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

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.

Accepted for publications in IEEE Transactions on Control of Network Systems

References in corpus (2)

• Disease spread over randomly switched large-scale networks
• Cost-Optimal Switching Protection Strategy in Adaptive Networks

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• Second-Order Moment-Closure for Tighter Epidemic Thresholds
• Katz Centrality of Markovian Temporal Networks: Analysis and Optimization
• Cost-Optimal Switching Protection Strategy in Adaptive Networks
• Geometric Programming for Optimal Positive Linear Systems
• Resource Allocation for Containing Epidemics from Temporal Network Data
• Resource Optimization of Product Development Projects with Time-Varying Dependency Structure