Optimal L⁸ Model reduction using genetic algorithms

Abstract

In this paper, we are concerned with the solution of optimal L⁸ model‐reduction problems using genetic algorithms (GAs). More precisely, we present an approach to facilitate using GAs to effectively search optimal reduced‐order models for high‐order linear time‐invariant systems such that the L⁸ ‐norm of approximation error is minimized. The proposed approach has the following distinct features: (i) the parameter space for GA search is bounded; (ii) the finite and infinite zero structures, as well as the stability of the original system is retained in the reduced‐order models; and (ii) the GA solution accuracy can be greatly enhanced. The first two features are achieved through representing a reduced‐order model in a transfer function parameterized in terms of Schur and anti‐Schur polynomials, whereas the third feature is gained by using schemes of region contraction and local improvement.

Key words:

• Genetic Algorithms
• Model Reduction
• Optimization

Notes

Correspondence addressee