Dissimilarity for Linear Dynamical Systems

Giorgio Bacci*, Giovanni Bacci, Kim Guldstrand Larsen, Giuseppe Squillace, Mirco Tribastone, Max Tschaikowski, Andrea Vandin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

We introduce backward dissimilarity (BD) for discrete-time linear dynamical systems (LDS), which relaxes existing notions of bisimulations by allowing for approximate comparisons. BD is an invariant property stating that the difference along the evolution of the dynamics governing two state variables is bounded by a constant, which we call dissimilarity. We demonstrate the applicability of BD in a simple case study and showcase its use concerning: (i) robust model comparison; (ii) approximate model reduction; and (iii) approximate data recovery. Our main technical contribution is a policy-iteration algorithm to compute BDs. Using a prototype implementation, we apply it to benchmarks from network science and discrete-time Markov chains and compare it against a related notion of bisimulation for linear control systems.
Original languageEnglish
Title of host publicationProceedings of the International Joint Conference for Quantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems
Volume14996
PublisherSpringer
Publication date2024
Pages125-142
ISBN (Print)978-3-031-68415-9
ISBN (Electronic)978-3-031-68416-6
DOIs
Publication statusPublished - 2024
EventQuantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems - Calgary, Canada
Duration: 9 Sept 202413 Sept 2024
Conference number: 1

Conference

ConferenceQuantitative Evaluation of Systems and Formal Modeling and Analysis of Timed Systems
Number1
Country/TerritoryCanada
CityCalgary
Period09/09/202413/09/2024

Keywords

  • Linear dynamical systems
  • Bisimulation
  • Robustness

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