本书主要介绍逻辑动态系统在应用方面的最新研究进展，特别关注在下列领域的应用研究：有限自动机、图论、运筹学与控制论以及布尔网络等。在有限自动机领域，本书讨论了自动机的动态建模问题、可达性问题及可控性问题。在图论领域，本书重点介绍了利用逻辑系统的方法去研究图的结构分析问题，以及图的结构分解在运筹学中的应用，例如多轨道任务分配问题的可解性条件等。在布尔网络方面，本书着重分析了布尔网络预测集的辨识问题以及代数化简等问题。本书适合控制科学与工程、工业自动化、系统科学、控制理论、数学、人工智能等专业的师生及科研人员阅读参考，也可作为相关学科高年级本科生及研究生的教学参考用书。
Preface
Chapter 1 Preliminaries
1．1 Semi-tensor Product of Matrices
1．2 Matrix Expression of Logical Functions
1．3 Summary of Finite State Machines
Chapter 2 Reachability of Finite Automata and Its Application
2．1 Introduction
2．2 Dynamic Equations of Finite Automata
2．3 Reachability Analysis of Finite Automata
2．4 Language Recognition of Finite Automata
2．5 Illustrative Examples
2．6 Conclusion
Chapter 3 Controllability and Stabilization of Finite Automata
3．1 Introduction
3．2 Controllability of Finite Automata
3．3 Stabilization of Finite Automata
3．4 Illustrative Examples
3．5 Conclusion
Chapter 4 Verification Analysis of Self-verifying Automata
4．1 Introduction
4．2 Bilinear State Transition Equations of Self-verifying Finite Automaton
4．3 Self-verifying Algorithms for Finite Automaton
4．4 Illustrative Examples
4．5 Conclusion
Chapter 5 Modelling and Control of Combined Finite Automata
5．1 Introduction
5．2 Composition of Finite Automata
5．3 Algebraic Construction of Combined Finite Automata
5．4 State and Output Control of Combined Finite Automata
5．5 Illustrative Examples
5．6 Conclusion
Chapter 6 Reachability Analysis of Discrete Event Dynamic Systems
6．1 Introduction
6．2 Mathematical Formulation of Logical Dynamics for Controlled Finite Automata
6．3 Algebraic Reachability Condition of Controlled Finite Automata
6．4 Algebraic Algorithm for Reachability of Controlled Finite Automata
6．5 Illustrative Examples
6．6 Conclusion
Chapter 7 Algebraic Method of Finding k-Degree and k-Balance Control Sets of Graphs
7．1 Introduction
7．2 Problem Statement
7．3 Algebraic Algorithm of Searching Control Sets of Graphs
7．4 Algebraic Algorithm of Searching k-Degree and k-Balance Control Sets of Graphs
7．5 Testing Examples
7．6 Conclusion
Chapter 8 Graph Approach to Solve k-Track Assignment Problem
8．1 Introduction
8．2 Searching k-internally Stable Sets of Graphs
8．3 Searching k-Absolute Maximum Internally Stable Sets of Graphs
8．4 Solvability of k-Track Assignment Problem
8．5 Illustrative Example
8．6 Conclusion
Chapter 9 Predictor Identification of Boolean Networks
9．1 Introduction
9．2 Judgment Criterion of Data-permitted Predictors
9．3 Logical Equations of Predictors
9．4 Solutions of Logical Equations
9．5 Identification of Predictors
9．6 Further Discussion on Predictors from Observed Data
9．7 Conclusion
Chapter 10 Algebraic Simplification of Boolean Networks
10．1 Introduction
10．2 Problem Description
10．3 Preserved Properties of Simplified Boolean Networks
10．4 Algebraic Algorithm of Finding Steady States and Cycles of Simplified Boolean Networks
10．5 Comparison with Other Methods
10．6 Testing Example
10．7 Conclusion
书单推荐
