Differential Equations and Nonlinear Mechanics 
Volume 2007 (2007), Article ID 18735, 16 pages
doi:10.1155/2007/18735
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

Recommended by John R. Cannon

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.