Sampled-data Control of Logical Networks

ISBN-13: 9789811982606 / Angielski / Twarda / 2023 / 219 str.

Yang Liu; Jianquan Lu; Liangjie Sun

Opis

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.

Spis treści

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 ����-stabilization

4.3.3 Infinite-time ����-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 an 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 ����-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

 

O autorze

Yang Liu (Senior Member, IEEE) is currently a Professor at the College of Mathematics and Computer Science, Zhejiang Normal University, China. He received his B.S. degree in mathematics from Zhejiang Normal University, Zhejiang, China, in 2003, and his Ph.D. degree from Tongji University, Shanghai, in 2008. He has authored over 100 publications and two books. He is an Associate Editor of Neural Processing Letters (Springer). He was recognized by Elsevier as a Most Cited Chinese Researcher in 2020-2021, and by Clarivate Analytics as a Highly Cited Researcher in 2019-2021. He was the supervisor of the ICCM Best Paper Award in 2016 and 2022. His research interests include distributed optimization, hybrid systems and logical systems.

Jianquan Lu (Senior Member, IEEE) is currently a Professor at the Department of Systems Science, School of Mathematics, Southeast University, Nanjing, China. He received his B.S. degree in mathematics from Zhejiang Normal University, Zhejiang, China, in 2003, his M.S. degree in mathematics from Southeast University, Nanjing, China, in 2006, and his Ph.D. degree in applied mathematics from City University of Hong Kong in 2009. From 2010 to 2012, he was an Alexander von Humboldt Research Fellow at the PIK, Germany. His current research interests include collective behavior in complex dynamical networks and multi-agent systems, logical networks, and hybrid systems. He has published over 90 papers in refereed international journals. Dr. Lu was named a Highly Cited Researcher by Clarivate Analytics from 2018 for three consecutive years, and he was elected one of the Most Cited Chinese Researchers by Elsevier in 2014-2019. He was part of the Program for New Century Excellent Talents in University by The Ministry of Education, China in 2010, and won the Second Award of Jiangsu Provincial Progress in Science and Technology in 2016 as the First Project Member, and the First Award of Jiangsu Provincial Progress in Science and Technology in 2010 as the Second Project Member. Dr. Lu is an associate editor of Neural Processing Letters (Springer), Journal of Franklin Institute (Elsevier), and Neural Computing and Applications (Springer), and a guest editor of Science China: Information Sciences, Mathematics and Computers in Simulation (Elsevier) and IET Control Theory & Applications.

Liangjie Sun is currently pursuing her Ph.D. degree at the Department of Mathematics, The University of Hong Kong. She received her B.S. degree in mathematics from Zhejiang Normal University, Zhejiang, China, in 2016, and her M.S. degree in mathematics from Southeast University, Nanjing, China, in 2019. Her undergraduate thesis: “On the Control Theory of Logical Systems: An Approach of Semi-Tensor Product of Matrices” won the New World Mathematics Awards, Bachelor Thesis Awards - Silver Prize in 2016. Her master’s thesis: “Sampled-data control of Boolean networks and some related qualitative problems” won the outstanding master’s degree award of Jiangsu Province in 2020. Her current research interests include logical dynamics systems and computational biology.