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

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Critical phenomena in complex networks

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, researchers have made important steps toward understanding the qualitatively new critical phenomena in complex networks. We review the results, concepts, and methods of this rapidly developing field. Here we mostly consider two closely related classes of these critical phenomena, namely structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. We also discuss systems where a network and interacting agents on it influence each other. We overview a wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, k-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks. We also discuss strong finite size effects in these systems and highlight open problems and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references, extende

Robust Engineering of Dynamic Structures in Complex Networks

Populations of nearly identical dynamical systems are ubiquitous in natural and engineered systems, in which each unit plays a crucial role in determining the functioning of the ensemble. Robust and optimal control of such large collections of dynamical units remains a grand challenge, especially, when these units interact and form a complex network. Motivated by compelling practical problems in power systems, neural engineering and quantum control, where individual units often have to work in tandem to achieve a desired dynamic behavior, e.g., maintaining synchronization of generators in a power grid or conveying information in a neuronal network; in this dissertation, we focus on developing novel analytical tools and optimal control policies for large-scale ensembles and networks. To this end, we first formulate and solve an optimal tracking control problem for bilinear systems. We developed an iterative algorithm that synthesizes the optimal control input by solving a sequence of state-dependent differential equations that characterize the optimal solution. This iterative scheme is then extended to treat isolated population or networked systems. We demonstrate the robustness and versatility of the iterative control algorithm through diverse applications from different fields, involving nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), electrochemistry, neuroscience, and neural engineering. For example, we design synchronization controls for optimal manipulation of spatiotemporal spike patterns in neuron ensembles. Such a task plays an important role in neural systems. Furthermore, we show that the formation of such spatiotemporal patterns is restricted when the network of neurons is only partially controllable. In neural circuitry, for instance, loss of controllability could imply loss of neural functions. In addition, we employ the phase reduction theory to leverage the development of novel control paradigms for cyclic deferrable loads, e.g., air conditioners, that are used to support grid stability through demand response (DR) programs. More importantly, we introduce novel theoretical tools for evaluating DR capacity and bandwidth. We also study pinning control of complex networks, where we establish a control-theoretic approach to identifying the most influential nodes in both undirected and directed complex networks. Such pinning strategies have extensive practical implications, e.g., identifying the most influential spreaders in epidemic and social networks, and lead to the discovery of degenerate networks, where the most influential node relocates depending on the coupling strength. This phenomenon had not been discovered until our recent study

Mathematical frameworks for oscillatory network dynamics in neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience

Distributed synchronization algorithms for wireless sensor networks

The ability to distribute time and frequency among a large population of interacting agents is of interest for diverse disciplines, inasmuch as it enables to carry out complex cooperative tasks. In a wireless sensor network (WSN), time/frequency synchronization allows the implementation of distributed signal processing and coding techniques, and the realization of coordinated access to the shared wireless medium. Large multi-hop WSN\u27s constitute a new regime for network synchronization, as they call for the development of scalable, fully distributed synchronization algorithms. While most of previous research focused on synchronization at the application layer, this thesis considers synchronization at the lowest layers of the communication protocol stack of a WSN, namely the physical and the medium access control (MAC) layer. At the physical layer, the focus is on the compensation of carrier frequency offsets (CFO), while time synchronization is studied for application at the MAC layer. In both cases, the problem of realizing network-wide synchronization is approached by employing distributed clock control algorithms based on the classical concept of coupled phase and frequency locked loops (PLL and FLL). The analysis takes into account communication, signaling and energy consumption constraints arising in the novel context of multi-hop WSN\u27s. In particular, the robustness of the algorithms is checked against packet collision events, infrequent sync updates, and errors introduced by different noise sources, such as transmission delays and clock frequency instabilities. By observing that WSN\u27s allow for greater flexibility in the design of the synchronization network architecture, this work examines also the relative merits of both peer-to-peer (mutually coupled - MC) and hierarchical (master-slave - MS) architectures. With both MC and MS architectures, synchronization accuracy degrades smoothly with the network size, provided that loop parameters are conveniently chosen. In particular, MS topologies guarantee faster synchronization, but they are hindered by higher noise accumulation, while MC topologies allow for an almost uniform error distribution at the price of much slower convergence. For all the considered cases, synchronization algorithms based on adaptive PLL and FLL designs are shown to provide robust and scalable network-wide time and frequency distribution in a WSN