Scalable positivity preserving model reduction using linear energy functions

In this paper, we explore positivity preserving model reduction. The reduction is performed by truncating the states of the original system without balancing in the classical sense. This may result in conservatism, however, this way the physical meaning of the individual states is preserved. The reduced order models can be obtained using simple matrix operations or using distributed optimization methods. Therefore, the developed algorithms can be applied to sparse large-scale systems.

[1]  Takayuki Ishizaki,et al.  Extraction of 1-dimensional reaction-diffusion structure in SISO linear dynamical networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

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

[3]  M. Khammash,et al.  The finite state projection algorithm for the solution of the chemical master equation. , 2006, The Journal of chemical physics.

[4]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[5]  Mi-Ching Tsai,et al.  Robust and Optimal Control , 2014 .

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

[7]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

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

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

[10]  H. Nicholson,et al.  On the structure of balanced and other principal representations of SISO systems , 1983 .

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

[12]  Brian D. O. Anderson,et al.  Singular perturbation approximation of balanced systems , 1989 .

[13]  Timo Reis,et al.  Positivity Preserving Model Reduction , 2009 .

[14]  Anders Rantzer,et al.  Distributed control of positive systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[15]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[16]  James Lam,et al.  Positivity-preserving H∞ model reduction for positive systems , 2011, Autom..