Optimal Control Problems Arising in Forest Management


Book Description

This book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.




Stability, Control and Differential Games


Book Description

This book presents the proceedings of the International Conference “Stability, Control, Differential Games” (SCDG2019, September 16 – 20, 2019, Yekaterinburg, Russia), organized by the Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences. Discussing the latest advances in the theory of optimal control, stability theory and differential games, it also demonstrates the application of new techniques and numerical algorithms to solve problems in robotics, mechatronics, power and energy systems, economics and ecology. Further, the book includes fundamental results in control theory, stability theory and differential games presented at the conference, as well as a number of chapters focusing on novel approaches in solving important applied problems in control and optimization. Lastly, it evaluates recent major accomplishments, and forecasts developments in various up-and-coming areas, such as hybrid systems, model predictive control, Hamilton–Jacobi equations and advanced estimation algorithms.




Turnpike Theory for the Robinson–Solow–Srinivasan Model


Book Description

This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson–Solow–Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists. The RSS is a well-known model of economic dynamics that was introduced in the 1960s and as many other models of economic dynamics, the RSS model is determined by an objective function (a utility function) and a set-valued mapping (a technology map). The set-valued map generates a dynamical system whose trajectories are under consideration and the objective function determines an optimality criterion. The goal is to find optimal trajectories of the dynamical system, using the optimality criterion. Chapter 1 discusses turnpike properties for some classes of discrete time optimal control problems. Chapter 2 present the description of the RSS model and discuss its basic properties. Infinite horizon optimal control problems, related to the RSS model are studied in Chapter 3. Turnpike properties for the RSS model are analyzed in Chapter 4. Chapter 5 studies infinite horizon optimal control problems related to the RSS model with a nonconcave utility function. Chapter 6 focuses on infinite horizon optimal control problems with nonautonomous optimality criterions. Chapter 7 contains turnpike results for a class of discrete-time optimal control problems. Chapter 8 discusses the RSS model and compares different optimality criterions. Chapter 9 is devoted to the study of the turnpike properties for the RSS model. In Chapter 10 the one-dimensional autonomous RSS model is considered and the continuous time RSS model is studied in Chapter 11.




Forest Management and Planning


Book Description

Forest Management and Planning, Second Edition, addresses contemporary forest management planning issues, providing a concise, focused resource for those in forest management. The book is intermixed with chapters that concentrate on quantitative subjects, such as economics and linear programming, and qualitative chapters that provide discussions of important aspects of natural resource management, such as sustainability. Expanded coverage includes a case study of a closed canopy, uneven-aged forest, new forest plans from South America and Oceania, and a new chapter on scenario planning and climate change adaptation. - Helps students and early career forest managers understand the problems facing professionals in the field today - Designed to support land managers as they make complex decisions on the ecological, economic, and social impacts of forest and natural resources - Presents updated, real-life examples that are illustrated both mathematically and graphically - Includes a new chapter on scenario planning and climate change adaptation - Incorporates the newest research and forest certification standards - Offers access to a companion website with updated solutions, geographic databases, and illustrations







Optimal Control of Age-structured Populations in Economy, Demography, and the Environment


Book Description

This book covers a wide range of topics within mathematical modelling and the optimization of economic, demographic, technological and environmental phenomena. Each chapter is written by experts in their field and represents new advances in modelling theory and practice. These essays are exemplary of the fruitful interaction between theory and practice when exploring global and local changes. The unifying theme of the book is the use of mathematical models and optimization methods to describe age-structured populations in economy, demography, technological change, and the environment. Emphasis is placed on deterministic dynamic models that take age or size structures, delay effects, and non-standard decision variables into account. In addition, the contributions deal with the age structure of assets, resources, and populations under study. Interdisciplinary modelling has enormous potential for discovering new insights in global and regional development. Optimal Control of Age-structured Populations in Economy, Demography, and the Environment is a rich and excellent source of information on state-of-the-art modelling expertise and references. The book provides the necessary mathematical background for readers from different areas, such as applied sciences, management sciences and operations research, which helps guide the development of practical models. As well as this the book also surveys the current practice in applied modelling and looks at new research areas for a general mathematical audience. This book will be of interest primarily to researchers, postgraduate students, as well as a wider scientific community, including those focussing on the subjects of applied mathematics, environmental sciences, economics, demography, management, and operations research.




Multiple-Use Management


Book Description

In this book, Bowes and Krutilla bring together what is known and relevant about valuing the nonmarket services of the public forests and propose a new theoretical framework that allows multiple uses, the biological dynamics of the forest, and the institutional and economic realities of public forest management to be taken into account in forest planning and budgeting. The authors begin by tracing the development of multiple use in forest management and by exploring the multiple uses of the public forests and the economics of multiple-use forestry. They offer a masterful analysis of the nineteenth-century model of the single timber stand on which much forestry practice has been premised. Bowes and Krutilla then take a giant step forward by developing a larger theoretical framework and showing how forest structure and dynamics can be included in the economic model. The authors' rigorous exposition theory provides the foundation for analyzing case studies of management for timber and water yields in the Rockies, of recreation valuation in the Black Hills and White Mountain national forests, and of joint production in the White Clouds Peaks --- analyses that demonstrate the authors' great skill in developing practical methodologies to meet actual forest management problems.




Optimization in Control Applications


Book Description

This book is a printed edition of the Special Issue "Optimization in Control Applications" that was published in MCA







Conservation


Book Description

A unified theory of conservation that addresses the broad problem of conservation, the principles that inform conservation choices, and the application of those principles to the management of the natural world. The conservation of natural resources, like that of any other asset, involves trade-offs. Yet, in a world faced with the harsh realities of climate change, crafting the right environmental policies is an increasingly urgent task. In Conservation, Charles Perrings and Ann Kinzig bring together new research in economics and biodiversity to investigate conservation decisions and the theory behind them. Perrings and Kinzig apply the concept of conservation broadly to examine how the principles of conservation apply to the management of the natural world. They demonstrate that the same basic principles serve as the foundation of all rational conservation decisions, from managing financial assets to safeguarding at-risk ecosystems. Whether someone is deciding to hold or dispose of a stock or whether to exploit or preserve a natural resource, they are better off choosing to conserve a resource when its value to them, if conserved, is greater than its value when converted. The book also considers the context of such conservation decisions. Just as national tax rules influence choices about financial investments, environmental regulations within countries, and environmental agreements between countries, impact the decisions regarding natural resources. Building on their basic theory of conservation, Perrings and Kinzig address key issues in the field of environmental economics, including the valuation of ecosystem services and environmental assets; the limits on the substitutability of produced and natural capital; and the challenges posed by the often weak markets for ecosystem services oriented toward the public good. They also address the problem of scale: while decisions might be easier to make at the local level, many conservation policies need to apply at either the national or international level to succeed. Written by experts from both social and hard sciences, this book presents a unified theory of conservation and provides a model for a more effective way to approach the vitally important issue.