Separable synthesis gradient estimation methods and convergence analysis for multivariable systems

Abstract

This paper studies the parameter identification problem for a large-scale multivariable systems. In terms of the identification obstacle causing by huge amounts of parameters of large-scale systems, a separable gradient (synthesis) identification algorithm is developed in accordance with the hierarchical computation principle. For the large-scale multivariable equation-error systems, the whole parameters are detached into several sub-parameter matrices based on the scales of the coefficient matrices of the inputs and outputs. On the basis of the detached parameter matrices, multiple parameter estimation sub-algorithms are presented for estimating the parameters of each sub-matrix through using the gradient search and multi-innovation theory from real-time measurements. Concerning the problem that the sub-algorithms are not effective because of the unknown parameters existing in the recursive computation, the previous estimates of the unknown parameters and the interactive estimation are introduced into the sub-algorithms to eliminate the associated items that make the sub-algorithms impossible to implement. In order to analyze the convergence of the proposed algorithms theoretically, we prove the convergence by using martingale convergence theory and stochastic principle. Finally, the performance tests of the proposed identification approaches for large-scale multivariable systems are carried out on several numerical examples and the simulation results demonstrate the effectiveness of the proposed methods.