Geometrical Frameworks in Identification Problem  

作　　者：Nikolay Karabutov Nikolay Karabutov(Department of Control Problems, MIREA—Russian Technological University, Moscow, Russia)

机构地区：[1]Department of Control Problems, MIREA—Russian Technological University, Moscow, Russia

出　　处：《Intelligent Control and Automation》2021年第2期17-43,共27页智能控制与自动化（英文）

摘　　要：The purpose of this review is to apply geometric frameworks in identification problems. In contrast to the qualitative theory of dynamical systems (DSQT), the chaos and catastrophes, researches on the application of geometric frameworks have not </span><span style="font-family:Verdana;">been </span><span style="font-family:Verdana;">performed in identification problems. The direct transfer of DSQT ideas is inefficient through the peculiarities of identification systems. In this paper, the attempt </span><span style="font-family:Verdana;">is </span><span style="font-family:Verdana;">made based on the latest researches in this field. A methodology for the synthesis of geometric frameworks (GF) </span><span style="font-family:Verdana;">is </span><span style="font-family:Verdana;">propose</span><span style="font-family:Verdana;">d</span><span style="font-family:Verdana;">, which reflects features of nonlinear systems. Methods based on GF analysis </span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">developed for the decision-making on properties and structure of nonlinear systems. The problem solution of structural identifiability </span><span style="font-family:Verdana;">is </span><span style="font-family:Verdana;">obtain</span><span style="font-family:Verdana;">ed</span><span style="font-family:Verdana;"> for nonlinear systems under uncertainty.The purpose of this review is to apply geometric frameworks in identification problems. In contrast to the qualitative theory of dynamical systems (DSQT), the chaos and catastrophes, researches on the application of geometric frameworks have not </span><span style="font-family:Verdana;">been </span><span style="font-family:Verdana;">performed in identification problems. The direct transfer of DSQT ideas is inefficient through the peculiarities of identification systems. In this paper, the attempt </span><span style="font-family:Verdana;">is </span><span style="font-family:Verdana;">made based on the latest researches in this field. A methodology for the synthesis of geometric frameworks (GF) </span><span style="font-family:Verdana;">is </span><span style="font-family:Verdana;">propose</span><span style="font-family:Verdana;">d</span><span style="font-family:Verdana;">, which reflects features of nonlinear systems. Methods based on GF analysis </span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">developed for the decision-making on properties and structure of nonlinear systems. The problem solution of structural identifiability </span><span style="font-family:Verdana;">is </span><span style="font-family:Verdana;">obtain</span><span style="font-family:Verdana;">ed</span><span style="font-family:Verdana;"> for nonlinear systems under uncertainty.

关 键 词：Framework Nonlinear Dynamic System Phase Portrait Structural Identifi-cation NONLINEARITY Structural Identifiability SYNCHRONIZABILITY LAG Lya-punov Exponent 

分 类 号：O17[理学—数学]