International Journal of Differential Equations

International Journal of Differential Equations / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 018735 | https://doi.org/10.1155/2007/18735

Vadim Azhmyakov, "Optimal Control of Mechanical Systems", International Journal of Differential Equations, vol. 2007, Article ID 018735, 16 pages, 2007. https://doi.org/10.1155/2007/18735

Optimal Control of Mechanical Systems

Academic Editor: John R. Cannon
Received07 Feb 2007
Accepted10 May 2007
Published22 Aug 2007

Abstract

In the present work, we consider a class of nonlinear optimal control problems, which can be called “optimal control problems in mechanics.” We deal with control systems whose dynamics can be described by a system of Euler-Lagrange or Hamilton equations. Using the variational structure of the solution of the corresponding boundary-value problems, we reduce the initial optimal control problem to an auxiliary problem of multiobjective programming. This technique makes it possible to apply some consistent numerical approximations of a multiobjective optimization problem to the initial optimal control problem. For solving the auxiliary problem, we propose an implementable numerical algorithm.

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Copyright © 2007 Vadim Azhmyakov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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