Extended Differential Balancing for Nonlinear Dynamical Systems

被引：3
|
作者：
Sarkar, Arijit [1 ]
Scherpen, Jacquelien M. A. [1 ]
机构：
[1] Univ Groningen, Fac Sci & Engn, Jan C Willems Ctr Syst & Control, Engn & Technol Inst Groningen, NL-9747 AG Groningen, Netherlands
来源：
IEEE CONTROL SYSTEMS LETTERS | 2022年 / 6卷
基金：
荷兰研究理事会;
关键词：
Observability; Controllability; Reduced order systems; Nonlinear dynamical systems; Computational modeling; Time-varying systems; Symmetric matrices; Balancing; contraction; LMIs; model reduction; nonlinear systems; MODEL ORDER REDUCTION; CONTROLLABILITY; OBSERVABILITY; REALIZATION; TRUNCATION;
D O I：
10.1109/LCSYS.2022.3183528
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this letter, we construct extended balancing theory for nonlinear systems in the contraction framework. At first, we introduce the concept of the extended differential observability Gramian and inverse of the extended differential controllability Gramian for nonlinear dynamical systems and show their correspondence with generalized differential Gramians. We also provide how extended differential balancing can be utilized for model reduction to get a smaller apriori error bound in comparison with generalized differential balancing. We illustrate the results with an example of a mass-spring-damper system considering friction.
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页码：3170 / 3175
页数：6
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