Synchronization For Wave Equations With Locally Distributed Controls

Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

This book reflects the latest developments in sliding-mode control (SMC) and variable-structure systems (VSS), comprising contributions by leading researchers and an international range of experts. Such contributions highlight advances in various branches of the field—conventional and higher-order SMC with continuous- and discrete-time implementation and theory and applications both receive attention. The book consists of six parts. In the first, new SMC/VSS algorithms are proposed and their properties are analyzed. The second part focuses on the use of observers to solve the estimation and output-feedback control problems. The third part discusses the discretization aspects of SMC algorithms. Parts IV and V provide important insights on the use of adaptation laws for non-overestimated control gains and chattering alleviation. The last part examines the applications of these SMC/VSS ideas to real-world systems. Sliding-Mode Control and Variable-Structure Systems introduces postgraduates and researchers to the state of the art in the field. It includes theory, methods, and applications relevant to workers in disciplines including control, automation, applied mathematics, electrical and mechanical engineering, instrumentation, electronics, computer science, robotics, transportation, and power engineering. Its clear style and deep exposition help readers to keep in touch with tools that are, thanks to the robustness and insensitivity to perturbations of the SMC/VSS paradigm, among the most efficient for dealing with uncertain systems.

The mastery of distributed applications demands a mastery of the foundations of the distributed algorithm. The object of this book is to present such foundations as far as synchronization, the key element of parallelism and distribution, is concerned.

There is algebraic structure in time, computation and biological systems. Algebraic engineering exploits this structure to achieve better understanding and design. In this book, pure and applied results in semigroups, language theory and algebra are applied to areas ranging from circuit design to software engineering to biological evolution.