Differential Equivalence for Linear Differential Algebraic Equations

• 成果类型: Article
• 署名作者: Tognazzi, Stefano; Tribastone, Mirco; Tschaikowski, Max; Vandin, Andrea
• 署名单位: University of Konstanz; IMT School for Advanced Studies Lucca; Aalborg University; Scuola Superiore Sant'Anna; Technical University of Denmark
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3108530
• 发表日期: 2022
• 页码: 3484-3493
• 关键词: Numerical models; Mathematical model; computational modeling; indexes; RLC circuits; Synthetic aperture sonar; scalability; Differential-algebraic systems; Linear systems; Modeling; MODEL; controller reduction

摘要

Differential-algebraic equations (DAEs) are a widespread dynamical model that describes continuously evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. As such, DAEs arise in many fields ranging from physics, chemistry, and engineering. In this article, we focus on linear DAEs, and develop a theory for their minimization up to an equivalence relation. We present differential equivalence, which relates DAE variables that have equal solutions at all time points (thus requiring them to start with equal initial conditions) and extends the line of research on bisimulations developed for Markov chains and ordinary differential equations. We apply our results to the electrical engineering domain, showing that differential equivalence can explain invariances in certain networks as well as analyze DAEs, which could not be originally treated due to their size.