Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 526167, 19 pages
Research Article

Optimization of Parameters of Asymptotically Stable Systems

1Department of Electromechanical Engineering, Centre for Aerospace Science and Technologies, UBI, University of Beira Interior, Calçada Fonte do Lameiro, 6201-001 Covilhã, Portugal
2Scientific Area of Mathematics, ESTGV, Polytechnic Institute of Viseu, Campus Politécnico, 3504-510 Viseu, Portugal
3Department of Mathematics and Applications, School of Sciences, Centre of Physics, University of Minho, Campus de Gualtar, 4710-057 Braga, Portugal

Received 29 June 2010; Revised 14 November 2010; Accepted 26 January 2011

Academic Editor: Oded Gottlieb

Copyright © 2011 Anna Guerman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.