Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 671869, 21 pages
Research Article

Nonlinear Nonconvex Optimization by Evolutionary Algorithms Applied to Robust Control

Computer and Systems Engineering Department, Faculty of Computer Engineering, University of Murcia, Campus de Espinardo, 30100 Murcia, Spain

Received 17 March 2009; Accepted 5 July 2009

Academic Editor: J. Rodellar

Copyright © 2009 Joaquín Cervera and Alfonso Baños. 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 focuses on the problem of automatic loop shaping in the context of robust control. More specifically in the framework given by Quantitative Feedback Theory (QFT), traditionally the search of an optimum design, a non convex and nonlinear optimization problem, is simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator and evolutionary optimization. The main idea in relation to previous work consists of the study of the use of fractional compensators, which give singular properties to automatically shape the open loop gain function with a minimum set of parameters, which is crucial for the success of evolutionary algorithms. Additional heuristics are proposed in order to guide evolutionary process towards close to optimum solutions, focusing on local optima avoidance.