内容简介：

　　布尔网络已成为描述和模拟细胞网络（其元素只有开关行为）的强大工具。本书提供了系统地分析和控制布尔网络的全新方法，基本工具是称为矩阵半张量积的这一新的矩阵乘法。使用矩阵半张量积可将逻辑函数表示成传统的离散时间线性系统，从而可以通过一组公式轻松揭示布尔网络拓扑结构的一些基本特性，如不动点、极限环、暂态期和吸引域等。这一理论框架使得动态控制系统的状态空间方法可应用于布尔网络的控制。布尔控制网络的双线性系统表示使得研究其能控、能观、镇定、干扰解耦、辨识、最优控制等基本控制问题成为可能。

　　本书自成体系，读者只需线性代数和线性控制系统的基本知识。本书开始于对命题逻辑和矩阵半张量积的简要介绍。然后用布尔（控制）网络的（双）线性表示研究其干扰解耦和分解等问题。最后，考虑到多值逻辑能够更准确地描述实际的网络，本书也对其做了介绍并引入随机布尔网络等。附录是相关的数值计算，相关的MATLAB®工具箱可从http://lsc.amss.ac.cn/~dcheng/下载。

　　本书可为从事系统生物学、控制、系统科学和物理相关领域的研究人员提供基本参考，也可成为研究生课程的教材。计算机科学家和逻辑学家或许也能从本书中找到感兴趣的内容。

 

英文目录：

1   Propositional Logic
　　1.1 Statements
　　1.2 Implication and Equivalence
　　1.3 Adequate Sets of Connectives
　　1.4 Normal Form
　　1.5 Multi-valued Logic
　　References
2   Semi-tensor Product of Matrices
　　2.1 Multiple-Dimensional Data
　　2.2 Semi-tensor Product of Matrices
　　2.3 Swap Matrix
　　2.4 Properties of the Semi-tensor Product
　　2.5 General Semi-tensor Product
　　References
3   Matrix Expression of Logic
　　3.1 Structure Matrix of a Logical Operator
　　3.2 Structure Matrix for k-valued Logic
　　3.3 Logical Matrices
　　References
4   Logical Equations
　　4.1 Solution of a Logical Equation
　　4.2 Equivalent Algebraic Equations
　　4.3 Logical Inference
　　4.4 Substitution
　　4.5 k-valued Logical Equations
　　4.6 Failure Location: An Application
　　　　4.6.1 Matrix Expression of Route Logic
　　　　4.6.2 Failure Location
　　　　4.6.3 Cascading Inference
　　References
5   Topological Structure of a Boolean Network
　　5.1 Introduction to Boolean Networks
　　5.2 Dynamics of Boolean Networks
　　5.3 Fixed Points and Cycles
　　5.4 Some Classical Examples
　　5.5 Serial Boolean Networks
　　5.6 Higher Order Boolean Networks
　　　　5.6.1 First Algebraic Form of Higher Order Boolean Networks
　　　　5.6.2 Second Algebraic Form of Higher Order Boolean Networks
　　References
6   Input-State Approach to Boolean Control Networks
　　6.1 Boolean Control Networks
　　6.2 Semi-tensor Product Vector Space vs. Semi-tensor Product Space
　　6.3 Cycles in Input-State Space
　　6.4 Cascaded Boolean Networks
　　6.5 Two Illustrative Examples
　　References
7   Model Construction via Observed Data
　　7.1 Reconstructing Networks
　　7.2 Model Construction for General Networks
　　7.3 Construction with Known Network Graph
　　7.4 Least In-degree Model
　　7.5 Construction of Uniform Boolean Network
　　7.6 Modeling via Data with Errors
　　References
8   State Space and Subspaces
　　8.1 State Spaces of Boolean Networks
　　8.2 Coordinate Transformation
　　8.3 Regular Subspaces
　　8.4 Invariant Subspaces
　　8.5 Indistinct Rolling Gear Structure
　　References
9   Controllability and Observability of Boolean Control Networks
　　9.1 Control via Input Boolean Network
　　9.2 Subnetworks
　　9.3 Controllability via Free Boolean Sequence
　　9.4 Observability
　　References
10   Realization of Boolean Control Networks
　　10.1 What Is a Realization?
　　10.2 Controllable Normal Form
　　10.3 Observable Normal Form
　　10.4 Kalman Decomposition
　　10.5 Realization
　　References
11   Stability and Stabilization
　　11.1 Boolean Matrices
　　11.2 Global Stability
　　11.3 Stabilization of Boolean Control Networks
　　References
12   Disturbance Decoupling
　　12.1 Problem Formulation
　　12.2 Y -friendly Subspace
　　12.3 Control Design
　　12.4 Canalizing Boolean Mapping
　　12.5 Solving DDPs via Constant Controls
　　References
13   Feedback Decomposition of Boolean Control Networks
　　13.1 Decomposition of Control Systems
　　13.2 The Cascading State-space Decomposition Problem
　　13.3 Comparable Regular Subspaces
　　13.4 The Parallel State-space Decomposition Problem
　　13.5 Input–Output Decomposition
　　References
14   k-valued Networks
　　14.1 A Review of k-valued Logic
　　14.2 Dynamics of k-valued Networks
　　14.3 State Space and Coordinate Transformations
　　14.4 Cycles and Transient Period
　　14.5 Network Reconstruction
　　14.6 k-valued Control Networks
　　14.7 Mix-valued Logic
　　References
15   Optimal Control
　　15.1 Input-State Transfer Graphs
　　15.2 Topological Structure of Logical Control Networks
　　15.3 Optimal Control of Logical Control Networks
　　15.4 Optimal Control of Higher-Order Logical Control Networks
　　References
16   Input-State Incidence Matrices
　　16.1 The Input-State Incidence Matrix
　　16.2 Controllability
　　16.3 Trajectory Tracking and Control Design
　　16.4 Observability
　　16.5 Fixed Points and Cycles
　　16.6 Mix-valued Logical Systems
　　References
17   Identification of Boolean Control Networks
　　17.1 What Is Identification?
　　17.2 Identification via Input-State Data
　　17.3 Identification via Input–Output Data
　　17.4 Numerical Solutions
　　　　17.4.1 General Algorithm
　　　　17.4.2 Numerical Solution Based on Network Graph
　　　　17.4.3 Identification of Higher-Order Systems
　　17.5 Approximate Identification
　　References
18   Applications to Game Theory
　　18.1 Strategies with Finite Memory
　　18.2 Cycle Strategy
　　18.3 Compounded Games
　　18.4 Sub-Nash Solution for Zero-Memory Strategies
　　18.5 Nash Equilibrium for μ-Memory Strategies
　　18.6 Common Nash (Sub-Nash) Solutions for μ-Memory Strategies
　　References
19   Random Boolean Networks
　　19.1 Markov Chains
　　19.2 Vector Form of Random Boolean Variables
　　19.3 Matrix Expression of a Random Boolean Network
　　19.4 Some Topological Properties
　　References
Appendix A   Numerical Algorithms
　　A.1 Computation of Logical Matrices
　　A.2 Basic Functions
　　A.3 Some Examples
Appendix B Proofs of Some Theorems Concerning the Semi-tensor Product