Synchronization and balancing on the N-torus

in Systems & Control Letters (2007), 56(5), 335-341

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 ... [more ▼]

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. [less ▲]

Analysis of interconnected oscillators by dissipativity theory

in IEEE Transactions on Automatic Control (2007), 52(2), 256-270

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a ... [more ▼]

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators. [less ▲]

Gradient-optimization on the orthogonal group for Independent Component Analysis

in 7th International Conference on Independent Component Analysis and Blind Signal Separation (ICA 2007) (2007)

Geometric optimization methods for the analysis of gene expression data

Part of book (2007)

Time-optimal control of a 3-level quantum system and its generalization

in Dynamics of Continuous, Discrete and Impulsive Systems Series (2007), 14

We solve the problem of steering a three-level quantum system from one eigen- state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level ... [more ▼]

We solve the problem of steering a three-level quantum system from one eigen- state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: Z2 ×S3 discrete sym- metry and S1 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system. [less ▲]

Discrete-time synchronization on the N-torus

in Proceedings of the 17th MTNS Symposium, Kyoto 2006 (2006, August)

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with ... [more ▼]

In this paper, we study the behavior of a discrete-time network of N agents, each evolving on the circle. The global convergence analysis on the N-torus is a distinctive feature of the present work with respect to previous synchronization results that have focused on convergence in the Euclidean space (R^n)^N. We address the question from a control perspective, but make several connections with existing models, including the Hopfield network, the Vicsek model and the (continuous-time) Kuramoto model. We propose two different distributed algorithms. The first one achieves convergence to equilibria in shape space that are the local extrema of a potential U_L built on the graph Laplacian associated to a fixed, undirected interconnection topology; it can be implemented with sensor-based interaction only, since each agent just relies on the relative position of its neighbors. The second one achieves synchronization under varying and/or directed communication topology using local estimates of a consensus variable that are communicated between interacting agents. Both algorithms are based on the notion of centroid and can be interpreted as descent algorithms. The proposed approach can be extended to other embedded compact manifolds. [less ▲]

Sensorless stabilization of bounce juggling

in IEEE Transactions on Robotics (2006), 22(1), 147-159

The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2-D bounce juggling. It is shown that some periodic orbits that are unstable in the elastic fixed wedge become ... [more ▼]

The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2-D bounce juggling. It is shown that some periodic orbits that are unstable in the elastic fixed wedge become exponentially stable in the nonelastic vibrating wedge. These orbits are linked with certain classical juggling patterns, providing an interesting benchmark for the study of the frequency-locking properties in human rhythmic tasks. Experimental results on sensorless stabilization of juggling patterns are described. [less ▲]

Timing Feedback Control of a Rhythmic System

in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference 2005 (2005, December)

This paper addresses the question relative to the role of sensory feedback in rhythmic tasks. We study the properties of a sinusoidally vibrating wedge-billiard as a model for 2-D bounce juggling. If this ... [more ▼]

This paper addresses the question relative to the role of sensory feedback in rhythmic tasks. We study the properties of a sinusoidally vibrating wedge-billiard as a model for 2-D bounce juggling. If this wedge is actuated with an harmonic sinusoidal input, it has been shown that some periodic orbits are exponentially stable. This paper explores an intuitive method to enlarge the parametric stability region of the simplest of these orbits. Accurate processing of timing is proven to be an important key to achieve frequency-locking in rhythmic tasks. [less ▲]

Collective motion and oscillator synchronization

in Cooperative Control (2005)

This paper studies connections between phase models of coupled oscillators and kinematic models of groups of self-propelled particles. These connections are exploited in the analysis and design of ... [more ▼]

This paper studies connections between phase models of coupled oscillators and kinematic models of groups of self-propelled particles. These connections are exploited in the analysis and design of feedback control laws for the individuals that stabilize collective motions for the group. [less ▲]

Oscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles

in Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (2005)

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic ... [more ▼]

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles in the splay state formation around the center of mass of the group. [less ▲]