Biblio

We show that competitive engagements within the agents of a network can result in resilience in consensus dynamics with respect to the presence of an adversary. We first show that interconnections with an adversary, with linear dynamics, can make the consensus dynamics diverge, or drive its evolution to a state different from the average.We then introduce a second network, interconnected with the original network via an engagement topology. This network has no information about the adversary and each agent in it has only access to partial information about the state of the other network. We introduce a dynamics on the coupled network which corresponds to a saddle-point dynamics of a certain zero-sum game and is distributed over each network, as well as the engagement topology. We show that, by appropriately choosing a design parameter corresponding to the competition between these two networks, the coupled dynamics can be made resilient with respect to the presence of the adversary.Our technical approach combines notions of graph theory and stable perturbations of nonsymmetric matrices.We demonstrate our results on an example of kinematic-based flocking in presence of an adversary.

We introduce a framework for controlling the energy provided or absorbed by distributed energy resources (DERs) in power distribution networks. In this framework, there is a set of agents referred to as aggregators that interact with the wholesale electricity market, and through some market-clearing mechanism, are requested (and will be compensated for) to provide (or absorb) certain amount of active (or reactive) power over some period of time. In order to fulfill the request, each aggregator interacts with a set of DERs and offers them some price per unit of active (or reactive) power they provide (or absorb); the objective is for the aggregator to design a pricing strategy for incentivizing DERs to change its active (or reactive) power consumption (or production) so as they collectively provide the amount that the aggregator has been asked for. In order to make a decision, each DER uses the price information provided by the aggregator and some estimate of the average active (or reactive) power that neighboring DERs can provide computed through some exchange of information among them; this exchange is described by a connected undirected graph. The focus is on the DER strategic decision-making process, which we cast as a game. In this context, we provide sufficient conditions on the aggregator's pricing strategy under which this game has a unique Nash equilibrium. Then, we propose a distributed iterative algorithm that adheres to the graph that describes the exchange of information between DERs that allows them to seek for this Nash equilibrium. We illustrate our results through several numerical simulations.

We introduce a framework for controlling the charging and discharging processes of plug-in electric vehicles (PEVs) via pricing strategies. Our framework consists of a hierarchical decision-making setting with two layers, which we refer to as aggregator layer and retail market layer. In the aggregator layer, there is a set of aggregators that are requested (and will be compensated for) to provide certain amount of energy over a period of time. In the retail market layer, the aggregator offers some price for the energy that PEVs may provide; the objective is to choose a pricing strategy to incentivize the PEVs so as they collectively provide the amount of energy that the aggregator has been asked for. The focus of this paper is on the decision-making process that takes places in the retail market layer, where we assume that each individual PEV is a price-anticipating decision-maker. We cast this decision-making process as a game, and provide conditions on the pricing strategy of the aggregator under which this game has a unique Nash equilibrium. We propose a distributed consensus-based iterative algorithm through which the PEVs can seek for this Nash equilibrium. Numerical simulations are included to illustrate our results.