Selection of reduction parameters of Rational Krylov methods for complex MIMO LTI models using evolutionary algorithm

This paper presents the determination of optimal reduction parameters for complex models of the Rational Krylov methods with using Evolutionary Algorithm. The presented algorithms facilitate a precise reduction of linear time invariant, multi-input and multi-output models. The elaborated algorithms are particularly significant for MIMO models, for which the individual channels differ significantly from each other. The prepared algorithms have been applied for the reduction of the subsystems models of a BP-1150 steam boiler.

[1]  PJ Pieter Heres,et al.  Robust and Efficient Krylov Subspace Methods for Model Order Reduction , 2005 .

[2]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[3]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[4]  Eduardo Gildin,et al.  Model and controller reduction of large-scale structures based on projection methods , 2006 .

[5]  Daniel Boley.  Krylov space methods on state-space control models , 1994 .

[6]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[7]  Marek Rydel,et al.  Hierarchical mathematical models of complex plants on the basis of power boiler example , 2010 .

[8]  Thomas Wolf,et al.  ℌ2 pseudo-optimality in model order reduction by Krylov subspace methods , 2013, 2013 European Control Conference (ECC).

[9]  A. Antoulas,et al.  A comparative study of 7 algorithms for model reduction , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  Tong Zhang,et al.  Two-Sided Arnoldi and Nonsymmetric Lanczos Algorithms , 2002, SIAM J. Matrix Anal. Appl..

[11]  A. Antoulas,et al.  H 2 Model Reduction for Large-scale Linear Dynamical Systems * , 2022 .

[12]  Serkan Gugercin,et al.  H2 Model Reduction for Large-Scale Linear Dynamical Systems , 2008, SIAM J. Matrix Anal. Appl..

[13]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[14]  Eric James Grimme,et al.  Krylov Projection Methods for Model Reduction , 1997 .

[15]  B. Lohmann,et al.  Structure Preserving Order Reduction of Large Scale Second Order Systems , 2004 .

[16]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[17]  Paul Van Dooren,et al.  H2-optimal model reduction of MIMO systems , 2008, Appl. Math. Lett..