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October  2008, 4(4): 697-712. doi: 10.3934/jimo.2008.4.697

An approach to controlled mechanical systems based on the multiobjective optimization technique

Vadim Azhmyakov 1,

1. 

Departamento de Control Automatico, CINVESTAV,, A.P. 14-740, CP 07000, Mexico D.F., Mexico

Received  November 2007 Revised  June 2008 Published  November 2008

This paper discusses the multiobjective optimization techniques for a class of optimal control problems in mechanics. We deal with constrained nonlinear control systems described by the Euler-Lagrange or Hamilton equations and study the variational structure of the solution of the corresponding boundary-value problems. We also reduce the original ''mechanical'' problem to an auxiliary multiobjective optimization problem. This approach makes it possible to apply the effective theoretical and computational results from multiobjective programming to the original problem. We consider first order computational schemes for optimal control problems governed by mechanical systems and examine some illustrative examples.
Keywords: multiobjective optimization., Optimal control, mechanical systems, nonlinear systems.
Mathematics Subject Classification: Primary: 70Q05; Secondary: 49S0.
Citation: Vadim Azhmyakov. An approach to controlled mechanical systems based on the multiobjective optimization technique. Journal of Industrial and Management Optimization, 2008, 4 (4) : 697-712. doi: 10.3934/jimo.2008.4.697
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