Optimal Control of Mechanical Systems

Differential Equations and Nonlinear Mechanics. 2007;2007 DOI 10.1155/2007/18735


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Journal Title: Differential Equations and Nonlinear Mechanics

ISSN: 1687-4099 (Print); 1687-4102 (Online)

Publisher: Hindawi Publishing Corporation

LCC Subject Category: Technology: Engineering (General). Civil engineering (General) | Science: Mathematics



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



Abstract | Full Text

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.