Disturbance decoupling of large-scale Boolean networks based on network aggregation and state-flipping control

Peilian Guo; Juhan Li; Yuanhua Wang; Ben Niu; Peilian Guo; Juhan Li; Yuanhua Wang; Ben Niu

doi:10.3934/math.2026300

AIMS Mathematics

2026, Volume 11, Issue 3: 7285-7303. doi: 10.3934/math.2026300

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Theory article

Disturbance decoupling of large-scale Boolean networks based on network aggregation and state-flipping control

1.
School of Computer Science and Artificial Intelligence, Shandong Normal University, Jinan 250014, China
2.
Business School, Shandong Normal University, Jinan 250014, China
3.
School of Control Science and Engineering, Dalian University of Technology, Liaoning 116024, China

Received: 18 January 2026 Revised: 25 February 2026 Accepted: 16 March 2026 Published: 20 March 2026
MSC : 93D09, 94C11

This paper addresses the disturbance decoupling problem for large-scale Boolean networks. First, the original network is decomposed into several smaller subnetworks via a network aggregation approach, which significantly reduces computational complexity. Then, a state-flipping control strategy is applied to achieve disturbance decoupling within these subnetworks. Necessary and sufficient conditions are established under both uncontrolled and controlled scenarios, leading to the overall disturbance decoupling of the original large-scale Boolean network. Furthermore, this paper proposes two algorithms: One for verifying the feasibility of disturbance decoupling in the original network, and the other for finding the minimum set of flipped nodes required to achieve disturbance decoupling in each subnetwork. Finally, a numerical example illustrates the effectiveness of the proposed methodology.
- large-scale Boolean networks,
- disturbance decoupling,
- network aggregation,
- state-flipping control,
- semi-tensor product
Citation: Peilian Guo, Juhan Li, Yuanhua Wang, Ben Niu. Disturbance decoupling of large-scale Boolean networks based on network aggregation and state-flipping control[J]. AIMS Mathematics, 2026, 11(3): 7285-7303. doi: 10.3934/math.2026300

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Abstract

This paper addresses the disturbance decoupling problem for large-scale Boolean networks. First, the original network is decomposed into several smaller subnetworks via a network aggregation approach, which significantly reduces computational complexity. Then, a state-flipping control strategy is applied to achieve disturbance decoupling within these subnetworks. Necessary and sufficient conditions are established under both uncontrolled and controlled scenarios, leading to the overall disturbance decoupling of the original large-scale Boolean network. Furthermore, this paper proposes two algorithms: One for verifying the feasibility of disturbance decoupling in the original network, and the other for finding the minimum set of flipped nodes required to achieve disturbance decoupling in each subnetwork. Finally, a numerical example illustrates the effectiveness of the proposed methodology.

References

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