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arXiv · 1504.02532

Optimal Design of Switched Networks of Positive Linear Systems via Geometric Programming

Masaki Ogura·Victor M. Preciado
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Abstract

In this paper, we propose an optimization framework to design a network of positive linear systems whose structure switches according to a Markov process. The optimization framework herein proposed allows the network designer to optimize the coupling elements of a directed network, as well as the dynamics of the nodes in order to maximize the stabilization rate of the network and/or the disturbance rejection against an exogenous input. The cost of implementing a particular network is modeled using posynomial cost functions, which allow for a wide variety of modeling options. In this context, we show that the cost-optimal network design can be efficiently found using geometric programming in polynomial time. We illustrate our results with a practical problem in network epidemiology, namely, the cost-optimal stabilization of the spread of a disease over a time-varying contact network.

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Masaki Ogura, Victor M. Preciado. 2015-04-10. Optimal Design of Switched Networks of Positive Linear Systems via Geometric Programming. https://doi.org/10.1109/tcns.2015.2489339

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