposition recursively.Finally,the simulation experiment of the Tennessee-Eastman chemical process is studied.(4)Aiming at some variables are hard to prediction on-line in production processes,the recursive subspace prediction based on the rotation of the principal angle is proposed.The continuous stirred tank heater process is of the continuous stochastic nature.In addition,the system is also subjected to the deterministic oscillatory disturbances frequently.The data of the continuous stirred tank heater process are used as the research basis.Firstly,the extended observability matrices of continuous-time stochastic systems are obtained by random distribution theory.Secondly,by using the angle between past and present subspaces spanned by the extended observability matrices,the future signal subspace is predicted by rotating the present subspace in the geometrical sense.In order to predict the future signal subspace,the angular velocity and acceleration of the signal subspace have been derived.For the changes of the system matrices are so fast,the recursive subspace prediction based on the rotation of the principal angle is presented.Finally,the simulation experiment of the continuous stirred tank heating system is studied.