Optimal Control Theory
Description
This new 4 th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining 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 encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework.
Exercises are included in each chapter, while the answers to selected exercises help deepen readers' understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties 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 the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.
Reviews / Votes
"The book is primarily addressed to students and researchers in management science, operations research, and economics. . the book contains enough mathematical tools to solve plenty of practical problems in management science and economics." (Gheorghe Moro?anu, zbMATH 1487.49001, 2022)More details
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Person
Suresh P. Sethi is the Eugene McDermott Chair Professor of Operations Management and Director of the Center for Intelligent Supply Networks (C4ISN) at the University of Texas at Dallas, USA. He has made significant contributions in the fields of manufacturing and operations management, finance and economics, marketing, industrial engineering, operations research, and optimal control. He is best known for his textbook on optimal control, developments of the Sethi advertising model and Sethi-Skiba points, pioneering works on stochastic inventory models especially with incomplete information, and seminal papers on consumption-investment problems with bankruptcy.
He has received numerous 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 the 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
1. What is Optimal Control Theory?.- 2. The Maximum Principle: Continuous Time.- 3. The Maximum Principle: Mixed Inequality Constraints.- 4. The Maximum Principle: Pure State and Mixed Inequality Constraints.- 5. Applications to Finance.- 6. Applications to Production and Inventory.- 7. Applications to Marketing.- 8. The Maximum Principle: Discrete Time.- 9. Maintenance and Replacement.- 10. Applications to Natural Resources.- 11. Applications to Economics.- 12. Stochastic Optimal Control.- 13. Differential Games.
