References of "Sepulchre, Rodolphe"
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See detailGeometric optimization methods for independent component analysis applied on gene expression data
Journee, Michel ULg; Teschendorff, A. E.; Absil, P.-A. et al

in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2007) (2007)

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See detailGeometric optimization methods for the analysis of gene expression data
Journee, Michel ULg; Teschendorff, A. E.; Absil, P.-A. et al

Part of book (2007)

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See detailTime-optimal control of a 3-level quantum system and its generalization
Chang, Dong Eui; Sepulchre, Rodolphe ULg

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 ▲]

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See detailFeedback Control of Impact Dynamics: the Bouncing Ball Revisited
Ronsse, Renaud; Sepulchre, Rodolphe ULg

in Proceedings of the 45th IEEE Conference on Decision and Control (2006, December)

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The ... [more ▼]

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The proposed control law uses the impact times as the sole feedback information. We show that the acceleration of the table at impact plays no role in the stability analysis but is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution. [less ▲]

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See detailDiscrete-time synchronization on the N-torus
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg; Leonard, Naomi

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 ▲]

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See detailDiscrete-time synchronization on the N-torus
Sarlette, Alain ULg; Sepulchre, Rodolphe ULg

Conference (2006, March)

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See detailSensorless stabilization of bounce juggling
Ronsse, R.; Lefevre, Philippe; Sepulchre, Rodolphe ULg

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 ▲]

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See detailCollective optimization over average quantities
Scardovi, Luca; Sepulchre, Rodolphe ULg

in Proceedings of the 45th IEEE Conference on Decision and Control (2006)

This paper addresses the design of algorithms for the collective optimization of a cost function defined over average quantities in the presence of limited communication. We argue that several meaningful ... [more ▼]

This paper addresses the design of algorithms for the collective optimization of a cost function defined over average quantities in the presence of limited communication. We argue that several meaningful collective optimization problems can be formulated in this way. As an application of the proposed approach, we propose a novel algorithm that achieves synchronization or balancing in phase models of coupled oscillators under mild connectedness assumptions on the (possibly time-varying and unidirectional) communication graphs. [less ▲]

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See detailTiming Feedback Control of a Rhythmic System
Ronsse, Renaud; Lefevre, Philippe; Sepulchre, Rodolphe ULg

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 ▲]

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See detailFeedback mechanisms for global oscillations in Lure systems
Sepulchre, Rodolphe ULg; Stan, G. B.

in Systems & Control Letters (2005), 54(8), 809-818

The paper presents two mechanisms for global oscillations in feedback systems, based on bifurcations in absolutely stable systems. The external characterization of the oscillators provides the basis for a ... [more ▼]

The paper presents two mechanisms for global oscillations in feedback systems, based on bifurcations in absolutely stable systems. The external characterization of the oscillators provides the basis for a (energy-based) dissipativity theory for oscillators, thereby opening new possibilities for rigorous stability analysis of high-dimensional systems and interconnected oscillators. (C) 2004 Elsevier B.V. All rights reserved. [less ▲]

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See detailCollective motion and oscillator synchronization
Sepulchre, Rodolphe ULg; Paley, Derek; Leonard, Naomi

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 ▲]

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See detailOscillators as Systems and Synchrony as a Design Principle
Sepulchre, Rodolphe ULg

in Menini, L.; Zaccarian, L.; Abdallah, C. T. (Eds.) Current trends in nonlinear systems and control (2005)

The chapter presents an expository survey of ongoing research by the author on a system theory for oscillators. Oscillators are regarded as open systems that can be interconnected to robustly stabilize ... [more ▼]

The chapter presents an expository survey of ongoing research by the author on a system theory for oscillators. Oscillators are regarded as open systems that can be interconnected to robustly stabilize ensemble phenomena characterized by a certain level of synchrony. The first part of the chapter provides examples of design (stabilization) problems in which synchrony plays an important role. The second part of the chapter shows that dissipativity theory provides an interconnection theory for oscillators. [less ▲]

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See detailOscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles
Paley, Derek; Leonard, Naomi; Sepulchre, Rodolphe ULg

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 ▲]

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See detailIs bounce juggling easier in a parabolic billiard than in a wedge
Chang, Dong Eui; Ronsse, Renaud; Sepulchre, Rodolphe ULg

in Proceedings of the 5th Euromech nonlinear dynamics conference (2005)

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See detailCollective Motion: Bistability and Trajectory Tracking
Paley, Derek; Leonard, Naomi; Sepulchre, Rodolphe ULg

in Proceedings of the 43rd IEEE Conference on Decision and Control (2004, December)

This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and ... [more ▼]

This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to bistability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking. [less ▲]

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See detailSTABILIZATION THROUGH WEAK AND OCCASIONAL INTERACTIONS : A BILLIARD BENCHMARK
Gerard, Manuel; Sepulchre, Rodolphe ULg

in Proceedings of the 6th IFAC Symposium on Nonlinear Control Systems (2004, September)

The paper addresses the stabilization of periodic orbits in a wedge billiard with actuated edges. It is shown how the rich dynamical properties of the open-loop dynamics, e.g. ergodicity properties and ... [more ▼]

The paper addresses the stabilization of periodic orbits in a wedge billiard with actuated edges. It is shown how the rich dynamical properties of the open-loop dynamics, e.g. ergodicity properties and KAM curves, can be exploited to design robust stabilizing feedbacks with large basins of attraction. [less ▲]

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See detailOPEN-LOOP STABILIZATION OF 2D IMPACT JUGGLING
Ronsse, Renaud; Lefèvre, Philippe; Sepulchre, Rodolphe ULg

in Proceedings of 6th IFAC Symposium on Nonlinear Control Systems (2004, September)

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

The paper studies the properties of a sinusoidally vibrating wedge billiard as a model for 2D impact juggling. It is shown that some periodic orbits that are unstable in the elastic xed wedge become exponentially stable in the (non-)elastic vibrating wedge. These orbits are linked with some classical juggling patterns, providing an interesting benchmark for the study of the frequency-locking properties in human rhythmic tasks. [less ▲]

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See detailContinuous dynamical systems that realize discrete optimization on the hypercube
Absil, P.-A.; Sepulchre, Rodolphe ULg

in Systems & Control Letters (2004), 52(3-4), 297-304

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0, 1}(n). The search is achieved by a gradient-like system in [0, 1](n) with cost function E. Under mild ... [more ▼]

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0, 1}(n). The search is achieved by a gradient-like system in [0, 1](n) with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0, 1}(n). Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. (C) 2004 Elsevier B.V. All rights reserved. [less ▲]

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See detailDISSIPATIVITY AND GLOBAL ANALYSIS OF LIMIT CYCLES IN NETWORKS OF OSCILLATORS
Stan, Guy-Bart; Sepulchre, Rodolphe ULg

in Proceedings of the 16th Symposium on Mathematical Theory of Networks and Systems (2004, July)

This paper is concerned with the global analysis of synchrone oscillations in special networks of oscillators. In previous work, we de ned a class of highdimensional, parameter-dependent nonlinear systems ... [more ▼]

This paper is concerned with the global analysis of synchrone oscillations in special networks of oscillators. In previous work, we de ned a class of highdimensional, parameter-dependent nonlinear systems exhibiting almost globally asymptotically stable limit cycle oscillations. In this paper, we show how (incremental) dissipativity may be used to extend the global analysis of limit cycle oscillations to networks of coupled identical systems. [less ▲]

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See detailRiemannian geometry of Grassmann manifolds with a view on algorithmic computation
Absil, P.-A.; Mahony, R.; Sepulchre, Rodolphe ULg

in Acta Applicandae Mathematicae (2004), 80(2), 199-220

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in R-n. In these ... [more ▼]

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in R-n. In these formulas, p-planes are represented as the column space of n x p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out. [less ▲]

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