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

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.

Propositional Logic.- Semi-tensor Product of Matrices.- Matrix Expression of Logic.- Logical Equation.- Topological Structure of Boolean Networks.- Input-state Approach of Boolean Control Networks.- Controllability and Observability of BCN.- Realization of BCN.- Stability and Stabilization.- Disturbance Decoupling.- k-valued Network.- Input–Output Decomposition.- Random Boolean Network.- Appendix: Numerical Algorithms.

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.