Multiple Model Approach To System Identification With EM Algorithm

With the rapid development of science and technology, industrial production control and optimization technology get more and more attention. While control theory and technology of existing research are mostly based on the model, however, most of the models are unknown, so identification is becoming an important field of research, and it is to obtain the mathematical models of the systems from the observation data with noise. So the research of system identification has important theoretical values and practical significance. Although the identification in linear system has been developed perfectly, in real system, the problem of nonlinearity, uncertainty and missing data are common, which makes the identification more complicated. To solve these problems, this paper adopts multi-model approach to identify the nonlinear system with scheduling variable by expectation maximization algorithm.The major research in this paper mainly includes:(1) Identification of nonlinear systems with an uncertain scheduling variable and missing output data. According to the multi-model approach, the nonlinear system is decomposed into several local models at different process operating points, and normalized exponential function is chosen as the weight function, and the whole dynamics of the nonlinear system is described by both of them. The response variable kD is introduced to characterize the data is missing or not at time k. Expectation maximization algorithm is used to deal with the missing data and identify the unknown parameters. The effectiveness of the proposed method is verified by simulation examples.(2) Identification of nonlinear systems with a random scheduling variable by multi-model approach which is based on expectation maximization algorithm. Due to the change of environment temperature or other factors, the dynamic characteristic of the scheduling variable maybe changed. To solve this problem, the application of Markov chain is proposed to describe it. Then the nonlinear system is decomposed into several simple subsystems according to different working conditions by using the multi-model approach. Auto regressive exogenous(ARX) models are chosen as local models, then the complete dynamics of the nonlinear system can be described. The unknown parameters of local models and the weight function are estimated by the expectation maximization algorithm. Some examples are used to demonstrate the proposed method.While several simulation experiments with a random scheduling variables and data missing are carried out, and they proved that the methods proposed in(1) and(2) are effective.