Bio-Inspired Synchronization of Pulse-Coupled Oscillators and its Application to Wireless Sensor Networks

Precise synchronization among networked agents is responsible for phenomena as diverse as coral spawning and consistency in stock market transactions. The importance of synchronization in biological and engineering systems has triggered an avalanche of studies analyzing the emergence of a synchronized behavior within a network of, possibly heterogeneous, agents. In particular, synchronization of networks of coupled oscillators has received great attention since limit cycle oscillators are a natural abstraction for systems where periodicity is a distinctive property. Examples of such systems include circadian rhythms and alternate-current power generators. This work deals with synchronization of pulse-coupled limit cycle oscillators (PCOs). A reverse engineering approach is taken with the objective of obtaining an abstraction for PCO networks able to capture the key properties observed in the classical biological PCO model, to finally implement it in an en gineering system. To this end, we first reformulate the PCO model as a hybrid system, able to integrate in a smooth manner the continuous-time dynamics of the individual oscillators and the impulsive effect of the coupling. Using our new model, we analyze the existence and stability of synchronization in a variety of PCO network topologies, starting from the simplest all-to-all network where global synchronization is proven to exist, to end giving synchronization conditions in the general strongly connected network case. Inspired by the strong synchronization properties of PCO networks we design a PCO-inspired time synchronization protocol for wireless sensor networks that enjoys all the advantages of our optimized PCO setup. A pilot implementation is presented going from a simulation stage to a hardware implementation in Gumstix development boards and industrial acoustic sensors. To test the potential of the protocol in a real application, we implement the PCO-based time synchronization protocol in a distributed acoustic event detection system, where a sensor network combines local measurements over an infrastructure-free wireless network to find the source of an acoustic event. An evaluation by simulation is given to illustrate the advantages of using the pulse-coupled synchronization strategy.The contributions of this thesis range from the theoretical synchronization conditions for a variety of PCO networks to the design and implementation of a synchronization strategy for wireless sensor networks that seems to be the natural choice when using an infrastructure-free wireless network due to its simple formulation and natural scalability

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

Attack Resilient Pulse Based Synchronization

Synchronization of pulse-coupled oscillators (PCOs) has gained significant attention recently due to increased applications in sensor networks and wireless communications. However, most existing results are obtained in the absence of malicious attacks. Given the distributed and unattended nature of wireless sensor networks, it is imperative to enhance the resilience of pulse-based synchronization against malicious attacks. To achieve this goal, we first show that by using a carefully designed phase response function (PRF), pulse-based synchronization of PCOs can be guaranteed despite the presence of a stealthy Byzantine attacker, even when legitimate PCOs have different initial phases. Next, we propose a new pulse-based synchronization mechanism to improve the resilience of pulse-based synchronization to multiple stealthy Byzantine attackers. We rigorously characterize the condition for mounting stealthy Byzantine attacks under the proposed new pulse-based synchronization mechanism and prove analytically that synchronization of legitimate oscillators can be achieved even when their initial phases are unrestricted, i.e., randomly distributed in the entire oscillation period. Since most existing results on resilient pulse-based synchronization are obtained only for all-to-all networks, we also propose a new pulse-based synchronization mechanism to improve the resilience of pulse-based synchronization that is applicable under general connected topologies. Under the proposed synchronization mechanism, we prove that synchronization of general connected legitimate PCOs can be guaranteed in the presence of multiple stealthy Byzantine attackers, irrespective of whether the attackers collude with each other or not. The new mechanism can guarantee resilient synchronization even when the initial phases of legitimate oscillators are distributed in a half circle. Then, to relax the limitation of the stealthy attacker model and the constraint on the legitimate oscillators\u27 initial phase distribution, we improved our synchronization mechanism and proved that finite time synchronization of legitimate oscillators can be guaranteed in the presence of multiple Byzantine attackers who can emit attack pulses arbitrarily without any constraint except that practical bit rate constraint renders the number of pulses from an attacker to be finite. The improved mechanism can guarantee synchronization even when the initial phases of all legitimate oscillators are arbitrarily distributed in the entire oscillation period. The new attack resilient pulse-based synchronization approaches in this dissertation are in distinct difference from most existing attack-resilient synchronization algorithms (including the seminal paper from Lamport and Melliar-Smith [1]) which require a priori (almost) synchronization among all legitimate nodes. Numerical simulations are given to confirm the theoretical results

Synchronization of Pulse-Coupled Oscillators to a Global Pacemaker

Pulse-coupled oscillators (PCOs) are limit cycle oscillators coupled by exchanging pulses at discrete time instants. Their importance in biology and engineering has motivated numerous studies aiming to understand the basic synchronization properties of a network of PCOs. In this work, we study synchronization of PCOs subject to a global pacemaker (or global cue) and local interactions between slave oscillators. We characterize solutions and give synchronization conditions using the phase response curve (PRC) as the design element, which is restricted to be of the delay type in the first half of the cycle, interval (0,π)(0,π), and of the advance type in the second half of the cycle, interval (π,2π)(π,2π). It is shown that global synchronization is feasible when using an advance-delay PRC if the influence of the global cue is strong enough. Numerical examples are provided to illustrate the analytical findings