TY - GEN

T1 - An inverse problem of tomographic type in population dynamics

AU - Zeng, Shen

AU - Waldherr, Steffen

AU - Allgower, Frank

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2014

Y1 - 2014

N2 - In this paper we address an inverse problem on populations described by probability distributions. From a theoretical point of view, this problem can be seen as a natural extension to the classical observability problem. We consider a population that is described by a classical linear finite-dimensional system in which the initial state is a random vector subject to a non-parametric probability distribution. The problem is to reconstruct this initial state distribution from the time-evolution of the probability distribution of the output. We reveal as a novel viewpoint, that, at its core, this problem is a tomography problem which is a well-known subject in the field of inverse problems. Furthermore we show how this tomography problem is inherently linked with the observability properties of the finite-dimensional system thereby establishing a beautiful link between a control theoretic question and tomography problems.

AB - In this paper we address an inverse problem on populations described by probability distributions. From a theoretical point of view, this problem can be seen as a natural extension to the classical observability problem. We consider a population that is described by a classical linear finite-dimensional system in which the initial state is a random vector subject to a non-parametric probability distribution. The problem is to reconstruct this initial state distribution from the time-evolution of the probability distribution of the output. We reveal as a novel viewpoint, that, at its core, this problem is a tomography problem which is a well-known subject in the field of inverse problems. Furthermore we show how this tomography problem is inherently linked with the observability properties of the finite-dimensional system thereby establishing a beautiful link between a control theoretic question and tomography problems.

UR - http://www.scopus.com/inward/record.url?scp=84988299746&partnerID=8YFLogxK

U2 - 10.1109/CDC.2014.7039635

DO - 10.1109/CDC.2014.7039635

M3 - Conference contribution

AN - SCOPUS:84988299746

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1643

EP - 1648

BT - 53rd IEEE Conference on Decision and Control,CDC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014

Y2 - 15 December 2014 through 17 December 2014

ER -