Calculus of variations and optimal control theory

Calculus of Variations to Optimal Control: A short Introduction

Optimal control problems in some sense can be viewed as dynamic optimization and hence it is considered as a generalization of the classical calculus of variations (CV). The subject CV is a pretty old subject (250 years or so) and it is motivated by well known problems from science and engineering. Some of the fundamental example are: Brachistochrone problem due to Johann Bernoulli in the late ...

Some Applications of Bv Functions in Optimal Control and Calculus of Variations 1 a Problem of Calculus of Variations

In this paper we discuss the use of bounded variation functions in the study of some optimal control problems as well as in the calculus of variations. The bounded variation functions are well adapted to the study of parameter identiication problems, such as the coeecients of an elliptic or parabolic operator. These functions are also convenient for the image recovery problems. These problems a...

Comments on Chapters 20 and 21 ( Calculus of Variations and Optimal Control Theory ) of ” Introduction to Mathematical Economics ” ( third edition

The textbook ”Introduction to Mathematical Economics” (third edition, 2008) by E.T. Dowling, ISBN 0-07-135896 (henceforth IME) is intended for economics and business students who seek to enrich their knowledge of mathematics in sofar as it is immediately applicable to economic and business problems in academics. In this connection IME can be used both for self-study or as a supplement to other ...

Carathéodory-Equivalence, Noether Theorems, and Tonelli Full-Regularity in the Calculus of Variations and Optimal Control

Carathéodory-Equivalence, Noether Theorems, and Tonelli Full-Regularity in the Calculus of Variations and Optimal Control

We study, in a unified way, the following questions related to the properties of Pontryagin extremals for optimal control problems with unrestricted controls: i) How the transformations, which define the equivalence of two problems, transform the extremals? ii) How to obtain quantities which are conserved along any extremal? iii) How to assure that the set of extremals include the minimizers pr...