Extended approaches based on Genetic Algorithms (GAs) for MIMO singular systems approximation

Abstract

In this paper we present an extension of three important model reduction techniques: namely, the stability equation, the modified pole clustering and the dominant modes methods for conventional (regular) systems to reduce complexity relating to high dimensionality of mathematical models representing physical, generalized (also called singular) systems. Combining these methods to Genetic Algorithms’ tools and exploiting a special representation base where a full order singular system is deflating into proper and improper subsystems, different natures of stable, optimal low order models are obtained. To show the effectiveness of the proposed algorithms, a numerical example is given, where six approximants are derived from a multi-input multi-output singular system. By the use of two optimal norms, the MOR errors are quantified and permits to conclude to the quality of the proposed reduced order models.

Keywords

Singular system model order reduction (MOR)Genetic Algorithms (GAs)stability equation modified pole clustering dominant modes norms ISE stability

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