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.

In the first part of the paper, we modeled and characterized the underwater radio channel in shallowwaters. In the second part,we analyze the application requirements for an underwaterwireless 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.

Zazo Ruiz, Javier (2017). Nonconvex quadratic problems and games with separable constraints. Thesis (Doctoral), E.T.S.I. Telecomunicación (UPM). https://doi.org/10.20868/UPM.thesis.47855. Quadratic programs are generally hard and difficult to solve, where many instances are known to be NP-hard. However, there are some few cases in which the quadratic problem has some hidden convexity and there are methods to solve the problems optimally in polynomial time. When this occurs, we say that strong duality holds, and that the primal problem has zero gap with its dual counterpart. We study this property in nonconvex quadratic problems with separable constraints. We exploit the disjoint structure of the constraints to analyze when strong duality may occur. We consider problems that may have both inequality or equality quadratic constraints, and we provide sufficient conditions that guarantee zero duality gap. Our results consider any number of constraints as long as they do not overlap between each other. In addition to these results, we propose two distributed algorithms that aim to solve the quadratic problem optimally whenever the strong duality holds. The first proposal uses a dual formulation and convergence relies on gradient or subgradient methods, depending on the nature of the problem. The second proposal uses a modern decomposition technique from the literature called NOVA and uses successive convex approximations to converge to the optimal solution, which is generally considered faster than first order methods. We then study two localization problems with ranged measurements. We reformulate them as nonconvex quadratic problems with quadratic constraints and explore their solutions. We refer to the first one as target localization and propose several distributed methods based on primal descent as well as dual ascent methods. On the one hand, descent methods assume the nonconvexity of the localization problem and may converge to local solutions if the number of measuring nodes is small. They are however fast and require little communication. On the other hand, dual ascent methods aim to solve the localization problem optimally assuming that there is zero duality gap between the primal and dual problem. The second localization problem we consider is the sensor network localization problem in which a set of nodes try to locate themselves having distance measurements between each other. This is a harder problem, and as before, we propose both distributed methods based on descent techniques as well as based in a dual decomposition. Finally, we also study the connection of nonconvex quadratic optimization with Nash equilibria in game theory. In order to do so, we propose a robust demand-side management problem in a smart grid, where the agents try to minimize their monetary expenditure. Because there is uncertainty in the real-time energy demand, the cost of energy is prone to variations and a robust model that attends to a worst-case scenario is proposed. This formulation is presented as a min-max game where the maximization game is nonconvex and where the agents have coupled constraints. We study this game and propose a distributed scheme with convergence guarantees to the NE of the game. We also study the game model under a real-time energy market where prices have been set on a day-ahead robust optimization.

We analyze the problem of localization algorithms for underwater sensor networks. We first characterize the underwater channel for radio communications and adjust a linear model with measurements of real transmissions. We propose an algorithm where the sensor nodes collaboratively estimate their unknown positions in the network. In this setting, we assume low connectivity of the nodes, low data rates, and nonzero probability of lost packets in the transmission. Finally, we consider the problem of a node estimating it's position in underwater navigation. We also provide simulations illustrating the previous proposals.

We use real measurements of the underwater channel to simulate a whole underwater RF wireless sensor networks, including propagation impairments (e.g., noise, interference), radio hardware (e.g., modulation scheme, bandwidth, transmit power), hardware limitations (e.g., clock drift, transmission buffer) and complete MAC and routing protocols. The results should be useful for designing centralized and distributed algorithms for applications like monitoring, event detection, localization and aid to navigation. We also explain the changes that have to be done to Castalia in order to perform the simulations.

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 \textit{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. And 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: energy demand control in a smart-grid network, network flow optimization in which the relays have bounded link capacity and limited battery life, uplink multiple access communication with users that have to optimize the use of their batteries, and two optimal scheduling games with nonstationary channels.