Optimal Control of Dynamic Systems Driven by Vector Measures
Optimal Control of Dynamic Systems Driven by Vector Measures

Author: N. U. Ahmed

Publisher: Springer Nature

Published: 2021-09-13

Total Pages: 328

ISBN-13: 3030821390

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This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.

Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control
Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control

Author: N. U. Ahmed

Publisher: Springer Nature

Published: 2023-09-12

Total Pages: 236

ISBN-13: 3031372603

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This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

Turnpike Conditions in Infinite Dimensional Optimal Control
Turnpike Conditions in Infinite Dimensional Optimal Control

Author: Alexander J. Zaslavski

Publisher: Springer

Published: 2019-07-23

Total Pages: 578

ISBN-13: 3030201783

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This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.

Emerging Networking in the Digital Transformation Age
Emerging Networking in the Digital Transformation Age

Author: Mikhailo Klymash

Publisher: Springer Nature

Published: 2023-03-20

Total Pages: 694

ISBN-13: 3031249631

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This book covers a range of leading-edge topics. It is suitable for teaching specialists for advanced lectures in the domains of systems architecture and distributed platforms. Furthermore, it serves as a basis for undergraduates as well as an inspiration for interesting postgraduates, looking for new challenges. It addresses a holistic view of QoS, which becomes nowadays via Digital Transformations less technically and more socially driven. This includes IoT, energy efficiency, secure transactions, blockchains, and smart contracting. Under the term Emerging Networking (EmN), we cover the steadily growing diversity of smart mobile and robotic apps and unmanned scenarios (UAV). EmN supports distributed intelligence across the combined mobile, wireless, and fixed networks in the edge-to-cloud continuum. The 6G driving factors and potentials in the mid-term are examined. Operative (emergency) networking, which assists rescue troops at sites, also belongs to the above-mentioned problems. The EmN architecture includes the components of SDN, blockchain, and AI with efficient slicing and cloud support. The design peculiarities in dynamically changing domains, such as Smart Shopping/Office/Home, Context-Sensitive Intelligent apps, are discussed. Altogether, the provided content is technically interesting while still being rather practically oriented and therefore straightforward to understand. This book originated from the close cooperation of scientists from Germany, Ukraine, Israel, Switzerland, Slovak Republic, Poland, Czech Republic, South Korea, China, Italy, North Macedonia, Azerbaijan, Kazakhstan, France, Latvia, Greece, Romania, USA, Finland, Morocco, Ireland, and the United Kingdom. We wish all readers success and lots of inspiration from this useful book!

Turnpike Phenomenon in Metric Spaces
Turnpike Phenomenon in Metric Spaces

Author: Alexander J. Zaslavski

Publisher: Springer Nature

Published: 2023-04-17

Total Pages: 366

ISBN-13: 3031272080

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This book is devoted to the study of the turnpike phenomenon arising in optimal control theory. Special focus is placed on Turnpike results, in sufficient and necessary conditions for the turnpike phenomenon and in its stability under small perturbations of objective functions. The most important feature of this book is that it develops a large, general class of optimal control problems in metric space. Additional value is in the provision of solutions to a number of difficult and interesting problems in optimal control theory in metric spaces. Mathematicians working in optimal control, optimization, and experts in applications of optimal control to economics and engineering, will find this book particularly useful. All main results obtained in the book are new. The monograph contains nine chapters. Chapter 1 is an introduction. Chapter 2 discusses Banach space valued functions, set-valued mappings in infinite dimensional spaces, and related continuous-time dynamical systems. Some convergence results are obtained. In Chapter 3, a discrete-time dynamical system with a Lyapunov function in a metric space induced by a set-valued mapping, is studied. Chapter 4 is devoted to the study of a class of continuous-time dynamical systems, an analog of the class of discrete-time dynamical systems considered in Chapter 3. Chapter 5 develops a turnpike theory for a class of general dynamical systems in a metric space with a Lyapunov function. Chapter 6 contains a study of the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces, which are not necessarily compact. Chapter 7 contains preliminaries which are needed in order to study turnpike properties of infinite-dimensional optimal control problems. In Chapter 8, sufficient and necessary conditions for the turnpike phenomenon for continuous-time optimal control problems on subintervals of the half-axis in metric spaces, is established. In Chapter 9, the examination continues of the turnpike phenomenon for the continuous-time optimal control problems on subintervals of half-axis in metric spaces discussed in Chapter 8.

Turnpike Phenomenon and Symmetric Optimization Problems
Turnpike Phenomenon and Symmetric Optimization Problems

Author: Alexander J. Zaslavski

Publisher: Springer Nature

Published: 2022-04-11

Total Pages: 339

ISBN-13: 3030969738

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Written by a leading expert in turnpike phenomenon, this book is devoted to the study of symmetric optimization, variational and optimal control problems in infinite dimensional spaces and turnpike properties of their approximate solutions. The book presents a systematic and comprehensive study of general classes of problems in optimization, calculus of variations, and optimal control with symmetric structures from the viewpoint of the turnpike phenomenon. The author establishes generic existence and well-posedness results for optimization problems and individual (not generic) turnpike results for variational and optimal control problems. Rich in impressive theoretical results, the author presents applications to crystallography and discrete dispersive dynamical systems which have prototypes in economic growth theory. This book will be useful for researchers interested in optimal control, calculus of variations turnpike theory and their applications, such as mathematicians, mathematical economists, and researchers in crystallography, to name just a few.

Optimal Event-Triggered Control Using Adaptive Dynamic Programming
Optimal Event-Triggered Control Using Adaptive Dynamic Programming

Author: Sarangapani Jagannathan

Publisher: CRC Press

Published: 2024-06-21

Total Pages: 348

ISBN-13: 1040049168

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Optimal Event-triggered Control using Adaptive Dynamic Programming discusses event triggered controller design which includes optimal control and event sampling design for linear and nonlinear dynamic systems including networked control systems (NCS) when the system dynamics are both known and uncertain. The NCS are a first step to realize cyber-physical systems (CPS) or industry 4.0 vision. The authors apply several powerful modern control techniques to the design of event-triggered controllers and derive event-trigger condition and demonstrate closed-loop stability. Detailed derivations, rigorous stability proofs, computer simulation examples, and downloadable MATLAB® codes are included for each case. The book begins by providing background on linear and nonlinear systems, NCS, networked imperfections, distributed systems, adaptive dynamic programming and optimal control, stability theory, and optimal adaptive event-triggered controller design in continuous-time and discrete-time for linear, nonlinear and distributed systems. It lays the foundation for reinforcement learning-based optimal adaptive controller use for infinite horizons. The text then: Introduces event triggered control of linear and nonlinear systems, describing the design of adaptive controllers for them Presents neural network-based optimal adaptive control and game theoretic formulation of linear and nonlinear systems enclosed by a communication network Addresses the stochastic optimal control of linear and nonlinear NCS by using neuro dynamic programming Explores optimal adaptive design for nonlinear two-player zero-sum games under communication constraints to solve optimal policy and event trigger condition Treats an event-sampled distributed linear and nonlinear systems to minimize transmission of state and control signals within the feedback loop via the communication network Covers several examples along the way and provides applications of event triggered control of robot manipulators, UAV and distributed joint optimal network scheduling and control design for wireless NCS/CPS in order to realize industry 4.0 vision An ideal textbook for senior undergraduate students, graduate students, university researchers, and practicing engineers, Optimal Event Triggered Control Design using Adaptive Dynamic Programming instills a solid understanding of neural network-based optimal controllers under event-sampling and how to build them so as to attain CPS or Industry 4.0 vision.

Informatics in Control, Automation and Robotics
Informatics in Control, Automation and Robotics

Author: Oleg Gusikhin

Publisher: Springer

Published: 2019-04-18

Total Pages: 827

ISBN-13: 3030112926

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The book focuses the latest endeavours relating researches and developments conducted in fields of Control, Robotics and Automation. Through more than twenty revised and extended articles, the present book aims to provide the most up-to-date state-of-art of the aforementioned fields allowing researcher, PhD students and engineers not only updating their knowledge but also benefiting from the source of inspiration that represents the set of selected articles of the book. The deliberate intention of editors to cover as well theoretical facets of those fields as their practical accomplishments and implementations offers the benefit of gathering in a same volume a factual and well-balanced prospect of nowadays research in those topics. A special attention toward “Intelligent Robots and Control” may characterize another benefit of this book.

Dynamic Systems And Control With Applications
Dynamic Systems And Control With Applications

Author: Nasir Uddin Ahmed

Publisher: World Scientific Publishing Company

Published: 2006-08-29

Total Pages: 468

ISBN-13: 9813106824

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In recent years significant applications of systems and control theory have been witnessed in diversed areas such as physical sciences, social sciences, engineering, management and finance. In particular the most interesting applications have taken place in areas such as aerospace, buildings and space structure, suspension bridges, artificial heart, chemotherapy, power system, hydrodynamics and computer communication networks. There are many prominent areas of systems and control theory that include systems governed by linear and nonlinear ordinary differential equations, systems governed by partial differential equations including their stochastic counter parts and, above all, systems governed by abstract differential and functional differential equations and inclusions on Banach spaces, including their stochastic counterparts. The objective of this book is to present a small segment of theory and applications of systems and control governed by ordinary differential equations and inclusions. It is expected that any reader who has absorbed the materials presented here would have no difficulty to reach the core of current research.