On the minimum number of general or dedicated controllers required for system controllability

Portal Ruiz, Alberto and Zufiria Zatarain, Pedro José (2019). On the minimum number of general or dedicated controllers required for system controllability. "Applied Mathematics and Computation", v. 355 ; pp. 417-427. ISSN 0096-3003. https://doi.org/10.1016/j.amc.2019.03.015.

Description

Title: On the minimum number of general or dedicated controllers required for system controllability
Author/s:
  • Portal Ruiz, Alberto
  • Zufiria Zatarain, Pedro José
Item Type: Article
Título de Revista/Publicación: Applied Mathematics and Computation
Date: 15 August 2019
ISSN: 0096-3003
Volume: 355
Subjects:
Freetext Keywords: Controllability; Optimal design; Dedicated controllers; Jordan form; Frobenius form
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The paper determines the minimum number of general or dedicated controllers which are required to guarantee the controllability of a class of dynamical systems. For this purpose, we begin by reformulating Kalman controllability condition for linear systems ( A , B ) in the context of the similarity equivalence class associated with A , and then we provide new al- ternative characterizations of such controllability condition based on the cases when ma- trix A is in Jordan or Frobenius form, so that theoretical aspects and computational re- quirements are comparatively commented. In the second part of the paper, given a system state matrix A , we solve the optimal design problem of determining the minimum number of controllers (columns of B ) required for making ( A , B ) controllable, resorting also to the Jordan and Frobenius canonical forms in the similarity equivalence class associated with A . These canonical forms are proven to be also fundamental to provide bounds on the minimum number of dedicated controllers (corresponding to columns of B with a single non-zero element) required to make ( A , B ) controllable. Some examples serve to illustrate the fundamental results.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2015-67396-PUnspecifiedUnspecifiedRedes complejas: modelado, dinámica y aplicaciones

More information

Item ID: 56747
DC Identifier: http://oa.upm.es/56747/
OAI Identifier: oai:oa.upm.es:56747
DOI: 10.1016/j.amc.2019.03.015
Official URL: https://www.sciencedirect.com/science/article/pii/S0096300319302085?via%3Dihub
Deposited by: Memoria Investigacion
Deposited on: 23 Mar 2020 16:27
Last Modified: 23 Mar 2020 16:27
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