Fast Desynchronization For Decentralized Multichannel Medium Access Control

Distributed desynchronization algorithms are key to wireless sensor networks as they allow for medium access control in a decentralized manner. In this paper, we view desynchronization primitives as iterative methods that solve optimization problems. In particular, by formalizing a well established desynchronization algorithm as a gradient descent method, we establish novel upper bounds on the number of iterations required to reach convergence. Moreover, by using Nesterov's accelerated gradient method, we propose a novel desynchronization primitive that provides for faster convergence to the steady state. Importantly, we propose a novel algorithm that leads to decentralized time-synchronous multichannel TDMA coordination by formulating this task as an optimization problem. Our simulations and experiments on a densely-connected IEEE 802.15.4-based wireless sensor network demonstrate that our scheme provides for faster convergence to the steady state, robustness to hidden nodes, higher network throughput and comparable power dissipation with respect to the recently standardized IEEE 802.15.4e-2012 time-synchronized channel hopping (TSCH) scheme.Comment: to appear in IEEE Transactions on Communication

Coordination and Privacy Preservation in Multi-Agent Systems

This dissertation considers two key problems in multi-agent systems: coordination (including both synchronization and desynchronization) and privacy preservation. For coordination in multi-agent systems, we focus on synchronization/desynchronization of distributed pulse-coupled oscillator (PCO) networks and their applications in collective motion coordination. Pulse-coupled oscillators were originally proposed to model synchronization in biological systems such as flashing fireflies and firing neurons. In recent years, with proven scalability, simplicity, accuracy, and robustness, the PCO based synchronization strategy has become a powerful clock synchronization primitive for wireless sensor networks. Driven by these increased applications in biological networks and wireless sensor networks, synchronization of pulse-coupled oscillators has gained increased popularity. However, most existing results address the local synchronization of PCOs with initial phases constrained in a half cycle, and results on global synchronization from any initial condition are very sparse. In our work, we address global PCO synchronization from an arbitrary phase distribution under chain or directed tree graphs. More importantly, different from existing global synchronization studies on decentralized PCO networks, our work allows heterogeneous coupling functions and perturbations on PCOs\u27 natural frequencies, and our results hold under any coupling strength between zero and one, which is crucial because a large coupling strength has been shown to be detrimental to the robustness of PCO synchronization to disturbances. Compared with synchronization, desynchronization of PCOs is less explored. Desynchronization spreads the phase variables of all PCOs uniformly apart (with equal difference between neighboring phases). It has also been found in many biological phenomena, such as neuron spiking and fish signaling. Recently, phase desynchronization has been employed to achieve round-robin scheduling, which is crucial in applications as diverse as media access control of communication networks, realization of analog-to-digital converters, and scheduling of traffic flows in intersections. In our work, we systematically characterize pulse-coupled oscillators based decentralized phase desynchronization and propose an interaction function that is more general than existing results. Numerical simulations show that the proposed pulse based interaction function also has better robustness to pulse losses, time delays, and frequency errors than existing results. Collective motion coordination is fundamental in systems as diverse as mobile sensor networks, swarm robotics, autonomous vehicles, and animal groups. Inspired by the close relationship between phase synchronization/desynchronization of PCOs and the heading dynamics of connected vehicles/robots, we propose a pulse-based integrated communication and control approach for collective motion coordination. Our approach only employs simple and identical pulses, which significantly reduces processing latency and communication delay compared with conventional packet based communications. Not only can heading control be achieved in the proposed approach to coordinate the headings (orientations) of motions in a network, but also spacing control for circular motion is achievable to design the spacing between neighboring nodes (e.g., vehicles or robots). The second part of this dissertation is privacy preservation in multi-agent systems. More specifically, we focus on privacy-preserving average consensus as it is key for multi-agent systems, with applications ranging from time synchronization, information fusion, load balancing, to decentralized control. Existing average consensus algorithms require individual nodes (agents) to exchange explicit state values with their neighbors, which leads to the undesirable disclosure of sensitive information in the state. In our work, we propose a novel average consensus algorithm for time-varying directed graphs which can protect the privacy of participating nodes\u27 initial states. Leveraging algorithm-level obfuscation, the algorithm does not need the assistance of any trusted third party or data aggregator. By leveraging the inherent robustness of consensus dynamics against random variations in interaction, our proposed algorithm can guarantee privacy of participating nodes without compromising the accuracy of consensus. The algorithm is distinctly different from differential-privacy based average consensus approaches which enable privacy through compromising accuracy in obtained consensus value. The approach is able to protect the privacy of participating nodes even in the presence of multiple honest-but-curious nodes which can collude with each other

Phase Desynchronization in Pulse-Coupled Oscillator Networks: A New Algorithm and Approach

In this thesis, we present a novel approach for achieving phase desynchronization in a pulse-coupled oscillator network. Ensuring phase desynchronization is a difficult problem, and existing results are constrained to a completely interconnected network and a fixed number of oscillators. Our approach is more robust than previous approaches, removing the constraint of a fixed number of oscillators. The removal of this constraint is significant because it allows the network to receive and drop nodes freely without any change to the phase update strategy. Also, to our knowledge, our approach is the first to prove the convergence to the desynchronized state for a topology that is more general than the all-to-all topology. More specifically, our approach is applicable to any circulant and symmetric network topology, including the circulant symmetric ring topology. Rigorous mathematical proofs are provided to support the result that any circulant symmetric network with ordered phases under our proposed algorithm will converge to uniform phase desynchronization. Simulation results are presented to demonstrate the algorithm\u27s performance, as well as experimental results on a physical system to further illustrate applications of pulse-coupled oscillator networks

Taming Instabilities in Power Grid Networks by Decentralized Control

Renewables will soon dominate energy production in our electric power system. And yet, how to integrate renewable energy into the grid and the market is still a subject of major debate. Decentral Smart Grid Control (DSGC) was recently proposed as a robust and decentralized approach to balance supply and demand and to guarantee a grid operation that is both economically and dynamically feasible. Here, we analyze the impact of network topology by assessing the stability of essential network motifs using both linear stability analysis and basin volume for delay systems. Our results indicate that if frequency measurements are averaged over sufficiently large time intervals, DSGC enhances the stability of extended power grid systems. We further investigate whether DSGC supports centralized and/or decentralized power production and find it to be applicable to both. However, our results on cycle-like systems suggest that DSGC favors systems with decentralized production. Here, lower line capacities and lower averaging times are required compared to those with centralized production.Comment: 21 pages, 6 figures This is a pre-print of a manuscript submitted to The European Physical Journal. The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2015-50136-

Self-Organized Dynamics of Power Grids: Smart Grids, Fluctuations and Cascades

Climate change is one of the most pressing issues of our time and mitigating it requires a reduction of CO2 emissions. A big step towards achieving this goal is increasing the share of renewable energy sources, as the energy sector currently contributes 35% to all greenhouse gas emissions. However, integrating these renewable energy sources challenges the current power system in two major ways. Firstly, renewable generation consists of more spatially distributed and smaller power plants than conventional generation by nuclear or coal plants, questioning the established hierarchical structures and demanding a new grid design. Restructuring becomes necessary because wind and solar plants have to be placed at favorable sites, e.g., close to coasts in the case of wind. Secondly, renewables do not provide a deterministic and controllable power output but introduce power fluctuations that have to be controlled adequately. Many solutions to these challenges are build on the concept of smart grids, which require an extensive information technology (IT) infrastructure communicating between consumers and generators to coordinate efficient actions. However, an intertwined power and IT system raises great privacy and security concerns. Is it possible to forgo a large IT infrastructure in future power grids and instead operate them purely based on local information? How would such a decentrally organized system work? What is the impact of fluctuation on short time scales on the dynamical stability? Which grid topologies are robust against random failures or targeted attacks? This thesis aims to establish a framework of such a self-organized dynamics of a power grid, analyzing its benefits and limitations with respect to fluctuations and discrete events. Instead of a centrally monitored and controlled smart grid, we propose the concept of Decentral Smart Grid Control, translating local power grid frequency information into actions to stabilize the grid. This is not limited to power generators but applies equally to consumers, naturally introducing a demand response. We analyze the dynamical stability properties of this framework using linear stability methods as well as applying numerical simulations to determine the size of the basin of attraction. To do so, we investigate general stability effects and sample network motifs to find that this self-organized grid dynamics is stable for large parameter regimes. However, when the actors of the power grid react to a frequency signal, this reaction has to be sufficiently fast since reaction delays are shown to destabilize the grid. We derive expressions for a maximum delay, which always desynchronizes the system based on a rebound effect, and for destabilizing delays based on resonance effects. These resonance instabilities are cured when the frequency signal is averaged over a few seconds (low-pass filter). Overall, we propose an alternative smart grid model without any IT infrastructure and analyze its stable operating space. Furthermore, we analyze the impact of fluctuations on the power grid. First, we determine the escape time of the grid, i.e., the time until the grid desynchronizes when subject to stochastic perturbations. We simulate these events and derive an analytical expression using Kramer's method, obtaining the scaling of the escape time as a function of the grid inertia, transmitted power, damping etc. Thereby, we identify weak links in networks, which have to be enhanced to guarantee a stable operation. Second, we collect power grid frequency measurements from different regions across the world and evaluate their statistical properties. Distributions are found to be heavy-tailed so that large disturbances are more common than predicted by Gaussian statistics. We model the grid dynamics using a stochastic differential equation to derive the scaling of the fluctuations based on power grid parameters, identifying effective damping as essential in reducing fluctuation risks. This damping may be provided by increased demand control as proposed by Decentral Smart Grid Control. Finally, we investigate discrete events, in particular the failure of a single transmission line, as a complementary form of disturbances. An initial failure of a transmission line leads to additional load on other lines, potentially overloading them and thereby causing secondary outages. Hence, a cascade of failures is induced that propagated through the network, resulting in a large-scale blackout. We investigate these cascades in a combined dynamical and event-driven framework, which includes transient dynamics, in contrast to the often used steady state analysis that only solves static flows in the grid while neglecting any dynamics. Concluding, we identify critical lines, prone to cause cascades when failing, and observe a nearly constant speed of the propagation of the cascade in an appropriate metric. Overall, we investigate the self-organized dynamics of power grids, demonstrating its benefits and limitations. We provide tools to improve current grid operation and outline a smart grid solution that is not reliant on IT. Thereby, we support establishing a 100% renewable energy system