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Mathematical Problems in Engineering
Volume 2010, Article ID 978736, 13 pages
Research Article

On a Variational Approach to Optimization of Hybrid Mechanical Systems

Departamento de Control Automatico, CINVESTAV, A.P. 14-740, Avenue Instituto Politecnico Nacional No. 2508, 07360 Mexico DF, Mexico

Received 9 December 2009; Accepted 27 May 2010

Academic Editor: Katica R. (Stevanovic) Hedrih

Copyright © 2010 Vadim Azhmyakov and Ruben Velazquez. 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.


This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical” problem to an auxiliary multiobjective programming reformulation. This approach motivates possible applications of theoretical and computational results from multiobjective optimization related to the original dynamical optimization problem. We consider first order optimality conditions for optimal control problems governed by hybrid mechanical systems and also discuss some conceptual algorithms.