System Identification Of State-Space Models

The aim of system identification is building dynamic models. It is an important step before system analysis, control and optimization. And there are many problems to be resolved in the field of system identification. The problems of parameter estimation of state-space models are considered in this thesis. The main work and the innovations of this thesis are as follows:(1) A parameter estimation method, based on gradient optimization search, is proposed for the linear time-invariant (LTI) state-space models. By the analysis of the similar transformation of LTI systems, the system parameters are updated to the orthogonal space to the manifold of observationally equivalent state-space systems, whose advantage is that local minimization can be advoided and the computational load can be decreased. Moreover, the relation between computational load and system properties such as the observability and controllability is also discussed in detail. Finally, simulation studies show the enhanced performance of the proposed method.(2) An output error identification method by projected gradient search is proposed for the parameter estimation of multivariable bilinear state-space systems. The system parameters are estimated by iteratively optimizing an output-error cost function. The nonuniqueness of the fully parameterized state-space model is taken into account by solving the optimization problem using a local gradient search that restricts the update of the parameters to directions that change the input-output behavior. In addition, the regulation parameter is adaptively determined by considering the local linear approximation of the output error. Moreover, the relation between the computational load and system properties such as the observability and controllability is discussed in detail. At the same time, the analytic expression of the convergence rate of the identification algorithm is also presented. Finally, the effectiveness of the proposed method is illustrated by practical study with data collected from a rare earth extraction process.(3) According to the local-linearization, a orthogonal gradient identification method is proposed for weighted state-space models, which is suited for nonlinear dynamical system modelling. The system parameters are determined by minimizing the output-error cost function. normalized radial basis functions are taken as weights of local state. And the orthogonal gradient computation method is given by considering the information of input-output equivalent class. At the same time, the iterative computation for parameters of system and radial basis function is given, and the iterative identification algorithm is also proposed. In addition, the influence of the subsystem's controbility and observability to the computational load is discussed in detail. Finally, a numerical study is given to illustrate the performance of the proposede method for non-linear dynamic systems.(4) A subspace identification method based on instrumental variable is proposed for parameter estimation of closed-loop state-space systems with known setpoint input and unknown controller information. The instrumental variable is designed according to the characteristics of identification problem. In addition, the orthogonal complement to the extended observability matrix can be estimated. And the extended observability matrix and lower triangular block-Toeplitz matrix are computed by the SVD decomposition. Finally, a simulation study of closed-loop dynamic system is implemented and the result illustructed the performance of the proposed method.(5) An identification method, based on the expectation maximization (EM) algorithm, is proposed for dynamic systems with missing state information. In the framework of EM algorithm, the expression of joint conditional expectation is obtained and the parameter computation for the maximization of the joint conditional expectation is also derived. In addition, the algorithmic robustness can be enhanced by the QR decomposition. The result of the numerical simulation shows the performance of the proposed method.(6) Based on adaptive nonparametric density estimation method, a maximum likelihood (ML) identification method is proposed for dynamic systems with unknown noise density distribution. The Gaussian kernel density estimator is designed and the ML estimation algorithm is presented. At the same time, the algorithmic convergence is also analysized in detail. The performance of the proposed method is illustracted by the simulation result.