Paper Info
Title
Identification of Sparse Continuous-Time Linear Systems with Low Sampling Rate: Exploring Matrix Logarithms.
Abstract
A continuous time linear dynamic in state space form has an $A$-matrix that reveals the connection between the states. Many dynamical systems allow a a sparse structure for this matrix. This means that the right-hand sides of the dynamical equations depend only on a subset of the states. If the system is unknown, one can try to identify it from data samples. This paper addresses identification of such sparse continuous time dynamical systems. We consider linear noise-driven dynamical systems evolving in continuous time. The assumption is that the sampling period is not small enough to apply methods where the continuous time system is identified directly from data. Instead a discrete time system is inferred in an intermediate step. Due to aliasing, different branches of the matrix logarithm might provide different degree of sparsity. We shed light on this issue, which has largely been overlooked in the community before and provide theoretical results for when a unique solution exists up to a finite equivalence class. We also provide a mixed integer linear programming formulation corresponding to a simplified version of our problem.
Year
Venue
Field
2016
arXiv: Systems and Control
Linear dynamical system,Mathematical optimization,Linear system,Control theory,Matrix (mathematics),State-space representation,Dynamical systems theory,State-transition matrix,Logarithm,Logarithm of a matrix,Mathematics
DocType
Volume
Citations 
Journal
abs/1605.08590
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Zuogong Yue101.35
Johan Thunberg213819.15
Lennart Ljung31993270.89
Jorge M. Gonçalves45119.23