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Analysis and Control of Boolean Networks: A Semi-tensor Product Approach [Kõva köide]

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  • Formaat: Hardback, 472 pages, kõrgus x laius: 235x155 mm, kaal: 1890 g, XVI, 472 p., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 02-Dec-2010
  • Kirjastus: Springer London Ltd
  • ISBN-10: 0857290967
  • ISBN-13: 9780857290960
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Analysis and Control of Boolean Networks: A Semi-tensor Product ApproachSuurem pilt
  • Formaat: Hardback, 472 pages, kõrgus x laius: 235x155 mm, kaal: 1890 g, XVI, 472 p., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 02-Dec-2010
  • Kirjastus: Springer London Ltd
  • ISBN-10: 0857290967
  • ISBN-13: 9780857290960
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780857290960.html
Märksõnad:
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.

This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.

Arvustused

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 Prepeli, Zentralblatt MATH, Vol. 1209, 2011)

1 Propositional Logic 1(18)
1.1 Statements
1(4)
1.2 Implication and Equivalence
5(3)
1.3 Adequate Sets of Connectives
8(3)
1.4 Normal Form
11(3)
1.5 Multivalued Logic
14(4)
References
18(1)
2 Semi-tensor Product of Matrices 19(36)
2.1 Multiple-Dimensional Data
19(10)
2.2 Semi-tensor Product of Matrices
29(8)
2.3 Swap Matrix
37(4)
2.4 Properties of the Semi-tensor Product
41(8)
2.5 General Semi-tensor Product
49(4)
References
53(2)
3 Matrix Expression of Logic 55(12)
3.1 Structure Matrix of a Logical Operator
55(4)
3.2 Structure Matrix for k-valued Logic
59(4)
3.3 Logical Matrices
63(2)
References
65(2)
4 Logical Equations 67(36)
4.1 Solution of a Logical Equation
67(1)
4.2 Equivalent Algebraic Equations
68(10)
4.3 Logical Inference
78(6)
4.4 Substitution
84(1)
4.5 k-valued Logical Equations
85(4)
4.6 Failure Location: An Application
89(11)
4.6.1 Matrix Expression of Route Logic
89(3)
4.6.2 Failure Location
92(5)
4.6.3 Cascading Inference
97(3)
References
100(3)
5 Topological Structure of a Boolean Network 103(38)
5.1 Introduction to Boolean Networks
103(1)
5.2 Dynamics of Boolean Networks
104(4)
5.3 Fixed Points and Cycles
108(11)
5.4 Some Classical Examples
119(5)
5.5 Serial Boolean Networks
124(2)
5.6 Higher Order Boolean Networks
126(13)
5.6.1 First Algebraic Form of Higher Order Boolean Networks
128(9)
5.6.2 Second Algebraic Form of Higher Order Boolean Networks
137(2)
References
139(2)
6 Input-State Approach to Boolean Control Networks 141(22)
6.1 Boolean Control Networks
141(2)
6.2 Semi-tensor Product Vector Space vs Semi-tensor Product Space
143(3)
6.3 Cycles in Input-State Space
146(5)
6.4 Cascaded Boolean Networks
151(3)
6.5 Two Illustrative Examples
154(7)
References
161(2)
7 Model Construction via Observed Data 163(26)
7.1 Reconstructing Networks
163(8)
7.2 Model Construction for General Networks
171(5)
7.3 Construction with Known Network Graph
176(1)
7.4 Least In-degree Model
177(4)
7.5 Construction of Uniform Boolean Network
181(3)
7.6 Modeling via Data with Errors
184(3)
References
187(2)
8 State Space and Subspaces 189(24)
8.1 State Spaces of Boolean Networks
189(2)
8.2 Coordinate Transformation
191(5)
8.3 Regular Subspaces
196(8)
8.4 Invariant Subspaces
204(3)
8.5 Indistinct Rolling Gear Structure
207(5)
References
212(1)
9 Controllability and Observability of Boolean Control Networks 213(20)
9.1 Control via Input Boolean Network
213(7)
9.2 Subnetworks
220(2)
9.3 Controllability via Free Boolean Sequence
222(5)
9.4 Observability
227(4)
References
231(2)
10 Realization of Boolean Control Networks 233(16)
10.1 What Is a Realization?
233(2)
10.2 Controllable Normal Form
235(4)
10.3 Observable Normal Form
239(3)
10.4 Kalman Decomposition
242(4)
10.5 Realization
246(2)
References
248(1)
11 Stability and Stabilization 249(26)
11.1 Boolean Matrices
249(4)
11.2 Global Stability
253(8)
11.3 Stabilization of Boolean Control Networks
261(12)
References
273(2)
12 Disturbance Decoupling 275(22)
12.1 Problem Formulation
275(1)
12.2 Y-friendly Subspace
276(7)
12.3 Control Design
283(6)
12.4 Canalizing Boolean Mapping
289(3)
12.5 Solving DDPs via Constant Controls
292(3)
References
295(2)
13 Feedback Decomposition of Boolean Control Networks 297(16)
13.1 Decomposition of Control Systems
297(1)
13.2 The Cascading State-space Decomposition Problem
298(5)
13.3 Comparable Regular Subspaces
303(2)
13.4 The Parallel State-space Decomposition Problem
305(3)
13.5 Input–Output Decomposition
308(3)
References
311(2)
14 k-valued Networks 313(34)
14.1 A Review of k-valued Logic
313(3)
14.2 Dynamics of k-valued Networks
316(4)
14.3 State Space and Coordinate Transformations
320(4)
14.4 Cycles and Transient Period
324(1)
14.5 Network Reconstruction
325(5)
14.6 k-valued Control Networks
330(10)
14.7 Mix-valued Logic
340(5)
References
345(2)
15 Optimal Control 347(24)
15.1 Input-State Transfer Graphs
347(4)
15.2 Topological Structure of Logical Control Networks
351(5)
15.3 Optimal Control of Logical Control Networks
356(5)
15.4 Optimal Control of Higher-Order Logical Control Networks
361(8)
References
369(2)
16 Input-State Incidence Matrices 371(18)
16.1 The Input-State Incidence Matrix
371(3)
16.2 Controllability
374(4)
16.3 Trajectory Tracking and Control Design
378(1)
16.4 Observability
379(3)
16.5 Fixed Points and Cycles
382(1)
16.6 Mix-valued Logical Systems
383(5)
References
388(1)
17 Identification of Boolean Control Networks 389(20)
17.1 What Is Identification9
389(1)
17.2 Identification via Input-State Data
390(3)
17.3 Identification via Input–Output Data
393(3)
17.4 Numerical Solutions
396(8)
17.4.1 General Algorithm
396(4)
17.4.2 Numerical Solution Based on Network Graph
400(3)
17.4.3 Identification of Higher-Order Systems
403(1)
17.5 Approximate Identification
404(3)
References
407(2)
18 Applications to Game Theory 409(22)
18.1 Strategies with Finite Memory
409(3)
18.2 Cycle Strategy
412(3)
18.3 Compounded Games
415(2)
18.4 Sub-Nash Solution for Zero-Memory Strategies
417(2)
18.5 Nash Equilibrium for A-Memory Strategies
419(2)
18.6 Common Nash (Sub-Nash) Solutions for A-Memory Strategies
421(8)
References
429(2)
19 Random Boolean Networks 431(20)
19.1 Markov Chains
431(8)
19.2 Vector Form of Random Boolean Variables
439(3)
19.3 Matrix Expression of a Random Boolean Network
442(5)
19.4 Some Topological Properties
447(3)
References
450(1)
Appendix A Numerical Algorithms 451(12)
A.1 Computation of Logical Matrices
451(2)
A.2 Basic Functions
453(5)
A.3 Some Examples
458(5)
Appendix B Proofs of Some Theorems Concerning the Semi-tensor Product 463(3)
References 466(1)
Index 467
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.