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Optimal Control

Part of the Modern Birkhäuser Classics Book Series

DOI: 10.1007/978-0-8176-8086-2

ISBN: 978-0-8176-4990-6

Publisher: Birkhäuser Boston - Springer Journals

Jun 12, 2010

1 - 10 of 12 Chapters

LitStream

Chapter 1Overview

Vinter, Richard

Pages: 1 –60

[Optimal Control emerged as a distinct field of research in the 1950s, to address in a unified fashion optimization problems arising in scheduling and the control of engineering devices, beyond the reach of traditional analytical and computational techniques. Aerospace engineering is an important...
LitStream

Chapter 2Measurable Multifunctions and Differential Inclusions

Vinter, Richard

Pages: 61 –108

[Differential inclusions 2.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}...
LitStream

Chapter 3Variational Principles

Vinter, Richard

Pages: 109 –126

[The Name “variational principle” is traditionally attached to a law of nature asserting that some quantity is minimized. Examples are Dirichlet’s Principle (the spatial distribution of an electrostatic field minimizes some quadratic functional), Fermat’s Principle (a light ray follows a shortest...
LitStream

Chapter 4Nonsmooth Analysis

Vinter, Richard

Pages: 127 –177

[Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar x \in...
LitStream

Chapter 5Subdifferential Calculus

Vinter, Richard

Pages: 179 –199

[In this chapter, we assemble a number of useful for calculating and estimating the limiting subdifferentials of composite functions in terms of their constituent mappings.]
LitStream

Chapter 6The Maximum Principle

Vinter, Richard

Pages: 201 –231

[This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al. was after all the...
LitStream

Chapter 7The Extended Euler–Lagrange and Hamilton Conditions

Vinter, Richard

Pages: 233 –284

[The distinguishing feature of optimal control problems, as compared with traditional variational problems is the presence of constraints on the velocity variable.]
LitStream

Chapter 8Necessary Conditions for Free End-Time Problems

Vinter, Richard

Pages: 285 –319

[Our investigation of the properties of optimal strategies has, up till now, been confined to optimal control problems for which the underlying time interval [S,T] has been fixed.]
LitStream

Chapter 9The Maximum Principle for State Constrained Problems

Vinter, Richard

Pages: 321 –360

[In this chapter, we return to the framework of Chapter 6, in which the dynamic constraint takes the form of a differential equation parameterized by control functions. Our goal is to extend the earlier derived necessary conditions of optimality, in the form of a Maximum Principle, to allow for...
LitStream

Chapter 10Necessary Conditions for Differential Inclusion Problems with State Constraints

Vinter, Richard

Pages: 361 –396

[In this, chapter we continue our investigation of necessary conditions for optimal control problems with pathwise state constraints. Now, however, the class of optimal control problems considered is one in which the dynamic constraint is formulated as a differential inclusion.]

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