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Identification of Boolean control networks with time delay.

Tiantian Mu¹, Jun-E Feng¹, Biao Wang²

¹School of Mathematics, Shandong University, No. 27 Shanda South Road, Jinan, PR China.

ISA Transactions

|October 21, 2023

Summary

This summary is machine-generated.

This study introduces methods for identifying time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) using the Cheng product. Algorithms are presented to determine network parameters and structure, enhancing system analysis.

Keywords:

Boolean control networks Cheng product of matrices Identification Observability Time delay

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Area of Science:

Systems Biology
Control Theory
Network Science

Background:

Boolean networks (BNs) are widely used to model complex biological systems.
Time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) introduce temporal dynamics crucial for accurate modeling.
Identifying the structure and parameters of these networks from input-output data is essential for understanding system behavior.

Purpose of the Study:

To develop novel methods for the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs).
To establish criteria for the identifiability of TBNs and TBCNs based on system observability.
To present algorithms for selecting delay parameters and reconstructing the internal structure of these networks.

Main Methods:

Utilizing the Cheng product for network analysis.
Defining identifiability based on admissible input-output sequences.
Designing algorithms for delay parameter selection and subsystem decomposition.
Applying observability criteria for structural identification.

Main Results:

A formal definition of identifiability for TBNs and TBCNs is provided.
Two algorithms are developed for selecting appropriate delay parameters.
Criteria for identifiability are derived using the concept of observability.
Constructing processes are presented to determine the internal network structures.

Conclusions:

The proposed methods offer a feasible approach for identifying TBNs and TBCNs.
The developed algorithms and criteria facilitate a deeper understanding of dynamic network properties.
Illustrative examples confirm the effectiveness of the presented identification techniques.