Skip to main content
SpringerLink
Log in

Observability and Detectability of Large-Scale Boolean Control Networks

  • Chapter
  • First Online:
Book cover Discrete-Time and Discrete-Space Dynamical Systems

Part of the book series: Communications and Control Engineering ((CCE))

  • 677 Accesses

Abstract

In Chaps. 4 and 5, we investigated how to verify different notions of observability and detectability for Boolean control networks (BCNs), and also studied how to determine the initial state (current state) of a BCN according to a particular notion of observability (detectability). In addition, we proved that the problems of verifying these notions are all NP-hard in the number of nodes. Hence, these problems are generally intractable. Actually, in general, for a BCN with more than 30 nodes, one cannot obtain whether it is observable or detectable in a reasonable amount of time by using a personal computer (PC). Hence BCNs with more than 30 nodes can be regarded as large-scale.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In Zhao et al. (2013), in order to compute attractors, the 3 input nodes are assumed to have constant values.

  2. 2.

    Some of the material in Sects. 6.1, 6.2, 6.3, and 6.5.2 were reproduced from Zhang and Johansson (2018) with permission @ 2018 IEEE.

References

  • Akutsu T et al (1998) A system for identifying genetic networks from gene expression patterns produced by gene disruptions and overexpressions. Genome Inform Work Genome Inform 9:151–160

    Google Scholar 

  • Fauré A et al (2006) Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14):e124

    Article  Google Scholar 

  • Fornasini E, Valcher ME (2013) Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Autom Control 58(6):1390–1401

    Article  MathSciNet  Google Scholar 

  • Ishii H, Tempo R, Bai EW (2012) A web aggregation approach for distributed randomized pagerank algorithms. IEEE Trans Autom Control 57(11):2703–2717

    Article  MathSciNet  Google Scholar 

  • Klamt S et al (2006) A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinform 7(56):1–26

    Google Scholar 

  • Laschov D, Margaliot M (2013) Minimum-time control of Boolean networks. SIAM J Control Optim 51(4):2869–2892

    Article  MathSciNet  Google Scholar 

  • Laschov D, Margaliot M, Even G (2013) Observability of Boolean networks: a graphtheoretic approach. Automatica 49(8):2351–2362

    Article  MathSciNet  Google Scholar 

  • Li R, Yang M, Chu T (2015) Controllability and observability of Boolean networks arising from biology. Chaos: Interdiscip J Nonlinear Sci 25(2):023104–15

    Article  MathSciNet  Google Scholar 

  • Liu Y-Y, Slotine J-J, Barabási A-L (2013) Observability of complex systems. Proc Natl Acad Sci 110(7):2460–2465

    Article  MathSciNet  Google Scholar 

  • Louati A, Aufaure MA, Lechevallier Y (2013) Graph aggregation: application to social networks. In: Guan R et al (eds) Advances in theory and applications of high dimensional and symbolic data analysis, vol RNTI-E-25, Hermann, pp 157–177

    Google Scholar 

  • Veliz-Cuba A et al (2014) Steady state analysis of Boolean molecular network models via model reduction and computational algebra. BMC Bioinform 15(1):221

    Google Scholar 

  • Zhang K, Johansson KH (2018) Efficient observability verification for large-scale Boolean control networks. In: 2018 37th Chinese control conference (CCC), pp 560–567

    Google Scholar 

  • Zhang K, Zhang L, Xie L (2015) Invertibility and nonsingularity of Boolean control networks. Automatica 60:155–164

    Article  MathSciNet  Google Scholar 

  • Zhang R et al (2008) Network model of survival signaling in large granular lymphocyte leukemia. Proc Natl Acad Sci USA 105:16308–13

    Article  Google Scholar 

  • Zhao Q (2005) A remark on scalar equations for synchronous boolean networks with biological applications by CF arrow, J Heidel, J Maloney, J Rogers. IEEE Trans Neural Netw 16(6):1715–1716

    Google Scholar 

  • Zhao Y, Ghosh BK, Cheng D (2016) Control of large-scale Boolean networks via network aggregation. IEEE Trans Neural Netw Learn Syst 27(7):1527–1536

    Article  MathSciNet  Google Scholar 

  • Zhao Y, Kim J, Filippone M (2013) Aggregation algorithm towards large-scale Boolean network analysis. IEEE Trans Autom Control 58(8):1976–1985

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm, Sweden

    Kuize Zhang

  2. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, China

    Lijun Zhang

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Lihua Xie

Authors
  1. Kuize Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lijun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lihua Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kuize Zhang .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zhang, K., Zhang, L., Xie, L. (2020). Observability and Detectability of Large-Scale Boolean Control Networks. In: Discrete-Time and Discrete-Space Dynamical Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-25972-3_6

Download citation

Publish with us

Policies and ethics

Search

Navigation