Efficient Iterative Algorithms for a Class of Nonlinear Systems using the Block Matrix Inversion and Hierarchical Principle

Abstract

This paper is concerned with the identification of the bilinear systems in the state-space form. The parameters to be identified of the considered system are coupled with the unknown states, which makes the identification problem difficult. To deal with the trouble, the iterative estimation theory is considered to derive the joint parameter and state estimation algorithm. Specifically, a moving data window least squares-based iterative (MDW-LSI) algorithm is derived to estimate the parameters by using the window data. Then, the unknown states are estimated by a bilinear state estimator. Moreover, for the purpose of improving the computational efficiency, a matrix decomposition-based MDW-LSI algorithm and a hierarchical MDW-LSI algorithm are developed according to the block matrix and the hierarchical identification principle. Finally, the computational efficiency is discussed and the numerical simulation is employed to test the proposed approaches.