Parallel distributed estimation for polynomial nonlinear state space models

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.