Discrete-Time and Discrete-Space Dynamical Systems

Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including:

• Boolean control networks;
• nondeterministic finite-transition systems;
• finite automata;
• labelled Petri nets; and
• cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology.
  Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.

Explains advanced theoretical contributions intuitively Graphical and practical examples appeal to a broad audience Offers cogent comparison between various example systems

Autorentext

Kuize Zhang received the B.S. and Ph.D. degrees in Mathematics and Systems Engineering from Harbin Engineering University, China, in 2009 and 2014, respectively. Since April 2015, he has been an associate professor with the College of Automation, Harbin Engineering University. He held visiting positions at University of Turku, Finland (September 2012-September 2013), and the Chinese Academy of Sciences (January-October 2015). He was a project officer of Nanyang Technological University, Singapore (October 2013-October 2014), postdoc at Chinese Academy of Sciences (November 2015-November 2017), and postdoc at Technical University of Munich (September 2016-August 2017). He is currently a postdoc at KTH Royal Institute of Technology, Sweden. His current research interests include formal methods, Boolean networks, discrete event systems, etc. Dr. Zhang is a Senior Member of IEEE, and received the 2016 Chinese Association of Automation (CAA) Outstanding Doctoral Thesis Nomination Award and the Humboldt Research Fellowship in 2019. Lijun Zhang received the Ph.D. degree in Systems Theory from Chinese Academy of Sciences, China, in 2003. From August 2003 to July 2005, he held a postdoc position at Tsinghua University, China. From March 2004 to November 2004, he worked as a visiting scholar at National University of Singapore. From October 2006 to January 2007, he worked as a visiting scholar at City University of Hong Kong. From August 2005 to November 2011, he was a professor of Harbin Engineering University. Since 2012, he has been with the College of Marine Science and Technology of Northwestern Polytechnical University, where he is currently a professor. He has been a reviewer of Mathematical Reviews since 2008. His research interests include nonlinear systems control and identification, logic dynamic systems theory, adaptive signal processing, etc. He was a recipient of New Century Excellent Talents in University of Ministry of Education of China. Currently he serves as Associate Editor of the Journal of Systems Sciences and Mathematics (in Chinese). He was also an author or coauthor of more than 60 journal or conference papers. Lihua Xie received the B.E. and M.E. degrees in electrical engineering from Nanjing University of Science and Technology in 1983 and 1986, respectively, and the Ph.D. degree in electrical engineering from the University of Newcastle, Australia, in 1992. Since 1992, he has been with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, where he is currently a professor and Director, Delta-NTU Corporate Laboratory for Cyber-Physical Systems. He served as the Head of Division of Control and Instrumentation from July 2011 to June 2014. He held teaching appointments in the Department of Automatic Control, Nanjing University of Science and Technology from 1986 to 1989. Dr. Xie's research interests include robust control and estimation, networked control systems, multi-agent networks, localization and unmanned systems. He is an Editor-in-Chief for Unmanned Systems and an Associate Editor for IEEE Transactions on Network Control Systems. He has served as an editor of IET Book Series in Control and an Associate Editor of a number of journals including IEEE Transactions on Automatic Control, Automatica, IEEE Transactions on Control Systems Technology, and IEEE Transactions on Circuits and Systems-II. He is an elected member of Board of Governors, IEEE Control System Society (January 2016-December 2018). Dr. Xie is a Fellow of the IEEE and Fellow of the IFAC.

Klappentext

Discrete-Time and Discrete-Space Dynamical Systems provides a systematic characterization of the similarities and differences of several types of discrete-time and discrete-space dynamical systems, including:Boolean control networks; nondeterministic finite-transition systems; finite automata; labelled Petri nets; and cellular automata. The book's perspective is primarily based on topological properties though it also employs semitensor-product and graph-theoretic methods where appropriate. It presents a series of fundamental results: invertibility, observability, detectability, reversiblity, etc., with applications to systems biology. Academic researchers with backgrounds in applied mathematics, engineering or computer science and practising engineers working with discrete-time and discrete-space systems will find this book a helpful source of new understanding for this increasingly important class of systems. The basic results to be found within are of fundamental importance for further study of related problems such as automated synthesis and safety control in cyber-physical systems using formal methods.

Inhalt
Introduction.- Preliminaries.- Introduction to Different Types of Discrete-Time and Discrete-Space Dynamical Systems.- Invertibility and Nonsingularity of Boolean Control Networks.- Observability of Boolean Control Networks.- Detectability of Boolean Control Networks.- Observability and Detectability of Large-Scale Boolean Control Networks.- Observability of Nondeterministic Finite-Transition Systems.- Detectability of Nondeterministic Finite-Transition Systems.- Detectability of Finite-State Automata.- Detectability of Labelled Petri Nets.- Generalized Reversibility of Topological Dynamical Systems and Cellular Automata.- Generalized Reversibility of Variant Cellular Automata.- Solutions.- Index.