Differential Equations and Nonlinear Mechanics
Volume 2007 (2007), Article ID 18735, 16 pages
Research Article

Optimal Control of Mechanical Systems

Vadim Azhmyakov

Departamento de Control Automatico, CINVESTAV, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico 07360, DF, Mexico

Received 7 February 2007; Accepted 10 May 2007

Academic Editor: John R. Cannon

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.


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.