Identification Methods For State Space Systems Based On Model Decomposition

Recently, state space system identification has attracted many researchers’ attention. For high dimensional state space systems, the computational costs of the identification algorithms are large, especially the computational costs of the matrix multiplication and the matrix inversion. To reduce computational burden, this paper chooses the thesis "Identification Methods for State Space Systems Based on Model Decomposition", and it has important theoretical significance and academic value. We study the identification problems for state space systems, the main research results obtained are as follows.1. For the single variable state space system, the identification model contains both the unknown states and the unknown parameters, and they involve the nonlinear prod-uct relations, which makes the identification problem more complicated. In order to solve this problem, this paper uses the interactive estimation theory to derive the combined state and parameter estimation algorithms by means of the recursive or iterative scheme. When computing the parameter estimates, the unknown states in the information vector of the identification algorithms are replaced with their esti-mates, the obtained parameter estimates are used to design the parameter estimates based state observer or the parameter estimates based Kalman filtering algorithm to estimate the states of the systems. Furthermore, by using the estimation states and the input and output data of the system, this paper presents the state observer based or the Kalman filtering based least squares (LS) identification algorithms and model decomposition LS identification algorithms.2. For the multivariable state space system, which has complex system structure and lots of parameters to be identified, the computational burden will be very heavy when the dimension of the system is high. To solve these problems, this paper extends the identification methods of the single variable state space system to the multivariable state space system, and presents the multi-innovation stochastic gradient (MISG) algorithm and the model decomposition based MISG algorithm for the multivariable state space systems, by using the state observer to estimate the unknown states. Furthermore, using the Kalman filtering this paper proposes the Kalman filtering base least squares iterative (LSI) algorithm and model decomposition LSI algorithm. Both the state observer and the Kalman filtering can obtain accurate estimated states and the latter is a bit more accurate. However, the Kalman filtering needs more calculations.3. For the bilinear state space systems, which are a special kind of nonlinear systems, there exist the product relations between the unknown states and the system inputs in the state equation. This paper extends the identification methods of the linear state space systems to the bilinear state space systems, derives the linear regression model of the bilinear state space system, and proposes the state observer based or the Kalman filtering base LS algorithms and gradient iterative (GI) algorithms, and the model decomposition based LS algorithms and GI algorithms. The study shows that the model decomposition based LS algorithms can obtain accurate estimated parameters, and have much smaller computation costs than the LS algorithms.This paper uses the simulations on the computer to show the effectiveness of the parameter estimation algorithms. Finally, the computational efficiency, the computational steps and the flowcharts of some typical algorithms are discussed.