Javier Zazo

Robust Worst-Case Analysis of Demand-Side Management in Smart Grids

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 real-time market, while at the same time it provides a reliable production cost estimate to the energy supplier.

Underwater Electromagnetic Sensor Networks, Part II: Localization and Network Simulations

In the first part of the paper, we modeled and characterized the underwater radio channel in shallow waters. In the second part, we analyze the application requirements for an underwater wireless sensor network (U-WSN) operating in the same environment and perform detailed simulations. We consider two localization applications, namely self-localization and navigation aid, and propose algorithms that work well under the specific constraints associated with U-WSN, namely low connectivity, low data rates and high packet loss probability. We propose an algorithm where the sensor nodes collaboratively estimate their unknown positions in the network using a low number of anchor nodes and distance measurements from the underwater channel. Once the network has been self-located, we consider a node estimating its position for underwater navigation communicating with neighboring nodes. We also propose a communication system and simulate the whole electromagnetic U-WSN in the Castalia simulator to evaluate the network performance, including propagation impairments (e.g., noise, interference), radio parameters (e.g., modulation scheme, bandwidth, transmit power), hardware limitations (e.g., clock drift, transmission buffer) and complete MAC and routing protocols. We also explain the changes that have to be done to Castalia in order to perform the simulations. In addition, we propose a parametric model of the communication channel that matches well with the results from the first part of this paper. Finally, we provide simulation results for some illustrative scenarios.

A new framework for solving dynamic scheduling games

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.

Learning in constrained stochastic dynamic potential games

We extend earlier works on continuous potential games to the most general case: stochastic time varying environment, stochastic rewards, non-reduced form and constrained state-action sets. We provide conditions for a Markov Nash equilibrium (MNE) of the game to be equivalent to the solution of a single control problem. Then, we address the problem of learning this MNE when the reward and state transition models are unknown. We follow a reinforcement learning approach and extend previous algorithms for working with constrained state-action subsets of real vector spaces. As an application example, we simulate a network flow optimization model, in which the relays have batteries that deplete with a random factor. The results obtained with the proposed framework are close to optimal.

How to implement doubly-stochastic matrices for consensus-based distributed algorithms

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.

Non-monotone quadratic potential games with single quadratic constraints

We consider the problem of solving a quadratic potential game with single quadratic constraints, under no monotonicity condition of the game, nor convexity in any of the players problem. We show existence of Nash equilibria (NE) in the game, and propose a framework to calculate Pareto efficient solutions. Regarding the corresponding non-convex potential function, we show that strong duality holds with its corresponding dual problem, give existence results of solutions and present conditions for global optimality. Finally, we propose a centralized method to solve the potential problem, and a distributed version for compact constraints. We also present simulations showing convergence behavior of the proposed distributed algorithm.

A new approach for solving anti-jamming games in stochastic scenarios as pursuit-evasion games

We solve a communication problem between a UAV and a set of relays, in the presence of a jamming UAV, using differential game theory tools. The standard solution involves a set of coupled Bellman equations which are hard to solve. We propose a new approach in which this kind of games can be approximated as pursuit-evasion games. The problem is posed in terms of optimizing capacity and it is approximated as a zero-sum, pursuit-evasion game. This game is solved using a set of differential equations known as Isaacs equations and simulations are run in order to validate the results.

Optimal attack and defence of large scale networks using mean field theory

We address the issue of large scale network security. It is known that traditional game theory becomes intractable when considering a large number of players, which is a realistic situation in todays networks where a centralized administration is not available. We propose a new model, based on mean field theory, that allows us to obtain optimal decentralised defence policy for any node in the network and optimal attack policy for an attacker. In this way we settle a promising framework for the development of a mean field game theory of large scale network security. We also present a case study with experimental results.

Distributed black-box optimization of nonconvex functions

We combine model-based methods and distributed stochastic approximation to propose a fully distributed algorithm for nonconvex optimization, with good empirical performance and convergence guarantees. Neither the expression of the objective nor its gradient are known. Instead, the objective is like a “black-box”, in which the agents input candidate solutions and evaluate the output. Without central coordination, the distributed algorithm naturally balances the computational load among the agents. This is especially relevant when many samples are needed (e.g., for high-dimensional objectives) or when evaluating each sample is costly. Numerical experiments over a difficult benchmark show that the networked agents match the performance of a centralized architecture, being able to approach the global optimum, while none of the individual noncooperative agents could by itself.