An Introduction To Optimal Control Problems In Life Sciences And Economics

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.

This fully revised 3rd edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It brings to students the concept of the maximum principle in continuous, as well as discrete, time by using dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations faced in business and economics. The book exploits optimal control theory to the functional areas of management including finance, production and marketing and to economics of growth and of natural resources. In addition, this new edition features materials on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. The book provides exercises for each chapter and answers to selected exercises to help deepen the understanding of the material presented. Also included are appendices comprised of supplementary material on the solution of differential equations, the calculus of variations and its relationships to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the author has applied to business management problems developed from his research and classroom instruction. The new edition has been completely refined and brought up to date. Ultimately this should continue to be a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers concerned with the application of dynamic optimization in their fields.

Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing – not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity. The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.

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

From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

The volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science. These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a ubiquitous tool in all areas of mathematical applications. This book covers both fundamental and applied research, ranging from studies of elliptic curves over finite fields with their applications to cryptography, to dynamic blocking problems, to random matrix theory with its innovative applications. The book provides the reader with state-of-the-art achievements in the development and application of new theories at the interface of applied mathematics, modeling, and computational science. This book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling, and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from applications ranging from engineering to life sciences, providing a rich ground for graduate student projects.