Analysis and Control of Boolean Networks

1. Front Matter

   Pages I-XVI

   PDF

2. Propositional Logic

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 1-18

3. Semi-tensor Product of Matrices

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 19-53

4. Matrix Expression of Logic

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 55-65

5. Logical Equations

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 67-101

6. Topological Structure of a Boolean Network

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 103-140

7. Input-State Approach to Boolean Control Networks

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 141-161

8. Model Construction via Observed Data

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 163-187

9. State Space and Subspaces

   • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

   Pages 189-212

10. Controllability and Observability of Boolean Control Networks

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 213-231

11. Realization of Boolean Control Networks

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 233-248

12. Stability and Stabilization

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 249-273

13. Disturbance Decoupling

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 275-296

14. Feedback Decomposition of Boolean Control Networks

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 297-311

15. k-valued Networks

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 313-345

16. Optimal Control

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 347-369

17. Input-State Incidence Matrices

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 371-388

18. Identification of Boolean Control Networks

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 389-407

19. Applications to Game Theory

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 409-429

20. Random Boolean Networks

    • Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

    Pages 431-450

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 etc.

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

From the reviews:

“The aim of the book is to provide a new framework for the study of Boolean control networks. … The book is self-contained and contains many examples which illustrate the concepts and the proposed techniques. … the book represents a fundamental reference for researchers in systems biology, systems science and physics.” (Valeriu Prepeliţă, Zentralblatt MATH, Vol. 1209, 2011)

• Academy of Mathematics & Systems Science, Institute of Systems Science, Chinese Academy of Sciences, Beijing, China, People's Republic

  Daizhan Cheng

• , Institute of Systems, AMSS, Chinese Academy of Sciences, Beijing, China, People's Republic

  Hongsheng Qi, Zhiqiang Li

Daizhan Cheng received the Ph.D. degree in systems science from Washington University, St. Louis, in 1985. Currently, he is a Professor with the Institute of Systems Science, Chinese Academy of Sciences, Beijing, China. His research interests include nonlinear systems, numerical method, complex systems, etc. Dr. Cheng is Chairman of the Technical Committee on Control Theory (since 2003), Chinese Association of Automation, a Fellow of the IEEE, and a Fellow of the International Federation of Automatic Control. Hongsheng Qi received the Ph.D. degree in systems theory from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2008. He is currently a post-doctoral fellow at the Key Laboratory of Systems and Control, Chinese Academy of Sciences. His research interests include nonlinear systems control, complex systems, etc. Zhiqiang Li received the M.S. degree from Zhengzhou University in 2007. He is currently a Ph.D. student in the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interests include nonlinear systems control, complex systems, etc.

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