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Author: Hajime Oniki Publisher: ISBN: Category : Languages : en Pages : 46
Book Description
The paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative are given in the form of initial-value problems of linear differential equations. Possibility of discontinuous optimal controls is fully taken care of. The derivative of the maximized objective function with respect to the parameter is expressed in a simple form by using the auxiliary variables. An example of the comparative dynamics is given in terms of a model of optimal capital accumulation.
Author: Hajime Oniki Publisher: ISBN: Category : Languages : en Pages : 46
Book Description
The paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative are given in the form of initial-value problems of linear differential equations. Possibility of discontinuous optimal controls is fully taken care of. The derivative of the maximized objective function with respect to the parameter is expressed in a simple form by using the auxiliary variables. An example of the comparative dynamics is given in terms of a model of optimal capital accumulation.
Author: Michael Ralph Caputo Publisher: Cambridge University Press ISBN: 9780521603683 Category : Business & Economics Languages : en Pages : 596
Book Description
Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.
Author: Suresh P. Sethi Publisher: Springer ISBN: 3319982370 Category : Business & Economics Languages : en Pages : 577
Book 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.
Author: L. Radanović Publisher: Elsevier ISBN: 1483223256 Category : Technology & Engineering Languages : en Pages : 457
Book Description
Sensitivity Methods in Control Theory is a collection of manuscripts presented as the Third International Symposium of Sensitivity Analysis, held at Dubrovnik, Yugoslavia on August 31-September 5, 1964, sponsored by The Theory Committee of International Federation of Automatic Control. Sensitivity theory or sensitivity analysis concerns the solution of problems associated with parameter variations within the general scope of control theory. This book is organized into five parts encompassing 30 chapters. Part I presents some basic approaches of sensitivity analysis, such the Lyapunov's theory of stability, invariant imbedding, nonlinear sampled data, and linear time-varying systems. This part also looks into the preliminary steps towards the development of game theory and some general applications of sensitivity analysis. Part II treats the problem of accuracy, reliability, self-adjustment, and optimization of sensitivity of automatic control systems, while Part III deals with the functional derivative technique of sensitivity analysis and its applications for designing self-adjusting control systems. Part IV describes the task of synthesizing control systems for linear plants with variable parameters satisfying specified performance criteria. Part V considers the association between sensitivity and optimality in various control systems. This book will prove useful to design and other specialized fields in engineering.
Author: Andrzej Wierzbicki Publisher: Elsevier Publishing Company ISBN: Category : Technology & Engineering Languages : en Pages : 424
Book Description
Mathematical models. Sensitivity analysis of mathematical models. Optimization and optimal control. Sensitivity analysis of the optimal control systems.
Author: Morton I. Kamien Publisher: Courier Corporation ISBN: 0486310280 Category : Mathematics Languages : en Pages : 402
Book Description
Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Author: Paul van Loon Publisher: Springer Science & Business Media ISBN: 3642464823 Category : Business & Economics Languages : en Pages : 202
Book Description
This volume is the final result of the research project ''Micro growth model", that was sponsored by the Central Research Pool of Tilburg University, the Netherlands. Apart from the University Council for this important financial support, I owe Prof. Dr. Fiet Verheyen very much for the way in which he introduced me into scientific circles and for the way in which he supervised and stimulated my work. Dr. Jan de Jong and Peter Janssen C. E. , Technical University of Eindhoven, piloted me safely through the mathe matics of optimal control theory and removed some technical barriers. Their help was indispensable for the success of this project. I would also like to mention the kind support of Prof. Dr. Jack Kleijnen, who gave me many valuable hints on how to present the results of this project. In this way I was able to contact with several resear chers inside and outside the Netherlands. Most grateful I am to Prof. Dr. Charles Tapiero, Jerusalem University, who commented on important parts of this book in a constructive way and who suggested many subjects for further research. Also Mr. Geert Jan vsn Schijndel, Tilburg University, should be mentioned here, because he closely read the work and I appreciated his remarks and corrections very much. Many collea gues have contributed to the results of this research project in a direct or indirect way. Especially I should like to mention my contacts with Prof. Dr.
Author: Hajime Oniki
Author: Hajime Oniki
Author: Michael Ralph Caputo
Author: Suresh P. Sethi
Author: Pierre N. V. Tu
Author: A L Dontchev
Author: L. Radanović
Author: John Robert Sesak
Author: Andrzej Wierzbicki
Author: Morton I. Kamien
Author: Paul van Loon