Back to Search
Start Over
Clustered model reduction of positive directed networks
- Source :
- Automatica, Automatica, Elsevier, 2015, 59, pp.238-247. ⟨10.1016/j.automatica.2015.06.027⟩
- Publication Year :
- 2015
- Publisher :
- Elsevier BV, 2015.
-
Abstract
- International audience; This paper proposes a clustered model reduction method for semistable positive linear systems evolving over directed networks. In this method, we construct a set of clusters, i.e., disjoint sets of state variables, based on a notion of cluster reducibility, defined as the uncontrollability of local states. By aggregating the reducible clusters with aggregation coefficients associated with the Frobenius eigenvector, we obtain an approximate model that preserves not only a network structure among clusters, but also several fundamental properties, such as semistability, positivity, and steady state characteristics. Furthermore, it is found that the cluster reducibility can be characterized for semistable systems based on a projected controllability Gramian that leads to an a priori H2-error bound of the state discrepancy caused by aggregation. The efficiency of the proposed method is demonstrated through an illustrative example of enzyme-catalyzed reaction systems described by a chemical master equation. This captures the time evolution of chemical reaction systems in terms of a set of ordinary differential equations.
- Subjects :
- 0209 industrial biotechnology
State variable
Reduction (recursion theory)
010103 numerical & computational mathematics
02 engineering and technology
Disjoint sets
01 natural sciences
[SPI.AUTO]Engineering Sciences [physics]/Automatic
020901 industrial engineering & automation
Master equation
[INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY]
Applied mathematics
0101 mathematics
Electrical and Electronic Engineering
Mathematics
Discrete mathematics
Model reduction
Controllability Gramian
Linear system
Chemical master equations
State (functional analysis)
Positive linear systems
Control and Systems Engineering
Ordinary differential equation
Network clustering
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Subjects
Details
- ISSN :
- 00051098
- Volume :
- 59
- Database :
- OpenAIRE
- Journal :
- Automatica
- Accession number :
- edsair.doi.dedup.....711a003f1a528b9b420a6ae4b472337b
- Full Text :
- https://doi.org/10.1016/j.automatica.2015.06.027