Dario Paccagnan

Distributed computation of generalized Nash equilibria in quadratic aggregative games with affine coupling constraints

We analyse deterministic aggregative games, with large but finite number of players, that are subject to both local and coupling constraints. Firstly, we derive sufficient conditions for the existence of a generalized Nash equilibrium, by using the theory of variational inequalities together with the specific structure of the objective functions and constraints. Secondly, we present a coordination scheme, belonging to the class of asymmetric projection algorithms, and we prove that it converges R-linearly to a generalized Nash equilibrium. To this end, we extend the available results on asymmetric projection algorithms to our setting. Finally, we show that the proposed scheme can be implemented in a decentralized fashion and it is suitable for the analysis of large populations. Our theoretical results are applied to the problem of charging a fleet of plug-in electric vehicles, in the presence of capacity constraints coupling the individual demands.

On aggregative and mean field games with applications to electricity markets

We study the existence and uniqueness of Nash equilibria for a certain class of aggregative games with finite and possibly large number of players. Sufficient conditions for these are obtained using the theory of variational inequalities together with the specific structure of the objective functions. We further present an algorithm that converges to the Nash equilibrium in a decentralized fashion with provable guarantees. The theoretical results are applied to the problem of managing the charging of a large fleet of plug-in electric vehicles and the results are compared with the existing work.

On the range of feasible power trajectories for a population of thermostatically controlled loads

We study the potential of a population of thermostatically controlled loads to track desired power signals with provable guarantees. Based on connecting the temperature state of an individual device with its internal energy, we derive necessary conditions that a given power signal needs to satisfy in order for the aggregation of devices to track it using non-disruptive probabilistic switching control. Our derivation takes into account hybrid individual dynamics, an accurate continuous-time Markov chain model for the population dynamics and bounds on switching rates of individual devices. We illustrate the approach with case studies.