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

TL;DR

This paper introduces a geometric programming-based optimization framework for designing switching networks of positive linear systems, enabling efficient cost-effective stabilization and disturbance rejection in dynamic networks.

Contribution

It develops a novel geometric programming approach for optimal design of switching positive linear networks with cost functions, applicable to real-world problems like disease spread control.

Findings

Cost-optimal network design computed efficiently using geometric programming.

Framework applicable to networks with Markovian switching structures.

Demonstrated on a disease spread stabilization problem.

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.