Optimal Control Of Dynamic Systems Driven By Vector Measures

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Optimal Control Of Dynamic Systems Driven By Vector Measures

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Author : N. U. Ahmed
language : en
Publisher: Springer Nature
Release Date : 2021-09-13

Optimal Control Of Dynamic Systems Driven By Vector Measures written by N. U. Ahmed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-13 with Mathematics categories.

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

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Author : N. U. Ahmed
language : en
Publisher: Springer Nature
Release Date : 2023-09-12

Measure Valued Solutions For Nonlinear Evolution Equations On Banach Spaces And Their Optimal Control written by N. U. Ahmed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with Mathematics categories.

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

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer
Release Date : 2019-07-23

Turnpike Conditions In Infinite Dimensional Optimal Control written by Alexander J. Zaslavski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Mathematics categories.

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.

Turnpike Phenomenon In Metric Spaces

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2023-04-17

Turnpike Phenomenon In Metric Spaces written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-17 with Mathematics categories.

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.

Control And Dynamic Systems V16

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Author : C.T. Leonides
language : en
Publisher: Elsevier
Release Date : 2012-12-02

Control And Dynamic Systems V16 written by C.T. Leonides and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Technology & Engineering categories.

Control and Dynamic Systems: Advances in Theory and Application, Volume 16 is concerned with applied dynamic systems control techniques. It describes various techniques for system modeling, which apply to several systems issues. This book presents a comprehensive treatment of powerful algorithmic techniques for solving dynamic-system optimization problems. It also describes approaches for systems model that apply to system issues such as time delays. The remaining chapters of this book explore the simulation of large closed-loop systems and optimization of low-order feedback controllers for discrete-time systems. Researchers who wish to broaden their understanding of dynamic systems control techniques will find this book invaluable.

Optimal Impulsive Control

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Author : Aram Arutyunov
language : en
Publisher: Springer
Release Date : 2018-12-17

Optimal Impulsive Control written by Aram Arutyunov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-17 with Technology & Engineering categories.

Optimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints. The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.

Emerging Networking In The Digital Transformation Age

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Author : Mikhailo Klymash
language : en
Publisher: Springer Nature
Release Date : 2023-03-20

Emerging Networking In The Digital Transformation Age written by Mikhailo Klymash and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-20 with Technology & Engineering categories.

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!

Optimization Of Dynamical Systems With Impulse Controls And Shocks

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Author : Boris Miller
language : en
Publisher: Springer Nature
Release Date : 2024-09-19

Optimization Of Dynamical Systems With Impulse Controls And Shocks written by Boris Miller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-19 with Science categories.

This text explores the state-of-the-art in the rapidly developing theory of impulse control and introduces the theory of singular space-time transformations, a new method for studying shock mechanical systems. Two approaches in the theory of impulse control are presented: The first, more traditional approach defines the impulsive action as a discontinuity of phase coordinates depending on the current time, the state preceding the action, and its magnitude. The second requires the use of modern methods for describing dynamical systems - differential equations with measures. The impulse is treated as an idealization of a very short action of high magnitude, which produces an almost abrupt change of phase coordinates. The relation between these two approaches is also discussed, and several applications, both traditional and emerging, are considered. This text is intended for graduate students and researchers in control engineering and optimal control theory for dynamical systems. Readers are assumed to be familiar with the theory of ODEs, optimal control, and functional analysis, though an appendix is included that covers many of the necessary mathematical concepts.

Turnpike Phenomenon And Symmetric Optimization Problems

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2022-04-11

Turnpike Phenomenon And Symmetric Optimization Problems written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-11 with Mathematics categories.

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.

Applied Mechanics Reviews

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Author :
language : en
Publisher:
Release Date : 1972

Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mechanics, Applied categories.