Analysis and Control of Boolean Networks

A Semi-tensor Product Approach

  • Daizhan Cheng
  • Hongsheng Qi
  • Zhiqiang Li
Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 1-18
  3. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 19-53
  4. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 55-65
  5. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 67-101
  6. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 103-140
  7. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 141-161
  8. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 163-187
  9. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 189-212
  10. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 213-231
  11. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 233-248
  12. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 249-273
  13. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 275-296
  14. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 297-311
  15. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 313-345
  16. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 347-369
  17. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 371-388
  18. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 389-407
  19. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 409-429
  20. Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
    Pages 431-450

About this book

Introduction

The Boolean network has become a powerful tool for describing and simulating cellular networks in which the elements behave in an on–off fashion. Analysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology – fixed points, cycles, transient times and basins of attractors – can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling, identification, optimal control, etc.

The book is self-contained, requiring only knowledge of linear algebra and the basics of the control theory of linear systems. It begins with a short introduction to prepositional logic and the concepts and properties of the STP and progressing via the (bi)linear expression of Boolean (control) networks to disturbance decoupling and decomposition of Boolean control systems. Finally multi-valued logic is considered as a more precise way of describing real networks and stochastic Boolean networks are touched upon. Relevant numerical calculations are explained in an appendix and a MATLAB® toolbox for the algorithms in the book can be downloaded from http://lsc.amss.ac.cn/~dcheng/.

Analysis and Control of Boolean Networks will be a fundamental reference for researchers in systems biology, control, systems science and physics. The book was developed for a short course for graduate students and is suitable for that purpose. Computer scientists and logicians may also find this book to be of interest.

Keywords

Boolean network Control Logic Semi-tensor product of matricies Topological structure

Authors and affiliations

  • Daizhan Cheng
    • 1
  • Hongsheng Qi
    • 2
  • Zhiqiang Li
    • 3
  1. 1.Academy of Mathematics & Systems Science, Institute of Systems ScienceChinese Academy of SciencesBeijingChina, People's Republic
  2. 2., Institute of Systems, AMSSChinese Academy of SciencesBeijingChina, People's Republic
  3. 3., Institute of Systems, AMSSChinese Academy of SciencesBeijingChina, People's Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-097-7
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-0-85729-096-0
  • Online ISBN 978-0-85729-097-7
  • Series Print ISSN 0178-5354