This book mainly focuses on the sampled-data control of logical networks. We believe that the methods (semi-tensor product of matrices), results (recent results on Boolean control networks under periodic sampled-data control, Boolean control networks under aperiodic sampled-data control, and logical control networks under event-triggered control) and topics (logical networks) in this book have become of particular interest to readers recently. Firstly, logical networks are of interest due to their rich range of applications in biology, game theory, coding, finite automata, graph theory, and other fields. Secondly, semi-tensor product of matrices offers a useful tool for formulating, analyzing and designing controllers for logical networks. Moreover, this book is the first to introduce sampled-data control into the study of logical control networks. All research results in this book are novel and worthy of further study.
The book’s content is divided into three parts (Boolean control networks under periodic sampled-data control, Boolean control networks under aperiodic sampled-data control, and logical control networks under event-triggered control), which essentially progress from easier to more difficult. In addition, corresponding examples and diagrams are included in each section to facilitate understanding.
Author(s): Yang Liu, Jianquan Lu, Liangjie Sun
Publisher: Springer
Year: 2023
Language: English
Pages: 227
City: Singapore
Foreword
Preface
Acknowledgments
Contents
Acronyms
Part I Introduction
1 Introduction
1.1 Background
1.2 Research Problems
1.2.1 Periodic Sampled-Data Control
1.2.2 Aperiodic Sampled-Data Control
1.2.3 Event-Triggered Control
1.3 Mathematical Preliminaries
1.3.1 Matrix Products
1.3.2 Swap Matrix
1.3.3 Semi-Tensor Product of Matrices
1.3.4 Boolean Matrix
1.3.5 Structure Matrix of a Logical Operator
References
Part II Periodic Sampled-Data Control
2 Stabilization of Sampled-Data Boolean Control Networks
2.1 Sampled-Data State Feedback Stabilization of Boolean Control Networks
2.1.1 Problem Formulation
2.1.2 Sampled-Data State Feedback Control for Boolean Control Networks
2.1.3 Piecewise Constant Control of Boolean Control Networks
2.2 Sampled-Data State Feedback Control for the Set Stabilization of Boolean Control Networks
2.2.1 Problem Formulation
2.2.2 Topological Structure of Boolean Control Networks Under Sampled-Data State Feedback Control
2.2.3 Set Stabilization for Boolean Control Networks Under Sampled-Data State Feedback Control
2.2.4 Example and Simulations
2.3 Summary
References
3 Controllability, Observability and Synchronization of Sampled-Data Boolean Control Networks
3.1 Controllability and Observability of Boolean Control Networks via Sampled-Data Control
3.1.1 Problem Formulation
3.1.2 Controllability of Sampled-Data Boolean Control Networks
3.1.3 Observability of Sampled-Data Boolean Control Networks
3.1.4 More Effective Algorithm for Observability
3.2 Sampled-Data Control for the Synchronization of Boolean Control Networks
3.2.1 Problem Formulation
3.2.2 Main Results
3.2.3 Example and Its Simulations
3.3 Summary
References
4 Stabilization of Probabilistic Boolean Control Networks Under Sampled-Data Control
4.1 Sampled-Data Stabilization of Probabilistic Boolean Control Networks
4.1.1 An Algebraic Form of a Probabilistic Boolean Control Network
4.1.2 Sampled-Data State Feedback Control for Probabilistic Boolean Control Networks
4.1.3 Examples
4.2 Sampled-Data Partial Stabilization of Probabilistic Boolean Control Networks
4.2.1 Problem Formulation
4.2.2 Main Results
4.2.3 Example and Simulations
4.3 Set Stabilization of Probabilistic Boolean Control Networks
4.3.1 Problem Formulation
4.3.2 Finite-Time Global S-Stabilization
4.3.3 Infinite-Time S-Stabilization
4.4 Summary
References
Part III Aperiodic Sampled-Data Control
5 Stabilization of Aperiodic Sampled-Data Boolean Control Networks
5.1 Stabilization of Boolean Control Networks Under Aperiodic Sampled-Data Control
5.1.1 Problem Formulation
5.1.2 Global Stability
5.1.3 Guaranteed Cost Analysis
5.1.4 Controller Design
5.1.5 Examples
5.2 Stabilization of Aperiodic Sampled-Data Boolean Control Networks with All Modes Unstable
5.2.1 Convert a Boolean Control Network Under Aperiodic Sampled-Data Control into a Switched Boolean Network
5.2.2 Main Results
5.2.3 A Biological Example
5.3 Stabilization of Aperiodic Sampled-Data Boolean Control Networks: A Delay Approach
5.3.1 System Description
5.3.2 Convert a Aperiodic Sampled-Data Control into a Delayed Control
5.3.3 Global Stability
5.3.4 Biological Example
5.4 Summary
References
Part IV Event-Triggered Control
6 Event-Triggered Control for Logical Control Networks
6.1 Stabilization of Logical Control Networks: An Event-Triggered Control Approach
6.1.1 Dynamics of k-Valued Logical Control Networks Under Event-Triggered Controllers
6.1.2 Design of the Time-Optimal Event-Triggered Controller
6.1.3 Design of Switching-Cost-Optimal Event-Triggered Stabilizer
6.2 Event-Triggered Control for the Disturbance Decoupling Problem
6.2.1 Definition of Disturbance Decoupling Problem
6.2.2 Event-Triggered Control of Boolean Control Networks
6.2.3 Event-Triggered Control of Boolean Partial Control Networks
6.3 Event-Triggered Control for Output Regulation of Probabilistic Logical Systems with Delays
6.3.1 Problem Formulation
6.3.2 The Existence of Solutions of the Output Regulation Problem
6.3.3 Event-Triggered Control Design I
6.3.4 Event-Triggered Control Design II
6.3.5 Examples
6.4 Summary
References
