TY - JOUR

T1 - On structural behavioural controllability of linear discrete time systems with delays

AU - van der Woude, Jacob

AU - Boukhobza, Taha

AU - Commault, Christian

PY - 2018

Y1 - 2018

N2 - In this paper we study the controllability of interconnected networks that are described by means of structured linear systems with state-like and control variables. We assume that the systems operate in discrete time with the set of integers as the time axis. Further, we assume that the state-like variables for their evolution only depend on recent values of their neighbours with, however, unknown weight factors. These recent values may be one step back in time, but also more steps. This yields a description of the systems by means of matrices containing fixed zeros and free parameters, together with a time lag structure. Knowing the dependency and lag structure, we represent (the structure of the) systems by means of weighted directed graphs and study questions concerning their structural controllability, where the latter has to be defined in an appropriate way, i.e., in behavioural sense. We provide a necessary and sufficient characterization of structural controllability of our systems using a graph representation. The obtained characterization makes use of well-known and efficient algorithms from graph theory. We prove that in this context finding the minimal number of driver (controller) nodes is an NP-hard problem. The concepts and results of the paper are illustrated on academic examples and on a gene regulatory network.

AB - In this paper we study the controllability of interconnected networks that are described by means of structured linear systems with state-like and control variables. We assume that the systems operate in discrete time with the set of integers as the time axis. Further, we assume that the state-like variables for their evolution only depend on recent values of their neighbours with, however, unknown weight factors. These recent values may be one step back in time, but also more steps. This yields a description of the systems by means of matrices containing fixed zeros and free parameters, together with a time lag structure. Knowing the dependency and lag structure, we represent (the structure of the) systems by means of weighted directed graphs and study questions concerning their structural controllability, where the latter has to be defined in an appropriate way, i.e., in behavioural sense. We provide a necessary and sufficient characterization of structural controllability of our systems using a graph representation. The obtained characterization makes use of well-known and efficient algorithms from graph theory. We prove that in this context finding the minimal number of driver (controller) nodes is an NP-hard problem. The concepts and results of the paper are illustrated on academic examples and on a gene regulatory network.

KW - Behavioural controllability

KW - Graph theory

KW - Linear discrete time models

KW - Structured systems

UR - http://www.scopus.com/inward/record.url?scp=85050083528&partnerID=8YFLogxK

U2 - 10.1016/j.sysconle.2018.06.008

DO - 10.1016/j.sysconle.2018.06.008

M3 - Article

AN - SCOPUS:85050083528

VL - 119

SP - 31

EP - 38

JO - Systems & Control Letters

JF - Systems & Control Letters

SN - 0167-6911

ER -