Latest Estimation Based Multi-innovation Stochastic Gradient Identification For Equation Error Models

Mathematical models are of great importance in analyzing the dynamic performance of a system. It is well known that system identification has been an effective approach to establish the mathematical models of complex systems. In addition, the techniques of system identification have also been widely applied in the controller design for some complex industry processes. The stochastic gradient algorithm is a classical identification algorithm. It is easily found that, in the existing stochastic gradient algorithms, all the parameters to be estimates are merged into a single vector. On the basis of the classical stochastic gradient identification algorithms, we propose the multi-innovation stochastic gradient identification algorithm based on the latest estimate information by using the hierarchical identification principle. In this thesis, the main research object is the equation error type models which include equation error models, equation error moving average models, equation error autoregressive models and equation error autoregressive moving average models. The main research contents and results of this dissertation are as follows.For equation error type models, the parameter vector in the classical stochastic gradient algorithms is decomposed into two sub parameter vectors by the hierarchical identification principle. For each of these two sub parameter vectors, the stochastic gradient identification algorithm is applied to estimate the parameters respectively. Then the hierarchical stochastic gradient identification algorithm is proposed for these equation error models.It is easily found that in the proposed hierarchical stochastic gradient algorithm, the estimation in the last step of the first sub parameter is used to estimate the second sub parameter vector. But the estimation of the first sub parameter vector at the current step is known. Logically speaking, the estimation of the parameter vector at the current step is closer to its true value. With this idea, the multi-innovation stochastic gradient identification algorithms based on the latest estimation are presented for the equation error type models, by replacing the estimation in the last step by the estimation in the current step.In addition, simulation research is also carried out for the proposed hierarchical stochastic gradient algorithms based on latest estimation. It is shown that the proposed identification algorithms based on the latest estimation possess better convergence performance and identification precision than the existing multi-innovation stochastic gradient algorithms. Besides, the proposed identification algorithms are also generalized to the case of multi-output single input system.