Discrete Dynamial Systems

This book comprises selected papers of the 25th International Conference on Difference Equations and Applications, ICDEA 2019, held at UCL, London, UK, in June 2019. The volume details the latest research on difference equations and discrete dynamical systems, and their application to areas such as biology, economics, and the social sciences. Some chapters have a tutorial style and cover the history and more recent developments for a particular topic, such as chaos, bifurcation theory, monotone dynamics, and global stability.

J. P. La Salle has developed in [20] a stability theory for systems of difference equations (see also [8]) which we introduce in the first chapter within the framework of metric spaces. The stability theory for such systems can also be found in [13] in a slightly modified form. We start with autonomous systems in the first section of chapter 1.

This book belongs to the subject of control and systems theory. The discrete-time adaptive iterative learning control (DAILC) is discussed as a cutting-edge of ILC and can address random initial states, iteration-varying targets, and other non-repetitive uncertainties in practical applications. This book begins with the design and analysis of model-based DAILC methods by referencing the tools used in the discrete-time adaptive control theory.

This book describes an effective approach to the cooperative and coordinated control of multivehicle systems. This rigorous analytic approach guarantees the stability of coordinated and cooperating vehicles using distributed protocols and uses low-energy, event-triggered mechanisms for networked vehicle control. The text covers:

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A.

This book presents powerful modern control techniques based on the parallelism and adaptive capabilities of biological nervous systems. The book builds systematically from actuator nonlinearities and strict feedback in nonlinear systems to nonstrict feedback, system identification, model reference adaptive control, and novel optimal control using the Hamilton-Jacobi-Bellman formulation. The author concludes by developing a framework for implementing intelligent control in actual industrial systems using embedded hardware.

More and more digital devices are being used for informa­ tion processing and control purposes in a variety of systems applications, including industrial processes, power networks, biological systems and communication networks. This trend has been helped by the advent of microprocessors and the consequent availability of cheap distributed computing power. For those applications, where digital devices are used, it is reasonable to model the system in discrete-time. In addition there are other application areas, e.g. econometric systems, business systems, certain command and control systems, environmental systems, where the underlying models are in discrete-time and here discrete-time approaches to analysis and control are the most appropriate.