Optimal Control and the Calculus of Variations - Brossura

Pinch, Enid R.

Brossura

ISBN 10: 0198514891 ISBN 13: 9780198514893

Casa editrice: Oxford University Press, USA, 1995

Riassunto

Optimal control is a modern development of the calculus of variations and classical optimization theory. For that reason, this introduction to the theory of optimal control starts by considering the problem of minimizing a function of many variables. It moves through an exposition of the calculus of variations, to the optimal control of systems governed by ordinary differential equations. This approach should enable students to see the essential unity of important areas of mathematics, and also allow optimal control and the Pontryagin maximum principle to be placed in a proper context. Although this book is written for the advanced undergraduate mathematician, engineers and scientists who regularly rely on mathematics will also find it a useful text.

Su questo libro

L'autore

Enid R. Pinch is at University of Manchester.

Contenuti

• 1: Introduction
• 1.1: The maxima and minima of functions
• 1.2: The calculus of variations
• 1.3: Optimal control
• Part 2: Optimization in
• 2.1: Functions of one variable
• 2.2: Critical points, end-points, and points of discontinuity
• 2.3: Functions of several variables
• 2.4: Minimization with constraints
• 2.5: A geometrical interpretation
• 2.6: Distinguishing maxima from minima
• Part 3: The calculus of variations
• 3.1: Problems in which the end-points are not fixed
• 3.2: Finding minimizing curves
• 3.3: Isoperimetric problems
• 3.4: Sufficiency conditions
• 3.5: Fields of extremals
• 3.6: Hilbert's invariant integral
• 3.7: Semi-fields and the Jacobi condition
• Part 4: Optimal Control I: Theory
• 4.1: Introduction
• 4.2: Control of a simple first-order system
• 4.3: Systems governed by ordinary differential equations
• 4.4: The optimal control problem
• 4.5: The Pontryagin maximum principle
• 4.6: Optimal control to target curves
• Part 5: Optimal Control II: Applications
• 5.1: Time-optimal control of linear systems
• 5.2: Optimal control to target curves
• 5.3: Singular controls
• 5.4: Fuel-optimal controls
• 5.5: Problems where the cost depends on X (t l)
• 5.6: Linear systems with quadratic cost
• 5.7: The steady-state Riccai equation
• 5.8: The calculus of variations revisited
• Part 6: Proof of the Maximum Principle of Pontryagin
• 6.1: Convex sets in
• 6.2: The linearized state equations
• 6.3: Behaviour of H on an optimal path
• 6.4: Sufficiency conditions for optimal control
• Appendix: Answers and hints for the exercises
• Bibliography
• Index

Dettagli dell?edizione

• Editore: Oxford University Press, USA
• Data di pubblicazione: 1995
• ISBN 10: 0198514891
• ISBN 13: 9780198514893
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 244
• Contatto del produttore: non disponibile