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Optimal Control of Mechanical Systems

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  • Vadim Azhmyakov

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.

Suggested Citation

  • Vadim Azhmyakov, 2007. "Optimal Control of Mechanical Systems," International Journal of Differential Equations, Hindawi, vol. 2007, pages 1-16, August.
    • Handle: RePEc:hin:jnijde:018735
    DOI: 10.1155/2007/18735
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