Distributed pinning controllers design for set stabilization of $ k $-valued logical control networks

Yanfei Wang; Changxi Li; Jun-e Feng; Yanfei Wang; Changxi Li; Jun-e Feng

doi:10.3934/mmc.2023006

Mathematical Modelling and Control

2023, Volume 3, Issue 1: 61-72. doi: 10.3934/mmc.2023006

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Distributed pinning controllers design for set stabilization of $ k $-valued logical control networks

School of Mathematics, Shandong University, Jinan 250100, China

Received: 23 September 2022 Revised: 28 January 2023 Accepted: 07 February 2023 Published: 15 February 2023

Design of distributed pinning controllers for set stabilization of $ k $-valued logical control networks is investigated in this paper. Firstly, by analyzing the coupling correlations among nodes, pinned node set is determined. Secondly, based on the solvability of a class of matrix equations, sufficient conditions which resort to local information are put forward for the design of pinning controllers. Furthermore, an algorithm for designing pinning feedback controllers is presented, where the designed controllers are related to part of state variables instead of all variables. Finally, two illustrative examples are presented to verify the effectiveness of the main results.
- distributed pinning control,
- $ k $-valued logical network,
- semi-tensor product of matrices
Citation: Yanfei Wang, Changxi Li, Jun-e Feng. Distributed pinning controllers design for set stabilization of $ k $-valued logical control networks[J]. Mathematical Modelling and Control, 2023, 3(1): 61-72. doi: 10.3934/mmc.2023006

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Abstract

Design of distributed pinning controllers for set stabilization of $ k $-valued logical control networks is investigated in this paper. Firstly, by analyzing the coupling correlations among nodes, pinned node set is determined. Secondly, based on the solvability of a class of matrix equations, sufficient conditions which resort to local information are put forward for the design of pinning controllers. Furthermore, an algorithm for designing pinning feedback controllers is presented, where the designed controllers are related to part of state variables instead of all variables. Finally, two illustrative examples are presented to verify the effectiveness of the main results.

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