Valuation Of The States Of A Class Of Nonlinear Generalized Systems

In recent years, with the rapid development of modern control technology, thecomplexity in control engineering project is becoming higher. Because nonlinearfactors always exist in the practical systems, it is usually difficult to accuratelydescribe the dynamics of a system by single linear system models or generalized linearsystem models. In order to establish a more accurate description of the control systemmodel, the nonlinear generalized system models are commonly used to describe theactual system, which combines the respective advantages of nonlinear systems andgeneralized systems.In this paper, extended Kalman filtering, unscented Kalman filtering, particlefiltering methods are utilized for solving the state estimation problem of the nonlineargeneralized systems. The main results of this paper include the followings:1. Because the classic Kalman filtering method can’t be directly used for dealingwith the state estimation problems of nonlinear generalized systems, the Taylor seriesexpansion method is adopted to transform the nonlinear generalized system into alinear generalized system by reserving one degree term of the Taylor series expansion.Extended Kalman state estimators for nonlinear generalized systems are given by usingsingular value decomposition method and classic Kalman filtering. The square-rootextended Kalman state estimator and singular value decomposition extended Kalmanstate estimator for nonlinear generalized systems are obtained by using Choleskyfactorization or singular value decomposition for filter error variance matrix P.2. The nonlinear generalized systems are changed into two order-reducedsubsystems by using singular value decomposition. Then state estimation problem ofthe nonlinear generalized system is transformed into two coupled nonlinear subsysteminformation fusion state estimation problem. Based on unscented Kalman filtering method, unscented Kalman state estimators for nonlinear generalized systems is givenunder the conditions of correlated noise and uncorrelated noise.3. In the fourth chapter the particle filter algorithm is used for nonlineargeneralized system state estimation problems. In order to avoid particle degeneration,reference resample technology is used. By selecting the appropriate threshold values todetermine whether reference resample is performed on each time, the complexity ofthe algorithm is reduced to a certain extent.