Leaderless synchronization of heterogeneous oscillators by adaptively learning the group model

International audienc

Harmonic synchronization under all three types of coupling: position, velocity, and acceleration

Synchronization of identical harmonic oscillators interconnected via position, velocity, and acceleration couplings is studied. How to construct a complex Laplacian matrix representing the overall coupling is presented. It is shown that the oscillators asymptotically synchronize if and only if this matrix has a single eigenvalue on the imaginary axis. This result generalizes some of the known spectral tests for synchronization. Some simpler Laplacian constructions are also proved to work provided that certain structural conditions are satisfied by the coupling graphs.Comment: 9 pages, 2 figure

Interaction Dynamics in Oscillator and Human-in-the-loop Systems.

This dissertation addresses control system analysis and system identification in three areas: error propagation in synchronization of harmonic oscillators, modeling of human active movement, and identification of human control strategies in manual pursuit tracking. 1) While most studies of synchronization in oscillator systems have focused on the existence of synchronous solutions in steady state, many problems pertaining to the transient dynamics have not been fully resolved. We extend the well-established theory of fundamental limitations to study the transient error propagation (string stability) in a string of synchronized harmonic oscillators. We first translate design requirements in terms of time-domain response and hardware limitations into a set of constraints on closed-loop frequency response. We further capture the conflict between string stability on the one hand and time-domain design requirements and hardware limitations on the other through a new Bode integral. 2) Modeling human active movement is a challenging problem not only because muscle has very sophisticated and highly nonlinear dynamics but also because neural and other signals internal to the body are difficult to observe directly. We seek a simple yet general and competent model to describe active movement in object manipulation tasks. Inspired by the Norton equivalent circuit in electrical engineering, we build a model based on the motion and force/torque signals that may be observed at the points of contact between the human body and the environment. The model consists of a motion source to represent a human's motor plan and a spring-mass-damper coupler to capture the time-varying driving point impedance of the human hand. The model is validated using occasional experimental trials in which a participant experiences unexpected loads in a grasp and twist task. 3) Although a large amount of literature has provided methods to identify feedback control in manual tracking tasks, very little research has been undertaken to experimentally identify feedforward control. We capitalize on the theory of fundamental limitations to study the link between a human's ability to simultaneously reject disturbances and perform pursuit tracking. We further develop an identification method to separate human feedback and feedforward control strategies in sinusoidal tracking tasks.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108853/1/ybo_1.pd

Resilient Output Consensus Control of Heterogeneous Multi-agent Systems against Byzantine Attacks: A Twin Layer Approach

This paper studies the problem of cooperative control of heterogeneous multi-agent systems (MASs) against Byzantine attacks. The agent affected by Byzantine attacks sends different wrong values to all neighbors while applying wrong input signals for itself, which is aggressive and difficult to be defended. Inspired by the concept of Digital Twin, a new hierarchical protocol equipped with a virtual twin layer (TL) is proposed, which decouples the above problems into the defense scheme against Byzantine edge attacks on the TL and the defense scheme against Byzantine node attacks on the cyber-physical layer (CPL). On the TL, we propose a resilient topology reconfiguration strategy by adding a minimum number of key edges to improve network resilience. It is strictly proved that the control strategy is sufficient to achieve asymptotic consensus in finite time with the topology on the TL satisfying strongly $(2f+1)$-robustness. On the CPL, decentralized chattering-free controllers are proposed to guarantee the resilient output consensus for the heterogeneous MASs against Byzantine node attacks. Moreover, the obtained controller shows exponential convergence. The effectiveness and practicality of the theoretical results are verified by numerical examples

An Overview of Recent Progress in the Study of Distributed Multi-agent Coordination

This article reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, task assignment, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau

Robust Observation and Control of Complex Networks

The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems. Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties, unmodeled dynamics or simply characterized by proper nonlinear dynamics. Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes. Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented

Robust Observation and Control of Complex Networks

The problem of understanding when individual actions of interacting agents display to a coordinated collective behavior has receiving a considerable attention in many research fields. Especially in control engineering, distributed applications in cooperative environments are achieving resounding success, due to the large number of relevant applications, such as formation control, attitude synchronization tasks and cooperative applications in large-scale systems. Although those problems have been extensively studied in Literature, themost of classic approaches use to consider the unrealistic scenario in which networks always consist of identical, linear, time-invariant entities. It’s clear that this assumption strongly approximates the effective behavior of a network. In fact agents can be subjected to parameter uncertainties, unmodeled dynamics or simply characterized by proper nonlinear dynamics. Therefore, motivated by those practical problems, the present Thesis proposes various approaches for dealing with the problem of observation and control in both the framework of multi-agents and complex interconnected systems. The main contributions of this Thesis consist on the development of several algorithms based on concepts of discontinuous slidingmode control. This techniques can be employed for solving in finite-time problems of robust state estimation and consensus-based synchronization in network of heterogenous nonlinear systems subjected to unknown but bounded disturbances and sudden topological changes. Both directed and undirected topologies have been taken into account. It is worth to mention also the extension of the consensus problem to networks of agents governed by a class parabolic partial differential equation, for which, for the first time, a boundary-based robust local interaction protocol has been presented

Stochasticity,complexity and synchronization in semiconductor lasers

The purpose of this Thesis is study the dynamical behavior of semiconductor lasers with optical feedback, as well as analyze the synchronization of this kind of systems under different coupling arquitectures. This study has been done from an experimental point of view, but in some cases we have used numerical models in order to verify and/or extend the experimental results. A semiconductor laser in absence of any optical feedback emits light at constant power. If one wants to induce dynamics in the laser, a good strategy is to introduce an external cavity able to reflect the emitted light back into the laser. Due to this feedback, the laser can show a large variety of dynamical behaviors. In this Thesis we will focus mainly in a dynamical regime known as low frequency fluctuations regime (LFF). The LFF regime takes place when the pump current of the laser is close to its threshold current and the feedback strength is sufficiently large, and it consists in sudden intensity dropouts arising at irregular times, followed by a gradual and stepwise recovery. During this Thesis, we have characterized in detail the dynamical behavior of the time between intensity dropouts for a semiconductor laser with feedback, by using different statistical techniques based on information theory concepts. We have quantified the probability of appearance of certain patterns within the temporal series, as well as its degree of complexity. As a result of these studies, we can conclude that the dynamics of a semiconductor laser with optical feedback is stochastic for pump current values close to the laser threshold. On the other hand, for larger pump currents the dynamics is basically deterministic (chaotic). Numerical simulations have shown a good qualitative and quantitive agreement with the experimental results. During this Thesis we have also studied the ability of semiconductor lasers to synchronize under different coupling architectures. First, we have characterized the leader-laggard dynamics showed by two semiconductor lasers bidirectionally coupled operating at the LFF regime, with a method that takes into account the number of forbidden patterns that appears in the temporal series. We have quantified the degree of stochasticity of the system as a function of the pump current of both lasers. A second coupling architecture studied here, consists in two lasers unidirectionally coupled via two paths. In this case, we have analyzed how the synchronization is affected under different values of the coupling strength of both paths, as well as the potential of this system (or rather, the lack thereof) to be used in chaotic communications. Finally we have characterized the synchronization at zero lag for two lasers coupled bidirectionally via a passive relay. In particular, we have studied the desynchronization events and their statistics for different pump currents. The experimental results obtained in this Thesis give a global perspective of the dynamical statistical properties of semiconductor laser dynamics, both isolated or coupled to other lasers, which contributes to a better understanding of this kind of dynamical systems.L’objectiu d’aquesta Tesi ´es l’estudi de la din`amica de l`asers de semiconductor amb retroalimentaci´o `optica, aix´ý com l’an`alisis de la sincronitzaci´o d’aquest tipus de sistemes sota diferents arquitectures d’acoblament. Aquest estudi s’ha fet sempre des d’un punt de vista b`asicament experimental, tot i que en alguns casos hem utilitzat models num`erics per tal de verificar i/o ampliar els resultats experimentals. Un l`aser de semiconductor en abs`encia de retroalimentaci´o `optica o altres perturbacions externes, emet llum a una intensitat pr`acticament constant. Aix´ý doncs, si el que es vol ´es indu¨ýr din`amica en el l`aser, una bona estrat`egia ´es introdu¨ýr una cavitat externa capa¸c de reflexar la llum cap al l`aser. Un cop la llum ´es reinjectada, els l`asers de semiconductor poden mostrar una gran varietat de comportaments din`amics. En aquesta tesis ens centrarem principalment en un r`egim din`amic anomenat r`egim de fluctuacions de baixa frequ`encia (LFF en les seves sigles en angl`es). El r`egim d’LFF es d´ona quan el corrent d’injecci´o del l`aser es troba a prop del seu corrent llindar i la intensitat de la retroalimentaci´o ´es suficientment gran, i est`a caracteritzat per sobtades caigudes de la intensitat a temps irregulars, seguides per una recuperaci´o gradual i escalonada. Durant aquesta Tesi, hem caracteritzat de forma detallada el comportament din`amic de la distribuci´o dels temps entre les caigudes d’intensitat d’un l`aser de semiconductor amb retroalimentaci´o `optica, utilitzant diferents m`etodes estad´ýstics basats en conceptes de teoria de la informaci´o. En particular, hem quantificat la probabilitat d’aparici´o de certs patrons dins les s`eries temporals, aix´ý com el grau de complexitat d’aquestes. Durant aquest estudi hem observat que la din`amica d’un l`aser de semiconductor amb retroalimentaci´o es estoc`astica per valors del corrent d’injecci´o propers al corrent llindar del l`aser. D’altra banda, per a valors m´es grans del corrent d’injecci´o la din`amica ´es m´es determinista (ca`otica). Les simulacions num`eriques realitzades han mostrat un acord qualitatiu i quantitatiu amb els resultats experimentals. Durant aquesta Tesi tamb´e hem estudiat la sincronitzaci´o entre l`asers de semiconductor. Hem analitzat diferents arquitectures d’acoblament. Primer hem caracteritzat la din`amica leader-laggard que presenten dos l`asers de semiconductor acoblats bidireccionalment operant en r`egim de LFFs, amb un m`etode que t´e en compte el nombre de patrons prohibits que apareixen en la s`erie temporal. Hem quantificat el grau d’estocasticitat del sistema en funci´o del nivell de bombeig al qual est`an sotmesos els dos l`asers. La seg¨uent arquitectura d’acoblament que hem estudiat consisteix en dos l`asers acoblats unidireccionalment a trav´es de dos camins. En aquest cas hem analitzat com es veu afectada la sincronitzaci´o sota diferents valors de l’acoblament dels dos camins, aix´ý com el potencial d’aquest esquema experimental per realitzar comunicacions ca`otiques. Per ´ultim hem caracteritzat la sincronitzaci´o a retard zero per dos l`asers acoblats bidireccionalment, a on els dos l`asers tenen la seva pr`opia realimentaci´o `optica. En particular, hem estudiat els events de desincronitzaci´o i la seva estad´ýstica per a diferents corrents d’injecci´o. Els resultats experimentals obtinguts en aquesta Tesi, ofereixen una prespectiva global de les propietats estad´ýstiques de la din`amica de l`asers de semiconductor, tant a¨ýllats com acoblats a altres l`asers, que contribueixen a entendre millor aquests sistemes din`amics