Parallel distributed estimation for polynomial nonlinear state space models
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Parallel distributed estimation for polynomial nonlinear state space models Wang Jian-hong1 · Wang Yan-xiang1 Received: 19 October 2019 / Revised: 21 April 2020 / Accepted: 12 September 2020 / Published online: 10 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, nonlinear system is modeled by one polynomial nonlinear state space model. Two polynomial functions of input or state are added in the common state space model and these two polynomial functions correspond to the nonlinear factors. This polynomial nonlinear state space model can be represented the special nonlinear closed feedback system. To identify every system matrix in the polynomial nonlinear state space model, firstly each system matrix is vectorized as an unknown parameter vector and then two parallel distribution algorithms are applied to identify this unknown parameter vector in the unconstrained or constrained conditions respectively. When some state equation equalities are deemed as the constrained conditions, the new optimization variables are the state instants and the unknown parameter vector, consisted by all system matrices. These complex optimization variables are solved by parallel distribution algorithm and the whole process about parallel distribution algorithm are given explicitly. Generally, the main contributions of this papre consist in two folds: one is to apply that polynomial function to represent the nonlinear factor, existing in the nonlinear state space model, and the other is to propose parallel distribution algorithm to identify the unknown parameter vector, while analyzing its property. Finally the simulation example is used to prove the efficiency of this parallel distribution algorithm. Keywords System identification · Polynomial nonlinear system · Parallel distribution algorithm
1 Introduction The essence of system identification belongs to the research field of adaptive control theory, it means that one mathematical model is constructed for our considered plant through the observed input–output data sequence, so that the constructed mathematical model is used as the basis for the next adaptive control. The categories of system identification can be divided as two kinds: linear system identification and nonlinear system identification. For linear system identification, as one linear relation exists between the input–output data, and this special linear relation can be expanded into the linear regression form, which simplifies the whole identification process. But this linear regression form is an ideal one, due to nonlinear form exists in our real life systems and phenomena widely, such as nature and engineering. The cause
B 1
Wang Yan-xiang [email protected] School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou 343100, China
of commonly used linear form is that the existing theory of linear system identification can be directly applied. Considered nonlinear system identification, the nonlinear system is always linea
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