Enid R. Pinch

Optimal Control and the Calculus of Variations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. The intorduction 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.

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Produktdetails

• Verlag: Oxford University Press
• Erscheinungstermin: 18. März 1993
• Englisch
• ISBN-13: 9780191590498
• Artikelnr.: 54582105

Inhaltsangabe

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