On First Order Necessary Conditions for Variational and Optimal Control Problems
On First Order Necessary Conditions for Variational and Optimal Control Problems

Author: Theodore Guinn

Publisher:

Published: 1964

Total Pages: 182

ISBN-13:

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A general variational problem is considered which contains most control problems as special cases. Included are differential constraints as well as isoparametric and finite inequalities on both state and control vairables. The method of M. R. Hestenes for proving first order necessary conditions is used to obtain similar conditions under weaker hypothesis, principally requiring Lebeque integrability of all functions with respect to time. It is then shown these results can be easily extended to include the problem with inequality constraints on the space variables independent of control variables. (Author).

Calculus of Variations and Optimal Control Theory
Calculus of Variations and Optimal Control Theory

Author: Daniel Liberzon

Publisher: Princeton University Press

Published: 2012

Total Pages: 255

ISBN-13: 0691151873

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This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control

Optimal Control Theory
Optimal Control Theory

Author: Zhongjing Ma

Publisher: Springer Nature

Published: 2021-01-30

Total Pages: 355

ISBN-13: 9813362928

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This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin’s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin’s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.

Optimal Control and the Calculus of Variations
Optimal Control and the Calculus of Variations

Author: Enid R. Pinch

Publisher: Oxford University Press

Published: 1995

Total Pages: 245

ISBN-13: 0198514891

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A paperback edition of this successful textbook for final year undergraduate mathematicians and control engineering students, this book contains exercises and many worked examples, with complete solutions and hints making it ideal not only as a class textbook but also for individual study. Theintorduction to optimal control begins by considering the problem of minimizing a function of many variables, before moving on to the main subject: the optimal control of systems governed by ordinary differential equations.

Applications to Regular and Bang-Bang Control
Applications to Regular and Bang-Bang Control

Author: Nikolai P. Osmolovskii

Publisher: SIAM

Published: 2014-02-27

Total Pages: 389

ISBN-13: 1611972353

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A book devoted to second-order optimality conditions in the calculus of variations and optimal control, suitable for researchers and engineers.

Optimal Control
Optimal Control

Author: Arturo Locatelli

Publisher: Springer Science & Business Media

Published: 2001-03

Total Pages: 318

ISBN-13: 9783764364083

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From the reviews: "The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. . . .In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-to-read fashion." —Measurement and Control

Differential Equations, Chaos and Variational Problems
Differential Equations, Chaos and Variational Problems

Author: Vasile Staicu

Publisher: Springer Science & Business Media

Published: 2008-03-12

Total Pages: 436

ISBN-13: 3764384824

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This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Optimal Periodic Control
Optimal Periodic Control

Author: Fritz Colonius

Publisher: Springer

Published: 2006-11-15

Total Pages: 183

ISBN-13: 3540391703

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This research monograph deals with optimal periodic control problems for systems governed by ordinary and functional differential equations of retarded type. Particular attention is given to the problem of local properness, i.e. whether system performance can be improved by introducing periodic motions. Using either Ekeland's Variational Principle or optimization theory in Banach spaces, necessary optimality conditions are proved. In particular, complete proofs of second-order conditions are included and the result is used for various versions of the optimal periodic control problem. Furthermore a scenario for local properness (related to Hopf bifurcation) is drawn up, giving hints as to where to look for optimal periodic solutions. The book provides mathematically rigorous proofs for results which are potentially of importance in chemical engineering and aerospace engineering.

Optimal Control Via Nonsmooth Analysis
Optimal Control Via Nonsmooth Analysis

Author: Philip Daniel Loewen

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 112

ISBN-13: 9780821869963

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This book provides a complete and unified treatment of deterministic problems of dynamic optimization, from the classical themes of the calculus of variations to the forefront of modern research in optimal control. At the heart of the presentation is nonsmooth analysis, a theory of local approximation developed over the last twenty years to provide useful first-order information about sets and functions lying beyond the reach of classical analysis. The book includes an intuitive and geometrically transparent approach to nonsmooth analysis, serving not only to introduce the basic ideas, but also to illuminate the calculations and derivations in the applied sections dealing with the calculus of variations and optimal control. Written in a lively, engaging style and stocked with numerous figures and practice problems, this book offers an ideal introduction to this vigorous field of current research. It is suitable as a graduate text for a one-semester course in optimal control or as a manual for self-study. Each chapter closes with a list of references to ease the reader's transition from active learner to contributing researcher.