Output Controllability of a Linear Dynamical System with Sparse Controls

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Abstract

In this article, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the Kalman rank test for output controllability. However, the verification of these conditions is computationally heavy due to their combinatorial nature. Therefore, we derive noncombinatorial conditions for output sparse controllability that can be verified with polynomial time complexity. Our results also provide bounds on the minimum sparsity level required to ensure output controllability of the system. This additional insight is useful for designing sparse control input that drives the system to any desired output.

Original languageEnglish
Pages (from-to)147-156
Number of pages10
JournalIEEE Transactions on Control of Network Systems
Volume10
Issue number1
DOIs
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public

Keywords

  • Controllability
  • linear dynamical systems
  • time-varying support
  • discrete-time system
  • sparsity
  • output controllability
  • Kalman rank test
  • optimal sparse control
  • general linear systems
  • minimal input

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