Biblio

We analyze the stability properties of a susceptible-infected-susceptible diffusion model over directed networks. Similar to the majority of infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the all-healthy state is globally asymptotically stable (GAS). Otherwise, an endemic state arises and the entire network could become infected. Using notions from positive systems theory, we prove that the endemic state is GAS in strongly connected networks. When the graph is weakly connected, we provide conditions for the existence, uniqueness, and global asymptotic stability of weak and strong endemic states. Several simulations demonstrate our results.

We study the problem of aggregator’s mechanism design for controlling the amount of active, or reactive, power provided, or consumed, by a group of distributed energy resources (DERs). The aggregator interacts with the wholesale electricity market and through some market-clearing mechanism is incentivized to provide (or consume) a certain amount of active (or reactive) power over some period of time, for which it will be compensated. The objective is for the aggregator to design a pricing strategy for incentivizing DERs to modify their active (or reactive) power consumptions (or productions) so that they collectively provide the amount that the aggregator has agreed to provide. The aggregator and DERs’ strategic decision-making process can be cast as a Stackelberg game, in which aggregator acts as the leader and the DERs are the followers. In previous work [Gharesifard et al., 2013b,a], we have introduced a framework in which each DER uses the pricing information provided by the aggregator and some estimate of the average energy that neighboring DERs can provide to compute a Nash equilibrium solution in a distributed manner. Here, we focus on the interplay between the aggregator’s decision-making process and the DERs’ decision-making process. In particular, we propose a simple feedback-based privacy-preserving pricing control strategy that allows the aggregator to coordinate the DERs so that they collectively provide the amount of active (or reactive) power agreed upon, provided that there is enough capacity available among the DERs. We provide a formal analysis of the stability of the resulting closed-loop system. We also discuss the shortcomings of the proposed pricing strategy, and propose some avenues of future work. We illustrate the proposed strategy via numerical simulations.

In this work, we analyze the stability properties of a recently proposed dynamical system that describes the evolution of the probability of infection in a network. We show that this model can be viewed as a concave game among the nodes. This characterization allows us to provide a simple condition, that can be checked in a distributed fashion, for stabilizing the origin. When the curing rates at the nodes are low, a residual infection stays within the network. Using properties of Hurwitz Mertzel matrices, we show that the residual epidemic state is locally exponentially stable. We also demonstrate that this state is globally asymptotically stable. Furthermore, we investigate the problem of stabilizing the network when the curing rates of a limited number of nodes can be controlled. In particular, we characterize the number of controllers required for a class of undirected graphs. Several simulations demonstrate our results.