Nonlinear nonconvex optimization by evolutionary algorithms applied to robust control.

*(English)*Zbl 1181.90220Summary: 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.

##### MSC:

90C26 | Nonconvex programming, global optimization |

90C59 | Approximation methods and heuristics in mathematical programming |

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\textit{J. Cervera} and \textit{A. Baños}, Math. Probl. Eng. 2009, Article ID 671869, 21 p. (2009; Zbl 1181.90220)

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