## International Journal of Differential Equations

- Int. J. Differ. Equ.
- Volume 2012 (2012), Article ID 173634, 18 pages.

### Direct Method for Resolution of Optimal Control Problem with Free Initial Condition

Louadj Kahina and Aidene Mohamed

#### Abstract

The theory of control analyzes the proprieties of commanded systems. Problems of optimal control (OC) have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle (Pontryagin et al., 1962) and dynamic programming (Bellman, 1963). For many of the problems of the optimal control theory (OCT), adequate solutions are found (Bryson and Yu-chi, 1969, Lee and Markus, 1967, Gabasov and Kirillova, 1977, 1978, 1980). Results of the theory were taken up in various fields of science, engineering, and economics. The present paper aims at extending the constructive methods of Balashevich et al., (2000) that were developed for the problems of optimal control with the bounded initial state is not fixed are considered.

#### Article information

**Source**

Int. J. Differ. Equ., Volume 2012 (2012), Article ID 173634, 18 pages.

**Dates**

Received: 22 September 2011

Accepted: 3 November 2011

First available in Project Euclid: 24 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ijde/1485226819

**Digital Object Identifier**

doi:10.1155/2012/173634

**Mathematical Reviews number (MathSciNet)**

MR2898147

**Zentralblatt MATH identifier**

1248.49043

#### Citation

Kahina, Louadj; Mohamed, Aidene. Direct Method for Resolution of Optimal Control Problem with Free Initial Condition. Int. J. Differ. Equ. 2012 (2012), Article ID 173634, 18 pages. doi:10.1155/2012/173634. https://projecteuclid.org/euclid.ijde/1485226819