Global state synchronization in networks of cyclic feedback systems

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. © 2011 IEEE.

Phase synchronization between stratospheric and tropospheric quasi-biennial and semi-annual oscillations

A combination of singular systems analysis and analytic phase techniques are used to investigate the possible occurrence in observations of coherent synchronization between quasi-biennial and semi-annual oscillations (QBOs; SAOs) in the stratosphere and troposphere. Time series of zonal mean zonal winds near the Equator are analysed from the ERA-40 and ERA-interim reanalysis datasets over a ∼ 50-year period. In the stratosphere, the QBO is found to synchronize with the SAO almost all the time, but with a frequency ratio that changes erratically between 4:1, 5:1 and 6:1. A similar variable synchronization is also evident in the tropical troposphere between semi-annual and quasi-biennial cycles (known as TBOs). Mean zonal winds from ERA-40 and ERA-interim, and also time series of indices for the Indian and West Pacific monsoons, are commonly found to exhibit synchronization, with SAO/TBO ratios that vary between 4:1 and 7:1. Coherent synchronization between the QBO and tropical TBO does not appear to persist for long intervals, however. This suggests that both the QBO and tropical TBOs may be separately synchronized to SAOs that are themselves enslaved to the seasonal cycle, or to the annual cycle itself. However, the QBO and TBOs are evidently only weakly coupled between themselves and are frequently found to lose mutual coherence when each changes its frequency ratio to its respective SAO. This suggests a need to revise a commonly cited paradigm that advocates the use of stratospheric QBO indices as a predictor for tropospheric phenomena such as monsoons and hurricanes. © 2012 Royal Meteorological Society.

Kick synchronization versus diffusive synchronization

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling. © 2012 IEEE.

Phase synchronization through entrainment by a consensus input

The paper proposes a synchronization mechanism in a set of nonlinear oscillators interconnected through a communication network. In contrast to many existing results, we do not employ strong, diffusive couplings between the individual oscillators. Instead, each individual oscillator is weakly forced by a linear resonator system. The resonator systems are synchronized using results from consensus theory. The synchronized resonator systems force the frequencies of the nonlinear oscillators to a constant frequency and thereby yield synchronization of the oscillators. We prove this result using the theory of small forcings of stable oscillators. This synchronization scheme allows for synchronization of nonlinear oscillators over uniformly connected communication graphs. ©2010 IEEE.

Synchronization with partial state feedback on SO(n)

In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ℝn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. ©2009 IEEE.

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient-but to some extent, also necessary-to ensure synchronization with the diffusive static output coupling often considered in the literature. © 2009 Elsevier Ltd. All rights reserved.

Autonomous rigid body attitude synchronization

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. 40th IEEE conf. decision and control (pp. 4598-4603); Nair, S., Leonard, N. E. (2007). Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2(4), 595-624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies' attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information. © 2008 Elsevier Ltd.

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear time-invariant state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. Stronger conditions are shown to be sufficient - but to some extent, also necessary - to ensure synchronization with the diffusive static output coupling often considered in the literature. © 2008 IEEE.

Autonomous rigid body attitude synchronization

This paper studies some extensions to the decentralized attitude synchronization of identical rigid bodies. Considering fully actuated Euler equations, the communication links between the rigid bodies are limited and the available information is restricted to relative orientations and angular velocities. In particular, no leader nor external reference dictates the swarm's behavior. The control laws are derived using two classical approaches of nonlinear control - tracking and energy shaping. This leads to a comparison of two corresponding methods which are currently considered for distributed synchronization - consensus and stabilization of mechanical systems with symmetries. © 2007 IEEE.

Cooperative attitude synchronization in satellite swarms: A consensus approach

The present paper considers the problem of autonomous synchronization of attitudes in a swarm of spacecraft. Building upon our recent results on consensus on manifolds, we model the spacecraft as particles on SO(3) and drive these particles to a common point in SO(3). Unlike the Euler angle or quaternion descriptions, this model suffers no singularities nor double-points. Our approach is fully cooperative and autonomous: we use no leader nor external reference. We present two types of control laws, in terms of applied control torques, that globally drive the swarm towards attitude synchronization: one that requires tree-like or all-to-all inter-satellite communication (most efficient) and one that works with nearly arbitrary communication (most robust).

Synchronization and balancing on the N-torus

In this paper, we study the behavior of a network of N agents, each evolving on the circle. We propose a novel algorithm that achieves synchronization or balancing in phase models under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous results that have focused on convergence in the Euclidean space. © 2006 Elsevier B.V. All rights reserved.