Differential Equations and Nonlinear Mechanics

Optimal Control of Mechanical Systems

Vadim Azhmyakov

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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.

Article information

Source
Differ. Equ. Nonlinear Mech., Volume 2007 (2007), Article ID 018735, 16 pages.

Dates
Received: 7 February 2007
Accepted: 10 May 2007
First available in Project Euclid: 26 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485399783

Digital Object Identifier
doi:10.1155/2007/18735

Mathematical Reviews number (MathSciNet)
MR2336263

Zentralblatt MATH identifier
1135.70010

Citation

Azhmyakov, Vadim. Optimal Control of Mechanical Systems. Differ. Equ. Nonlinear Mech. 2007 (2007), Article ID 018735, 16 pages. doi:10.1155/2007/18735. https://projecteuclid.org/euclid.ijde/1485399783


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