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E-raamat: Analysis and Control of Finite-Valued Systems

(Shandong Normal University), (Shandong Normal University), (Shandong Normal University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-May-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351368308
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Analysis and Control of Finite-Valued SystemsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 11-May-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351368308
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A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems. These results occupy the highest position in the analysis and control of this field. It not only covers all aspects of research in finite-value systems, but also presents the mathematical derivation for each conclusion in depth. The book contains examples to provide a better understanding of the practical applications of finite-value systems.

It will serve as a textbook for graduate students of Cybernetics, Mathematical, and Biology, and a reference for readers interested in the theory of finite-value systems.

Arvustused

This book can be viewed as an important and timely update of nite value system analysis and control using semi-tensor products (STPs) after the inuential work by D. Cheng, H. S. Qi and Z. Li [ Analysis and control of Boolean networks, Comm. Control Engrg. Ser., Springer, London, 2011; MR2761796]. It focuses on the work published after 2011 by the authors (from Yuzhen Wangs group) with numerical examples taken from various elds such as biology, physics, and mathematics.

The book is self-contained and well organized. New topics in this book which expand the list of problems that can be cast into the framework of STPs include delayed and switched logical networks, nonlinear feedback shift registers, graph problems, and nite eld networks. One limitation of the book is that no computational complexity analysis is given and all examples are in relatively small scale.

- Qianchuan Zhao - Mathematical Reviews Clippings - June 2019

Dedication v
Preface vii
List of Figures
xiii
List of Tables
xv
PART I THEORY
1 Introduction and Preliminaries
3(8)
1.1 Finite-Value Networks
3(2)
1.2 Notations
5(1)
1.3 Semi-Tensor Product of Matrices
6(5)
2 Boolean Networks
11(30)
2.1 Introduction to Boolean Networks
11(1)
2.2 Topological Structure of Boolean Networks
12(3)
2.3 Lyapunov-Based Stability Analysis
15(7)
2.4 Function Perturbation of Boolean Networks
22(4)
2.5 Feedback Stabilization of Boolean Control Networks
26(5)
2.6 Output Tracking of Boolean Control Networks
31(10)
2.6.1 Constant Reference Signal
31(2)
2.6.2 Time-Varying Reference Signal
33(8)
3 Mix-Valued Logical Networks
41(24)
3.1 Introduction to Mix-Valued Logical Networks
41(1)
3.2 Topological Structure of Mix-Valued Logical Networks
42(3)
3.3 Disturbance Decoupling of Mix-Valued Logical Control Networks
45(11)
3.3.1 Problem Formulation
46(1)
3.3.2 Y-Friendly Subspace
46(4)
3.3.3 Control Design
50(3)
3.3.4 An Illustrative Example
53(3)
3.4 General Expression of Pseudo Logical Function
56(9)
3.4.1 General Expression of Pseudo Logical Function
57(2)
3.4.2 General Expression of Pseudo Mix-Valued Logical Function
59(3)
3.4.3 An Illustrative Example
62(3)
4 Delayed Logical Networks
65(24)
4.1 Introduction to Delayed Logical Networks
65(1)
4.2 Topological Structure of Delayed Logical Networks
66(6)
4.3 Trajectory Controllability of Delayed Logical Control Networks
72(10)
4.4 Control Design for Output Tracking of Delayed Boolean Control Networks
82(7)
5 Switched Logical Networks
89(40)
5.1 Introduction to Switched Logical Networks
89(1)
5.2 Stability Analysis Via Switching-Point Reachability
90(8)
5.3 Controllability Analysis and Control Design with State and Input Constraints
98(21)
5.4 Disturbance Decoupling Controller Design
119(10)
6 Probabilistic Logical Networks
129(36)
6.1 Introduction to Probabilistic Logical Networks
129(2)
6.2 Controllability of Context-Sensitive Probabilistic Logical Control Networks
131(9)
6.2.1 An Algebraic Form for Context-sensitive Probabilistic MLCNs
131(2)
6.2.2 An Algebraic Form of Probabilistic MLCNs with Constraints
133(1)
6.2.3 Controllability of Probabilistic MLCNs with Constraints
134(6)
6.3 Optimal Control for Probabilistic Logical Control Networks
140(8)
6.3.1 Optimal Finite-Horizon Control of the Probabilistic Mix-Valued Logical Networks
140(3)
6.3.2 First-passage Model Based Optimal Control
143(5)
6.4 Output Tracking Control of Probabilistic Logical Control Networks
148(17)
PART II APPLICATIONS
7 Networked Evolutionary Games
165(30)
7.1 Introduction to Networked Evolutionary Games
165(4)
7.2 Algebraic Formulation of Networked Evolutionary Games
169(7)
7.3 Convergence Analysis of Networked Evolutionary Games
176(8)
7.4 Optimization of Networked Evolutionary Games
184(11)
8 Nonlinear Feedback Shift Registers
195(20)
8.1 Introduction to Shift Registers
195(1)
8.2 Analysis of Feedback Shift Registers Via Boolean Networks
196(6)
8.2.1 Construction of the Shortest NFSR for a given Nonperiodic Sequence
196(2)
8.2.2 Construction of the Shortest NFSR for a given Periodic Sequence
198(1)
8.2.3 Construction of Full-length n-NFSR
199(1)
8.2.4 Construction of More Full-Length n-NFSRs
200(2)
8.3 Analysis of Feedback Shift Registers Via Multi-Valued Logical Networks
202(13)
8.3.1 Nonsingularity of FSRs
202(5)
8.3.2 Number of Cycles for a Feedback Shift Register
207(1)
8.3.3 Cycle Decomposition and Synthesis for FSRs
208(4)
8.3.4 An Illustrative Example
212(3)
9 Graph Theory
215(44)
9.1 Introduction to Graph Theory
215(1)
9.2 Graph Maximum Stable Set and Coloring Problems
216(19)
9.3 Robust Graph Coloring Problem
235(14)
9.4 T-Coloring and List Coloring Problems
249(10)
9.4.1 T-Coloring Problem
249(4)
9.4.2 List Coloring Problem
253(6)
10 Finite-Field Networks
259(16)
10.1 Introduction to Finite-Field Networks
259(1)
10.2 Consensus of Finite-Field Networks with Switching Topologies and Linear Protocols
260(5)
10.3 Leader-Follower Consensus of Multi-Agent Systems over Finite Fields
265(10)
Index 275
Haitao Li received his Ph.D. degree from Shandong University, China in 2014. From January 2014 to January 2015, he worked as a Research Fellow at School of EEE Nanyang Technological University, Singapore. Currently, he has been an associate professor at School of Mathematics and Statistics, Shandon Normal University. He received the "Natural Science Fund for Distinguished Young Scholars of Shandong Province" in 2016. He has served as a Guest Editor for IET Control Theory & Applications since 2016.

Zhaoguo Dong, Ph.D. candidate at School of Control Science and Engineering, Shandong University. He received his master's degree from Qufu Normal University in 2013.

Peilian Guo received her Ph.D. degree from Shandon University, Chimna in 2016. She has been a lecturer at School of Information Science and Engineering, Shandong Normal University.

Zhenbin Liu received his Ph.D degree from Shandon University. He received the "National Natural Science Fund of China" in 2016. Currently, he has been as associate professor at Science and Information College, Qindao Agricultural University.
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