Analysis and Control of Boolean Networks: A Semi-tensor Product Approach

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Springer Science & Business Media, Nov 23, 2010 - Science - 472 pages
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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.
 

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Contents

Propositional Logic
1
Semitensor Product of Matrices
19
Matrix Expression of Logic
54
Logical Equations
67
Topological Structure of a Boolean Network
102
InputState Approach to Boolean Control Networks
141
Model Construction via Observed Data
163
State Space and Subspaces
188
Feedback Decomposition of Boolean Control Networks
297
kvalued Networks
313
Optimal Control
346
InputState Incidence Matrices
371
Identification of Boolean Control Networks
389
Applications to Game Theory
408
Random Boolean Networks
431
Appendix A Numerical Algorithms
451

Controllability and Observability of Boolean Control Networks
213
Realization of Boolean Control Networks
233
Stability and Stabilization
249
Disturbance Decoupling
274
Appendix B Proofs of Some Theorems Concerning the Semitensor Product
463
Index
467
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About the author (2010)

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.