ABSTRACT

This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.

chapter 1|33 pages

The Basic Problem

chapter 2|24 pages

Piecewise-Smooth Extremals

chapter 3|27 pages

Modifications of the Basic Problem

chapter 4|28 pages

A Weak Minimum

chapter 5|26 pages

A Strong Minimum

chapter 6|28 pages

The Hamiltonian

chapter 7|31 pages

Lagrangian Mechanics

chapter 8|35 pages

Direct Methods

chapter 9|33 pages

Dynamic Programming

chapter 10|43 pages

Isoperimetric Constraints

chapter 11|29 pages

Pointwise Constraints on Extremals

chapter 12|34 pages

Nonholonomic Constraints

chapter 13|33 pages

Optimal Control with Linear Dynamics

chapter 14|46 pages

Optimal Control with General Lagrangians

chapter 15|41 pages

Several Independent Variables

chapter 16|41 pages

Linear Theory of Elasticity

chapter 17|39 pages

Plate Theory

chapter 18|27 pages

Fluid Mechanics