In a noncooperative dynamic game, multiple agents operating in a changing environment aim to optimize their utilities over an infinite time horizon. Time-varying environments allow to model more realistic scenarios (e.g., mobile devices equipped with batteries, wireless communications over a fading channel, etc.). However, solving a dynamic game is a difficult task that requires dealing with multiple coupled optimal control problems. We focus our analysis on a class of problems, named dynamic potential games, whose solution can be found through a single multivariate optimal control problem. Our analysis generalizes previous studies by considering that the set of environment's states and the set of players' actions are constrained, as it is required by most of the applications. We also show that the theoretical results are the natural extension of the analysis for static potential games. We apply the analysis and provide numerical methods to solve four key example problems, with different features each: i) energy demand control in a smartgrid network, ii) network flow optimization in which the relays have bounded link capacity and limited battery life, iii) uplink multiple access communication with users that have to optimize the use of their batteries, and iv) two optimal scheduling games with nonstationary channels.

Abstract-Demand-side management presents significant benefits in reducing the energy load in smart grids by balancing consumption demands or including energy generation and/or storage devices in the user's side. These techniques coordinate the energy load so that users minimize their monetary expenditure. However, these methods require accurate predictions in the energy consumption profiles, which make them inflexible to real demand variations. In this paper we propose a realistic model that accounts for uncertainty in these variations and calculates a robust price for all users in the smart grid. We analyze the existence of solutions for this novel scenario, propose convergent distributed algorithms to find them, and perform simulations considering energy expenditure. We show that this model can effectively reduce the monetary expenses for all users in a realtime market, while at the same time it provides a reliable production cost estimate to the energy supplier.

Abstract-Doubly-stochastic matrices are usually required by consensus-based distributed algorithms. We propose a simple and efficient protocol and present some guidelines for implementing doubly-stochastic combination matrices even in noisy, asynchronous and changing topology scenarios. The proposed ideas are validated with the deployment of a wireless sensor network, in which nodes run a distributed algorithm for robust estimation in the presence of nodes with faulty sensors.

Optimum scheduling is a key objective in many communications systems where different users have to share a common resource. Typically, centralized implementations are capable of guaranteeing certain fairness. In our approach, we follow a different path modeling the scheduling process as a dynamic infinite horizon discrete-time game. This formulation allows us to include any kind of dynamics and distributed implementations. Despite, these games are very difficult to solve, we are able to show that they are in fact dynamic potential games equivalent to a non-stationary multivariate optimum control problem. The dynamic control problem is solved via an augmented Bellman equation including time as an extra state.

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