Optimal Control Theory
Description
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.
Reviews / Votes
"The mathematical background required in the book is two-three semesters of calculus and some differential equations and linear algebra, it can be easily used for a course in the junior or senior undergraduate years or in the early years of graduate studies. But, it can be also useful for management scientists, mathematicians, engineers and economists working in the field of optimal control and applications." (Doina Carp, zbMath 1412.49001, 2019)More details
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Person
Suresh P. Sethi is Eugene McDermott Chair Professor of Operations Management and Director of the Center for Intelligent Supply Networks (C4ISN) at The University of Texas at Dallas. He has contributed significantly in the fields of manufacturing and operations management, finance and economics, marketing, industrial engineering, operations research, and optimal control. He is well known for his developments of the Sethi advertising model and Sethi-Skiba points, and for his text book on optimal control.
He has received prestigious honors and awards such as IEEE Fellow, INFORMS Fellow, SIAM Fellow, POMS Fellow, AAAS Fellow, IITB Distinguished Alum, Tepper School of Business-Alumni Achievement Award, and POMS President (2012). Two conferences have been organized in his honor: in Aix en Provence in 2005 and at UT Dallas in 2006 with Harry M. Markowitz, a 1990 Nobel Laureate in Economics, as the keynote speaker. Also, two books have been edited in his honor.
His past and present editorial positions include Departmental Editor of Production and Operations Management, Corresponding Editor of SIAM Journal on Control and Optimization, and Associate Editor of Operations Research, M&SOM, and Automatica.
Content
Chapter 1. What is Optimal Control Theory?- Chapter 2. The Maximum Principle: Continuous Time.- Chapter 3. The Maximum Principle: Mixed Inequality Constraints.- Chapter 4. The Maximum Principle: Pure State and Mixed Inequality Constraints.- Chapter 5. Applications to Finance.- Chapter 6. Applications to Production and Inventory.- Chapter 7. Applications to Marketing.- Chapter 8. The Maximum Principle: Discrete Time.- Chapter 9. Maintenance and Replacement.- Chapter 10. Applications to Natural Resources.- Chapter 11. Applications to Economics.- Chapter 12. Stochastic Optimal Control.- Chapter 13. Differential Games.