ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

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

:	Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
:	Analysis and Control of Boolean Networks A Semi-tensor Product Approach
:	Springer-Verlag
:	9780857290977
:	1
:	CHF 85.50
:

:	Sonstiges
:	English

:	472
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

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.

	Preface	6
	References	10
	Contents	11
	Notation	15
	Propositional Logic	17
	Statements	17
	Implication and Equivalence	21
	Adequate Sets of Connectives	24
	Normal Form	27
	Multivalued Logic	30
	References	34
	Semi-tensor Product of Matrices	35
	Multiple-Dimensional Data	35
	Semi-tensor Product of Matrices	45
	Swap Matrix	53
	Properties of the Semi-tensor Product	57
	General Semi-tensor Product	65
	References	69
	Matrix Expression of Logic	70
	Structure Matrix of a Logical Operator	70
	Structure Matrix for k-valued Logic	74
	Logical Matrices	78
	References	80
	Logical Equations	81
	Solution of a Logical Equation	81
	Equivalent Algebraic Equations	82
	Logical Inference	92
	Substitution	98
	k-valued Logical Equations	99
	Failure Location: An Application	103
	Matrix Expression of Route Logic	103
	Failure Location	106
	Cascading Inference	111
	References	114
	Topological Structure of a Boolean Network	116
	Introduction to Boolean Networks	116
	Dynamics of Boolean Networks	117
	Fixed Points and Cycles	121
	Some Classical Examples	132
	Serial Boolean Networks	137
	Higher Order Boolean Networks	139
	First Algebraic Form of Higher Order Boolean Networks	141
	Second Algebraic Form of Higher Order Boolean Networks	150
	References	152
	Input-State Approach to Boolean Control Networks	154
	Boolean Control Networks	154
	Semi-tensor Product Vector Space vs. Semi-tensor Product Space	156
	Cycles in Input-State Space	159
	Cascaded Boolean Networks	164
	Two Illustrative Examples	167
	References	174
	Model Construction via Observed Data	175
	Reconstructing Networks	175
	Model Construction for General Networks	183
	Construction with Known Network Graph	188
	Least In-degree Model	189
	Construction of Uniform Boolean Network	193
	Modeling via Data with Errors	196
	References	199
	State Space and Subspaces	200
	State Spaces of Boolean Networks	200
	Coordinate Transformation	202
	Regular Subspaces	207
	Invariant Subspaces	215
	Indistinct Rolling Gear Structure	218
	References	223
	Controllability and Observability of Boolean Control Networks	224
	Control via Input Boolean Network	224
	Subnetworks	231
	Controllability via Free Boolean Sequence	233
	Observability	238
	References	242
	Realization of Boolean Control Networks	243
	What Is a Realization?	243
	Controllable Normal Form	245
	Observable Normal Form	249
	Kalman Decomposition	252
	Realization	256
	References	258
	Stability and Stabilization	259
	Boolean Matrices	259
	Global Stability	263
	Stabilization of Boolean Control Networks	271
	References	283
	Disturbance Decoupling	284
	Problem Formulation	284
	Y-friendly Subspace	285
	Control Design	292
	Canalizing Boolean Mapping	298