{"product_id":"turnpike-phenomenon-in-metric-spaces-9783031272073","title":"Turnpike Phenomenon in Metric Spaces","description":"\u003cp\u003e\u003c\/p\u003e\u003cblockquote\u003e\n\u003cbr\u003eThis book is about the turnpike phenomenon in optimal control theory, focusing on results, conditions, and stability. It develops a large class of optimal control problems in metric spaces and provides solutions to difficult problems. It is useful for mathematicians, optimization, and applications in economics and engineering. \u003c\/blockquote\u003e\u003cp\u003e\u003cstrong\u003eFormat\u003c\/strong\u003e: Hardback\u003cbr\u003e\u003cstrong\u003eLength\u003c\/strong\u003e: 362 pages\u003cbr\u003e\u003cstrong\u003ePublication date\u003c\/strong\u003e: 18 April 2023\u003cbr\u003e\u003cstrong\u003ePublisher\u003c\/strong\u003e: Springer International Publishing AG\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cbr\u003eThis comprehensive book delves into the study of the turnpike phenomenon, a significant aspect of optimal control theory. It specifically focuses on turnpike results, conditions for the occurrence of the turnpike phenomenon, and its stability when subjected to small perturbations of objective functions. One of the key highlights of this book is its development of a vast and versatile class of optimal control problems in metric spaces. This expanded scope offers significant value, as it provides solutions to numerous challenging and intriguing problems within the realm of optimal control theory in metric spaces. Mathematicians, researchers, and practitioners in the fields of optimal control, optimization, and the applications of optimal control to economics and engineering will find this book immensely useful.\u003cbr\u003e\u003cbr\u003eThe book is organized into nine chapters, each contributing to the understanding of the turnpike phenomenon. Chapter 1 serves as an introduction, providing a foundational framework for the subsequent chapters. Chapter 2 delves into Banach space-valued functions, set-valued mappings in infinite-dimensional spaces, and related continuous-time dynamical systems. It presents some convergence results and establishes the necessary prerequisites for the study of turnpike properties.\u003cbr\u003e\u003cbr\u003eChapter 3 explores a discrete-time dynamical system characterized by a Lyapunov function in a metric space induced by a set-valued mapping. It examines the properties and behavior of such systems, including the concept of turnpike behavior. Chapter 4 extends the analysis to a class of continuous-time dynamical systems, akin to the discrete-time systems considered in Chapter 3. It introduces turnpike theory and discusses its application to these systems.\u003cbr\u003e\u003cbr\u003eChapter 5 develops a turnpike theory for a broad class of general dynamical systems in metric spaces possessing a Lyapunov function. It establishes sufficient conditions for the turnpike phenomenon to occur and provides insights into its stability properties. Chapter 6 focuses on the turnpike phenomenon for discrete-time nonautonomous problems on subintervals of half-axis in metric spaces. It considers cases where the problem domains may not be compact and explores the conditions for the turnpike phenomenon to hold.\u003cbr\u003e\u003cbr\u003eChapter 7 provides the necessary preliminaries to study turnpike properties of infinite-dimensional optimal control problems. It introduces concepts and tools that are essential for understanding the behavior of optimal control systems in high-dimensional spaces. Chapter 8 presents sufficient and necessary conditions for the turnpike phenomenon in infinite-dimensional optimal control problems. It further explores the stability analysis of turnpike solutions and discusses the implications of these conditions in practical applications.\u003cbr\u003e\u003cbr\u003eThroughout the book, all main results obtained are novel and original. The monograph offers a comprehensive and in-depth exploration of the turnpike phenomenon in optimal control theory, making it a valuable resource for scholars and practitioners alike. Its extensive coverage, detailed explanations, and practical examples make it accessible to a wide range of audiences, from advanced students to seasoned researchers.\u003cbr\u003e\u003cbr\u003eIn conclusion, this book is a groundbreaking contribution to the field of optimal control theory. By developing a large and general class of optimal control problems in metric spaces and providing solutions to challenging problems, it has significantly advanced our understanding of the turnpike phenomenon and its applications. It is a must-read for mathematicians, researchers, and practitioners interested in optimal control, optimization, and their interdisciplinary applications.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eWeight\u003c\/strong\u003e: 723g\u003cbr\u003e\u003cstrong\u003eDimension\u003c\/strong\u003e: 235 x 155 (mm)\u003cbr\u003e\u003cstrong\u003eISBN-13\u003c\/strong\u003e: 9783031272073\u003cbr\u003e \u003cstrong\u003eEdition number\u003c\/strong\u003e: 1st ed. 2023\u003c\/p\u003e","brand":"Alexander J. Zaslavski","offers":[{"title":"Hardback","offer_id":44307638649082,"sku":"9783031272073","price":108.28,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0522\/4297\/2845\/products\/noImage_1_7c47ef7f-2319-43f4-9069-e3c39f55b67d.jpg?v=1688110813","url":"https:\/\/shulphink.com\/products\/turnpike-phenomenon-in-metric-spaces-9783031272073","provider":"Shulph Ink","version":"1.0","type":"link"}