Cirillo, G. I., Mauroy, A., Renson, L., Kerschen, G., & Sepulchre, R. (2016). A spectral characterization of nonlinear normal modes.

*Journal of Sound and Vibration, 377*, 284-301.Peer reviewed (verified by ORBi)

This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we ...

Liegeois, R. (2015).

*Dynamical modelling from resting-state brain imaging*. Unpublished doctoral thesis, Université de Liège, Liège, Belgique.The statistical dependencies among neuroimaging time courses observed in different brain regions are collectively named functional connectivity (FC). This quantity is widely used in order to characterize ...

Dethier, J. (2015).

*The role of feedback in maintaining robustness and modulation across scales: Insights from cellular and network neurophysiology*. Unpublished doctoral thesis, Université de Liège, Liège, Belgique.The brain is a complex system made of many components acting at very dif- ferent resolution levels, from the microsecond and nanometer scales with ion channels to hours and brain-wide scale with proteins. The ...

Liegeois, R., Ziegler, E., Bahri, M. A., Phillips, C., Geurts, P., Gomez, F., Yeo, T., VANHAUDENHUYSE, A., Soddu, A., LAUREYS, S., & Sepulchre, R. (2015, July). Cerebral functional connectivity periodically (de)synchronizes with anatomical constraints.

*Brain Structure and Function*.Peer reviewed

This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber ...

Drion, G., Franci, A., Dethier, J., & Sepulchre, R. (2015, February 18). Dynamic Input Conductances Shape Neuronal Spiking.

*eNeuro*.Peer reviewed

Assessing the role of biophysical parameter variations in neuronal activity is critical to the understanding of modulation, robustness and homeostasis of neuronal signaling. The paper proposes that this ...

Dethier, J.* , Drion, G.* , Franci, & Sepulchre, R. (2015). A positive feedback at the cellular level promotes robustness and modulation at the circuit level.

*Journal of Neurophysiology*.Peer reviewed (verified by ORBi)

This article highlights the role of a positive feedback gating mechanism at the cellular level in the robustness and modulation properties of rhythmic activities at the circuit level. The results are presented ...

* These authors have contributed equally to this work.

Drion, G., O'Leary, T., Dethier, J., Franci, A., & Sepulchre, R. (2015). Neuronal behaviors: A control perspective.

*Proceedings of the IEEE Conference on Decision and Control, 54*, 1923-1944.Peer reviewed

The purpose of this tutorial is to introduce and analyze models of neurons from a control perspective and to show how recently developed analytical tools help to address important biological questions. A first ...

Liegeois, R., Phillips, C., Bahri, M. A., LAUREYS, S., & Sepulchre, R. (2015).

*Total connectivity: a marker of dynamical functional connectivity applied to consciousness*. Poster session presented at Organization for Human Brain Mapping, USA.Peer reviewed

In the last years functional connectivity (FC) has become one of the most popular tools to explore and characterize information contained in fMRI =me series. The classical hypothesis on FC consists of ...

Mishra, B. (2014).

*A Riemannian approach to large-scale constrained least-squares with symmetries*. Unpublished doctoral thesis, Université de Liège, Liège, Belgique.This thesis deals with least-squares optimization on a manifold of equivalence relations, e.g., in the presence of symmetries which arise frequently in many applications. While least-squares cost functions ...

Wehenkel, M. (2014).

*Cellular regulation mechanisms : case study of up and down states in the Purkinje cell*. Unpublished master thesis, Université de Liège, Liège, Belgique.In 1963, Hodgkin and Huxley obtained the Nobel Prize to have shown that the electrical activity of a neuron could be modelled by an electrical RC circuit containing non-linear conductances. This discovery made ...

Forni, F., & Sepulchre, R. (2014). A differential Lyapunov framework for contraction analysis.

*IEEE Transactions on Automatic Control, 59*(3), 614-628.Peer reviewed (verified by ORBi)

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to ...

Franci, A., Drion, G., & Sepulchre, R. (2014). Modeling the Modulation of Neuronal Bursting: A Singularity Theory Approach.

*SIAM Journal on Applied Dynamical Systems, 13*(2), 798-829.Peer reviewed (verified by ORBi)

Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and ...

Liegeois, R., Sepulchre, R., & LAUREYS, S. (2014).

*Cerebral functional connectivity periodically (de)synchronizes with anatomical constraints*. Eprint/Working paper retrieved from http://www.montefiore.ulg.ac.be/~rliegeois/.This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber ...

Liegeois, R., Ziegler, E., Phillips, C., Gomez, F., Soddu, A., LAUREYS, S., & Sepulchre, R. (2014).

*Assessing dynamical correlations between functional and structural brain connectivity*. Poster session presented at 20th Conference of the Organization for Human Brain Mapping, Hamburg, Germany.Peer reviewed

The link between resting‐state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC) has been repeatedly investigated recently. Meanwhile ...

Sacré, P., & Sepulchre, R. (2014). Sensitivity analysis of circadian entrainment in the space of phase response curves. In V. V., Kulkarni, G.-B., Stan, & K., Raman (Eds.),

*A Systems Theoretic Approach to Systems and Synthetic Biology II: Analysis and Design of Cellular Systems*(pp. 59-81). Netherlands: Springer.Peer reviewed

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input–output ...

Sacré, P. (2013).

*Systems analysis of oscillator models in the space of phase response curves*. Unpublished doctoral thesis, University of Liège, Liège, Belgium.Oscillators---whose steady-state behavior is periodic rather than constant---are observed in every field of science. While they have been studied for a long time as closed systems, they are increasingly ...

Collard, A. (2013).

*Geometric statistical processing of brain diffusion tensor images*. Unpublished doctoral thesis, Université de Liège, Liège, Belgique.Nowadays, the functioning of the human brain is still one of the biggest mysteries of humanity. The multiple holes in the understanding of the human brain explain why an intensification of brain-oriented ...

Trotta, L. (2013).

*Analysis of performance and robustness of biological switches: local tools for non-local dynamical phenomena*. Unpublished doctoral thesis, Université de Liège, Liège, Belgique.Biological switches are frequently encountered in mathematical modeling
of biological systems because binary decisions are at the core of many
cellular processes. A bistable switch presents two stable steady ...

Trotta, L., Franci, A., & Sepulchre, R. (2013, July 08).

*First spike latency sensitivity of spiking neuron models*. Poster session presented at Twenty Second Annual Computational Neuroscience Meeting: CNS2013.Peer reviewed

First spike latency is the long-lasting period preceding the first spike of a neuron submitted to a super-threshold stimulus. It has been suggested that this latency could code for stimulus recognition in ...

Drion, G. (2013).

*Regulation of Excitability, Pacemaking, and Bursting: Insights from Dopamine Neuron Electrophysiology*. Unpublished doctoral thesis, Université de Liège, Liège, Belgique.The present thesis attempts to extract the dynamical mechanisms underlying neuronal excitability and its regulation, through the use of experimental and mathematical techniques. In particular, tools of ...

Bonnabel, S., Collard, A., & Sepulchre, R. (2013). Rank-preserving geometric means of positive semi-definite matrices.

*Linear Algebra & its Applications, 438*(8), 3202-3216.Peer reviewed (verified by ORBi)

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix ...

Forni, F., & Sepulchre, R. (2013). On differentially dissipative dynamical systems.

*IFAC-PapersOnLine website*.Peer reviewed

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle ...

Forni, F., Sepulchre, R., & van der Schaft, A. (2013). On differential passivity of physical systems.

*52nd IEEE Conference on Decision and Control*.Peer reviewed

Differential passivity is a property that allows to check with a pointwise criterion that a system is incrementally passive, a property that is relevant to study interconnected systems in the context of ...

Franci, A.* , Drion, G.* , Seutin, V., & Sepulchre, R. (2013). A Balance Equation Determines a Switch in Neuronal Excitability.

*PLoS Computational Biology, 9*, 1003040.Peer reviewed (verified by ORBi)

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance ...

* These authors have contributed equally to this work.

Mauroy, A., & Sepulchre, R. (2013). Global analysis of a continuum model for monotone pulse-coupled oscillators.

*IEEE Transactions on Automatic Control, 58*(5), 1154-1166.Peer reviewed (verified by ORBi)

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupledmodels, the stability results ...

Forni, F., Zaccarian, L., & Sepulchre, R. (2012). Antiwindup regulation of saturated linear systems.

*51st IEEE Conference on Decision and Control*.Peer reviewed

We consider the output regulation problem for linear systems subject to actuators saturation. A state-feedback unconstrained regulator is transformed into an error-feedback bounded regulator by introducing an ...

Mauroy, A., Sacré, P., & Sepulchre, R. (2012). Kick synchronization versus diffusive synchronization.

*Proceedings of the 51st IEEE Conference on Decision and Control (invited tutorial session)*(pp. 7171-7183).Peer reviewed

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 ...

Drion, G.* , Franci, A.* , Seutin, V., & Sepulchre, R. (2012). A novel phase portrait for neuronal excitability.

*PLoS ONE, 7*(8).Peer reviewed (verified by ORBi)

Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of ...

* These authors have contributed equally to this work.

Trotta, L., Bullinger, E., & Sepulchre, R. (2012, March).

*Decision making in noisy bistable switches A local analysis for non local predictions*. Paper presented at 31st Benelux Meeting on Systems and Control.In this paper, we try to estimate some statistics about the decision making process in a bistable model submitted to noise by studying the local properties of the system around an hyperbolic saddle point ...

Drion, G., Sepulchre, R., & Seutin, V. (2012). Mitochondrion- and endoplasmic reticulum-induced SK channel dysregulation as a potential origin of the selective neurodegeneration in Parkinson’s disease. In P., Wellstead & M., Cloutier (Eds.),

*The Systems Biology of Parkinson's Disease*. Springer.Peer reviewed

Mitochondrial dysfunction and metabolic issues are known to have strong implications in the pathogenesis of Parkinson’s disease (PD). But it is also known that the neuronal loss leading to PD symptoms is ...

Franci, A.* , Drion, G.* , & Sepulchre, R. (2012). An Organizing Center in a Planar Model of Neuronal Excitability.

*SIAM Journal on Applied Dynamical Systems, 11*(4), 1698-1722.Peer reviewed (verified by ORBi)

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative ...

* These authors have contributed equally to this work.

Mauroy, A., & Sepulchre, R. (2012). Contraction of monotone phase-coupled oscillators.

*Systems & Control Letters, 61*(11), 1097-1102.Peer reviewed (verified by ORBi)

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The ...

Mishra, B., Karavadi, A. A., & Sepulchre, R. (2012).

*A Riemannian geometry for low-rank matrix completion*. Eprint/Working paper retrieved from http://arxiv.org/abs/1211.1550.We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on ...

Mishra, B., Meyer, G., Bach, F., & Sepulchre, R. (2012).

*Low-rank optimization with trace norm penalty*. Eprint/Working paper retrieved from http://arxiv.org/abs/1112.2318.The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized ...

Mishra, B., Meyer, G., Bonnabel, S., & Sepulchre, R. (2012).

*Fixed-rank matrix factorizations and Riemannian low-rank optimization*. Eprint/Working paper retrieved from http://arxiv.org/abs/1209.0430.Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed ...

Mishra, B., Meyer, G., & Sepulchre, R. (2011). Low-rank optimization for distance matrix completion.

*Proceedings of the 50th IEEE Conference on Decision and Control*.Peer reviewed

This paper addresses the problem of low-rank
distance matrix completion. This problem amounts to recover
the missing entries of a distance matrix when the dimension of
the data embedding space is possibly ...

Sacré, P., & Sepulchre, R. (2011). Matching an oscillator model to a phase response curve.

*Proceedings of the Joint 50th IEEE Conference on Decision and Control and European Control Conference*(pp. 3909-3914).Peer reviewed

The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a ...

Mauroy, A. (2011).

*On the dichotomic collective behaviors of large populations of pulse-coupled firing oscillators*. Unpublished doctoral thesis, Université de Liège, Liège, Belgium.The study of populations of pulse-coupled firing oscillators is a general and simple paradigm to investigate a wealth of natural phenomena, including the collective behaviors of neurons, the synchronization of ...

Meyer, G. (2011).

*Geometric optimization algorithms for linear regression on fixed-rank matrices*. Unpublished doctoral thesis, Université de Liège, Belgique.Nowadays, large and rapidly evolving data sets are commonly encountered in many modern applications. Efficiently mining and exploiting these data sets generally results in the extraction of valuable ...

Sacré, P., & Sepulchre, R. (2011, May 23).

*Sensitivity analysis of phase response curves*. Paper presented at SIAM Conference on Applications of Dynamical Systems, Snowbird, UT.The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models to one-dimensional phase models. We introduce the sensitivity analysis of this important mathematical ...

Meyer, G., Bonnabel, S., & Sepulchre, R. (2011). Regression on fixed-rank positive semidefinite matrices: a Riemannian approach.

*Journal of Machine Learning Research, 12*(Feb), 593−625.Peer reviewed (verified by ORBi)

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high ...

Mauroy, A., & Sepulchre, R. (2011). Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators.

*Proceedings of the IEEE Conference on Decision and Control*, 6754-6759.Peer reviewed

In this paper, we investigate the behavior of pulse-coupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the ...

Meyer, G., Bonnabel, S., & Sepulchre, R. (2011). Linear regression under fixed-rank constraints: a Riemannian approach.

*Proceedings of the 28th International Conference on Machine Learning*.Peer reviewed

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop ...

Sepulchre, R., Sarlette, A., & Rouchon, P. (2010). Consensus in non-commutative spaces.

*Proceedings of the 49th IEEE Conference on Decision and Control*(pp. 6596-6601). Atlanta, GA: IEEE.Peer reviewed

Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus ...

Sepulchre, R. (2010). Consensus on Nonlinear Spaces.

*Proceedings of the 8th IFAC Symposium on Nonlinear Control Systems*.Peer reviewed

Consensus problems have attracted significant attention in the control community
over the last decade. They act as a rich source of new mathematical problems pertaining to
the growing field of cooperative ...

Bonnabel, S., Meyer, G., & Sepulchre, R. (2010). Adaptive filtering for estimation of a low-rank positive semidefinite matrix.

*Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems*.Peer reviewed

In this paper, we adopt a geometric viewpoint to tackle the problem of estimating a linear model whose parameter is a fixed-rank positive semidefinite matrix. We consider two gradient descent flows associated ...

Mauroy, A., Hendrickx, J., Megretski, A., & Sepulchre, R. (2010). Global Analysis of Firing Maps.

*Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems*(pp. 1775-1782).Peer reviewed

In this paper, we study the behavior of pulse-coupled integrate-and-fire oscillators. Each oscillator is characterized by a state evolving between two threshold values. As the state reaches the upper threshold ...

Hafner, M., Sacré, P., Symul, L., Sepulchre, R., & Koeppl, H. (2010). Multiple feedback loops in circadian cycles: robustness and entrainment as selection criteria.

*Proceedings of the Seventh International Workshop on Computational Systems Biology, WCSB 2010*.Peer reviewed

This paper discusses the contribution of an additional feedback loop to the entrainment and the robustness of a circadian system. To quantify robustness, we perform a global analysis of the system's parameter ...

Sepulchre, R., Absil, P.-A., & Bonnabel, S. (2010). Géométrie des matrices positives semi-définies de rang fixé : un peu de théorie et beaucoup d’applications.

*Proceedings of Sixième Conférence Internationale Francophone d'Automatique (CIFA 2010)*.Peer reviewed

Cet article est une introduction au calcul et `a
l’optimisation sur les matrices sym´etriques positives semid
´efinies de rang (faible) fix´e. L’approche propos´ee est bas´ee
sur deux g´eom´etries ...

Sarlette, A., Bonnabel, S., & Sepulchre, R. (2010). Coordinated motion design on Lie groups.

*IEEE Transactions on Automatic Control, 55*(5), 1047-1058.Peer reviewed (verified by ORBi)

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it ...

Absil, P.-A., Mahony, R., & Sepulchre, R. (2010). Optimization on manifolds : methods and applications.

*Recent Advances in Optimization and its Applications in Engineering*(pp. 125-144). Springer-Verlag.Summary. This paper provides an introduction to the topic of optimization on
manifolds. The approach taken uses the language of differential geometry, however,
we choose to emphasise the intuition of the ...

Journée, M., Bach, F., Absil, P.-A., & Sepulchre, R. (2010). Refining Sparse Principal Components. In M., Diehl (Ed.),

*Recent Advances in Optimization and its Applications in Engineering*(pp. 165-171). Springer-Verlag.In this paper, we discuss methods to refine locally optimal solutions of
sparse PCA. Starting from a local solution obtained by existing algorithms, these
methods take advantage of convex relaxations of the ...

Lageman, C., & Sepulchre, R. (2010). Optimal Data Fitting on Lie Groups: a Coset Approach. In M., Diehl (Ed.),

*Recent Advances in Optimization and its Applications in Engineering*(pp. 173-182). Springer-Verlag.This work considers the problem of fitting data on a Lie group by a
coset of a compact subgroup. This problem can be seen as an extension of the problem
of fitting affine subspaces in Rn to data which can be ...

Efimov, D., Sacré, P., & Sepulchre, R. (2009). Controlling the phase of an oscillator: a phase response curve approach.

*Proceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference*(pp. 7692–7697).Peer reviewed

The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC) calculated ...

Lageman, C., Sarlette, A., & Sepulchre, R. (2009). Synchronization with partial state feedback on SO(n).

*Proceedings of the 48th IEEE Conference on Decision and Control*(pp. 1696-1701).Peer reviewed

This paper considers 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 ...

Sarlette, A., & Sepulchre, R. (2009). Consensus on homogeneous manifolds.

*Proceedings of the 48th IEEE Conference on Decision and Control*(pp. 6438-6443).Peer reviewed

The present paper considers distributed consensus algorithms for agents evolving on a connected compact homogeneous (CCH) manifold. The agents track no external reference and communicate their relative state ...

Sarlette, A., & Sepulchre, R. (2009). A PDE viewpoint on basic properties of coordination algorithms with symmetries.

*Proceedings of the 48th IEEE Conference on Decision and Control*(pp. 5139-5144).Peer reviewed

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation ...

Collard, A. (2009).

*Résonance stochastique dans les modèles neuronaux de type Hodgkin-Huxley : Etude et Application*. Unpublished master thesis, Université de Liège, Belgique.En 1981, Benzi et al ont introduit le phénomène de résonance stochastique pour expliquer leurs observations sur les changements climatiques de notre planète. Depuis, ce phénomène a été largement étudié dans ...

Sarlette, A., Sepulchre, R., & Leonard, N. (2009). Autonomous rigid body attitude synchronization.

*Automatica, 45*(2), 572-577.Peer reviewed (verified by ORBi)

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 ...

Sarlette, A. (2009).

*Geometry and Symmetries in Coordination Control*. Unpublished doctoral thesis, Université de Liège.The present dissertation studies speciﬁc issues related to the coordination of a set of “agents” evolving on a nonlinear manifold, more particularly a homogeneous manifold or a Lie group. The viewpoint is ...

Sarlette, A., & Sepulchre, R. (2009). Consensus optimization on manifolds.

*SIAM Journal on Control & Optimization, 48*(1), 56-76.Peer reviewed (verified by ORBi)

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative ...

Meyer, G., Journée, M., Bonnabel, S., & Sepulchre, R. (2009). From subspace learning to distance learning: a geometrical optimization approach.

*Proceedings of the 2009 IEEE Workshop on Statistical Signal Processing (SSP2009)*(pp. 385 - 388).In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this prob- lem can be cast into the estimation of a fixed-rank positive semidefinite (PSD ...

Scardovi, L., & Sepulchre, R. (2009). Synchronization in Networks of Identical Linear Systems.

*Automatica, 45*(11), 2557-2562.Peer reviewed (verified by ORBi)

Sarlette, A., Bonnabel, S., & Sepulchre, R. (2008). Coordination on Lie groups.

*Proceedings of the 47th IEEE Conference on Decision and Control*(pp. 1275-1279).Peer reviewed

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left- or right-invariance with respect to the absolute position on the group lead to two different characterizations of ...

Mauroy, A., & Sepulchre, R. (2008). Clustering behaviors in networks of integrate-and-fire oscillators.

*Chaos, 18*, 037122.Peer reviewed (verified by ORBi)

Clustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse
coupling. When considering a population of identical oscillators, the main result is a proof of global ...

Sarlette, A., Tuna, S. E., Blondel, V., & Sepulchre, R. (2008). Global synchronization on the circle.

*Proceedings of the 17th IFAC World Congress*(pp. 9045-9050).Peer reviewed

The convexity arguments used in the consensus literature to prove synchronization in vector spaces can be applied to the circle only when all agents are initially located on a semicircle. Existing strategies ...

Ronsse, R., Lefèvre, P., & Sepulchre, R. (2008). Robotics and neuroscience: A rhythmic interaction.

*Neural Networks, 21*(4), 577-583.Peer reviewed (verified by ORBi)

At the crossing between motor control neuroscience and robotics system theory, the paper presents
a rhythmic experiment that is amenable both to handy laboratory implementation and simple
mathematical ...

Sepulchre, R., Paley, D., & Leonard, N. E. (2008). Stabilization of Planar Collective Motion With Limited Communication.

*IEEE Transactions on Automatic Control, 53*(3), 706-719.Peer reviewed (verified by ORBi)

This paper proposes a designmethodology to stabilize
relative equilibria in a model of identical, steered particles moving
in the plane at unit speed. Relative equilibria either correspond
to parallel ...

Ronsse, R., Thonnard, J. L., Lefevre Philippe, & Sepulchre, R. (2008, February 10). Control of Bimanual Rhythmic Movements: Trading Efficiency for Robustness Depending on the Context.

*Experimental Brain Research = Experimentelle Hirnforschung = Expérimentation Cérébrale*.Peer reviewed (verified by ORBi)

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts with ...

Absil, P.-A., Sepulchre, R., & Mahony, R. (2008). Continuous-time susbspace flows related to the symmetric eigenvalue problem.

*Pacific Journal of Optimization, 4*(2), 179--194.Peer reviewed

The classes of continuous-time flows on Rn×p that induce the same flow
on the set of p-dimensional subspaces of Rn are described. The power
flow is briefly reviewed in this framework, and a subspace ...

Scardovi, L., Leonard, N. E., & Sepulchre, R. (2008). STABILIZATION OF THREE-DIMENSIONAL COLLECTIVE MOTION.

*Communications in Information and Systems, 8*(4), 473-500.Peer reviewed

This paper proposes a methodology to stabilize relative equilibria in a model of
identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group
structure of the resulting ...

Paley, D., Leonard, N., Sepulchre, R., & Couzin, I. D. (2007). Spatial Models of Bistability in Biological Collectives.

*Proceedings of the 46th IEEE Conference on Decision and Control*(pp. 4851-4856).Peer reviewed

We explore collective behavior in biological systems
using a cooperative control framework. In particular, we
study a hysteresis phenomenon in which a collective switches
from circular to parallel motion ...

Sanfelice, R. G., Teel, A. R., & Sepulchre, R. (2007). A Hybrid Systems Approach to Trajectory Tracking Control for Juggling Systems.

*Proceedings of the 46th IEEE Conference on Decision and Control*(pp. 5282-5287).Peer reviewed

From a hybrid systems point of view, we provide
a modeling framework and a trajectory tracking control design
methodology for juggling systems. We present the main ideas
and concepts in a one degree-of ...

Sarlette, A., Sepulchre, R., & Leonard, N. (2007). Autonomous rigid body attitude synchronization.

*Proceedings of the 46th IEEE Conference on Decision and Control*(pp. 2566-2571).Peer reviewed

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 ...

Scardovi, L., Leonard, N., & Sepulchre, R. (2007). Stabilization of Collective Motion in Three Dimensions : A Consensus Approach.

*Proceedings of 46th IEEE Conference on Decision and Control*(pp. 2931-2936).Peer reviewed

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-
dimensional Euclidean space. Exploiting the Lie group structure of the resulting ...

Swain, D. T., Leonard, N. E., Couzin, I. D., Kao, A., & Sepulchre, R. (2007). Alternating Spatial Patterns for Coordinated Group Motion.

*Proceedings of the 46th IEEE Conference on Decision and Control*(pp. 2925-2931).Peer reviewed

Abstract—Motivated by recent observations of fish schools,
we study coordinated group motion for individuals with oscillatory
speed. Neighbors that have speed oscillations with
common frequency, amplitude ...

tuna, S. E., & Sepulchre, R. (2007). Consensus under general convexity.

*Proceedings of the 46th IEEE Conference on Decision and Control*(pp. 294-299).Peer reviewed

A method is proposed to characterize contraction
of a set through orthogonal projections. For discrete-time
multi-agent systems, quantitative estimates of convergence (to
a consensus) rate are provided by ...

Ronsse, R., Lefevre, P., & Sepulchre, R. (2007). Rhythmic feedback control of a blind planar juggler.

*IEEE Transactions on Robotics, 23*(4), 790-802.Peer reviewed (verified by ORBi)

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness ...

Teschendorff, A. E., Journee, M., Absil, P.-A., Sepulchre, R., & Caldas, C. (2007). Elucidating the altered transcriptional programs in breast cancer using independent component analysis.

*PLoS Computational Biology, 3*(8), 1539-1554.Peer reviewed (verified by ORBi)

The quantity of mRNA transcripts in a cell is determined by a complex interplay of cooperative and counteracting biological processes. Independent Component Analysis ( ICA) is one of a few number of ...

tuna, S. E., & Sepulchre, R. (2007). Quantitative onvergence analysis of multi-agent systems.

*Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems*(pp. 236-241).Peer reviewed

We introduce a characterization of contraction for bounded convex sets. For discrete-time multi-agent systems we provide an explicit upperbound on the rate of convergence to a consensus under the assumptions ...

Chang, D. E., & Sepulchre, R. (2007). Time-optimal control of a 3-level quantum system and its generalization to an n-level system.

*Proceedings of the 26th American Control Conference (ACC 2007)*.Peer reviewed

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 ...

Scardovi, L., Sepulchre, R., & Leonard, N. (2007). Stabilization Laws for Collective Motion in Three Dimensions.

*Proceedings of the European Control Conference*.Peer reviewed

This paper proposes a framework for the design of
control laws that stabilize relative equilibria in a model of identical,
steered particles moving in three-dimensional Euclidean
space. Under the assumption ...

Mauroy, A. (2007).

*Phénomènes dynamiques de synchronisation par couplage impulsif*. Unpublished master thesis, Université de Liège.Synchronization phenomena are extremely important and omnipresent in nature. So they are part of the most observed biological behaviours. For instance, they point up the way of working of some brain mechanisms ...

Sarlette, A. (2007).

*Towards coordination algorithms on compact Lie groups*. Unpublished DEA/DES thesis, Université de Liège.The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a so ...

Sarlette, A., Sepulchre, R., & Leonard, N. (2007). Cooperative attitude synchronization in satellite swarms: a consensus approach.

*Proceedings of the 17th IFAC Symposium on Automatic Control in Aerospace*(pp. 02.1).Peer reviewed

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 ...

Scardovi, L., Sarlette, A., & Sepulchre, R. (2007). Synchronization and balancing on the N-torus.

*Systems & Control Letters, 56*(5), 335-341.Peer reviewed (verified by ORBi)

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 ...

Sepulchre, R., Paley, D., & Leonard, N. E. (2007). Stabilization of planar collective motion: All-to-all communication.

*IEEE Transactions on Automatic Control, 52*(5), 811-824.Peer reviewed (verified by ORBi)

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria ...

Stan, G. B., & Sepulchre, R. (2007). Analysis of interconnected oscillators by dissipativity theory.

*IEEE Transactions on Automatic Control, 52*(2), 256-270.Peer reviewed (verified by ORBi)

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 ...

Leonard, N. E., Paley, D., Lekien, F., Sepulchre, R., Fratantoni, D. M., & Davis, R. E. (2007). Collective motion, sensor networks, and ocean sampling.

*Proceedings of the IEEE, 95*(1), 48-74.Peer reviewed (verified by ORBi)

This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and ...

Bonjean, M., Phillips, C., Dang Vu, T. T., Sepulchre, R., & Maquet, P. (2007). An in computo investigation of the Landau-Kleffner syndrome.

*Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference, 2007*, 2730-4.Peer reviewed

We describe a computational model of the thalamus and the cortex able to reproduce some essential epileptiform features commonly observed in the Landau-Kleffner syndrome. Investigation with this realistic ...

Chang, D. E., & Sepulchre, R. (2007). Time-optimal control of a 3-level quantum system and its generalization.

*Dynamics of Continuous, Discrete and Impulsive Systems Series, 14*, 575-592.Peer reviewed

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 ...

Ronsse, R., & Sepulchre, R. (2006). Feedback Control of Impact Dynamics: the Bouncing Ball Revisited.

*Proceedings of the 45th IEEE Conference on Decision and Control*.Peer reviewed

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 ...

Sarlette, A., Sepulchre, R., & Leonard, N. (2006). Discrete-time synchronization on the N-torus.

*Proceedings of the 17th MTNS Symposium, Kyoto 2006*(pp. 2408-2414).Peer reviewed

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 ...

Ronsse, R., Lefevre, P., & Sepulchre, R. (2006). Sensorless stabilization of bounce juggling.

*IEEE Transactions on Robotics, 22*(1), 147-159.Peer reviewed (verified by ORBi)

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 ...

Scardovi, L., & Sepulchre, R. (2006). Collective optimization over average quantities.

*Proceedings of the 45th IEEE Conference on Decision and Control*(pp. 3369-3374).Peer reviewed

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 ...

Ronsse, R., Lefevre, P., & Sepulchre, R. (2005). Timing Feedback Control of a Rhythmic System.

*Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference 2005*.Peer reviewed

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 ...

Sepulchre, R., & Stan, G. B. (2005). Feedback mechanisms for global oscillations in Lure systems.

*Systems & Control Letters, 54*(8), 809-818.Peer reviewed (verified by ORBi)

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 ...

Paley, D., Leonard, N., & Sepulchre, R. (2005). Oscillator Models and Collective Motion: Splay State Stabilization of Self-Propelled Particles.

*Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference*.Peer reviewed

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 ...

Sepulchre, R. (2005). Oscillators as Systems and Synchrony as a Design Principle. In L., Menini, L., Zaccarian, & C. T., Abdallah (Eds.),

*Current trends in nonlinear systems and control*. Springer-Verlag.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 ...

Sepulchre, R., Paley, D., & Leonard, N. (2005). Collective motion and oscillator synchronization.

*Cooperative Control*(pp. 189-205). Berlin: Springer-Verlag Berlin.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 ...

Paley, D., Leonard, N., & Sepulchre, R. (2004). Collective Motion: Bistability and Trajectory Tracking.

*Proceedings of the 43rd IEEE Conference on Decision and Control*.Peer reviewed

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 ...

Gerard, M., & Sepulchre, R. (2004). STABILIZATION THROUGH WEAK AND OCCASIONAL INTERACTIONS : A BILLIARD BENCHMARK.

*Proceedings of the 6th IFAC Symposium on Nonlinear Control Systems*(pp. 73-78).Peer reviewed

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 ...

Ronsse, R., Lefèvre, P., & Sepulchre, R. (2004). OPEN-LOOP STABILIZATION OF 2D IMPACT JUGGLING.

*Proceedings of 6th IFAC Symposium on Nonlinear Control Systems*(pp. 1157-1162).Peer reviewed

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 ...

Absil, P.-A., & Sepulchre, R. (2004). Continuous dynamical systems that realize discrete optimization on the hypercube.

*Systems & Control Letters, 52*(3-4), 297-304.Peer reviewed (verified by ORBi)

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 ...

Stan, G.-B., & Sepulchre, R. (2004). DISSIPATIVITY AND GLOBAL ANALYSIS OF LIMIT CYCLES IN NETWORKS OF OSCILLATORS.

*Proceedings of the 16th Symposium on Mathematical Theory of Networks and Systems*.Peer reviewed

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 ...

Absil, P.-A., Mahony, R., & Sepulchre, R. (2004). Riemannian geometry of Grassmann manifolds with a view on algorithmic computation.

*Acta Applicandae Mathematicae, 80*(2), 199-220.Peer reviewed

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 ...

Absil, P.-A., Sepulchre, R., Van Dooren, P., & Mahony, R. (2004). Cubically convergent iterations for invariant subspace computation.

*SIAM Journal on Matrix Analysis and Applications, 26*(1), 70-96.Peer reviewed (verified by ORBi)

We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of R-n and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in ...

Sepulchre, R., & Gerard, M. (2003). Stabilization of periodic orbits in a wedge billiard.

*Proceedings of the 42nd IEEE Conference on Decision and Control*.Peer reviewed

This paper introduces a stabilization problem for
an elementary impact control system in the plane. The rich
dynamical properties of the wedge billiard, combined to the
relevance of the associated ...

Absil, P.-A., Mahony, R., Sepulchre, R., & Van Dooren, P. (2002). A Grassmann-Rayleigh quotient iteration for computing invariant subspaces.

*SIAM Review, 44*(1), 57-73.Peer reviewed (verified by ORBi)

The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQl which computes a p-dimensional ...

Sepulchre, R., Arcak, M., & Teel, A. R. (2002). Trading the Stability of Finite Zeros for Global Stabilization of Nonlinear Cascade Systems.

*IEEE Transactions on Automatic Control, 47*(3), 521-525.Peer reviewed (verified by ORBi)

This note analyzes the stabilizability properties of nonlinear
cascades in which a nonminimum phase linear system is interconnected
through its output to a stable nonlinear system. It is shown that the ...

Moreau, L., Aeyels, D., Peuteman, J., & Sepulchre, R. (2002). A duality principle for homogeneous vector fields with applications.

*Systems & Control Letters, 47*(1), 37-46.Peer reviewed (verified by ORBi)

We introduce a duality principle for homogeneous vectorfields. As an application of this duality principle, stability and boundedness results for negative order homogeneous differential equations are obtained ...

Grognard, F., & Sepulchre, R. (2001). Global analysis of a continuous-time flow whith computes time-optimal switchings.

*Proceedings of the 40th IEEE Conference on Decision and Control*(pp. 3826-3831).Peer reviewed

The minimum-time bounded control of linear systems is generically bang-bang and the number of switchings does not exceed the dimension of the system if the eigenvalues of the system matrix are real. This ...

Grognard, F., Jadot, F., Magni, L., Bastin, G., Sepulchre, R., & Wertz, V. (2001). Robust global state feedback stabilization of cement mills.

*IEEE Transactions on Automatic Control, 46*(4), 618-623.Peer reviewed (verified by ORBi)

Plugging is well known to be a major cause of instability in industrial cement mills. A
simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown
how a nonlinear robust ...

Michiels, W., Sepulchre, R., & Roose, D. (2001). Stability of perturbed functional differential equations and stabilization of nonlinear cascades.

*SIAM Journal on Control & Optimization, 40*.Peer reviewed (verified by ORBi)

In this paper the effect of bounded input perturbation on the stability of nonlinear globally asymptotically stable delay differential equations is analyzed. We investigate under which conditions global ...

Grognard, F., Sepulchre, R., & Bastin, G. (1999). Global stabilization of feedforward systems with exponentially unstable Jacobian linearization.

*Systems & Control Letters, 37*(2), 107-115.Peer reviewed (verified by ORBi)

The global stabilization of a class of feedforward systems having an
exponentially unstable Jacobian linearization is achieved by a high
gain feedback saturated at a low level. The control law forces the ...

Mazenc, F., Sepulchre, R., & Jankovic, M. (1999). Lyapunov functions for stable cascades and applications to global stabilization.

*IEEE Transactions on Automatic Control, 44*(9), 1795-1800.Peer reviewed (verified by ORBi)

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems one of which is stable rather than asymptotically stable. A new a cross term construction in the Lyapunov function ...

Sepulchre, R., & Kokotovic, P. (1998). Shape signifiers for throttle control of a low-order compressor model.

*IEEE Transactions on Automatic Control, 43*(11), 1643-1648.Peer reviewed (verified by ORBi)

Rotating stall and surge, two instability mechanisms limiting
the performance of aeroengines compressors, are studied on the
third-order Moore–Greitzer model. The skewness of the compressor
characteristic ...

Aeyels, D., Sepulchre, R., & Peuteman, J. (1998). Asymptotic stability conditions for time-variant systems and observability : uniform and non-uniform criteria.

*Mathematics of Control, Signals & Systems, 11*, 1-27.Peer reviewed (verified by ORBi)

This paper presents some new criteria for uniform and non uniform asymtotic stability of equilibria for time-variant differential equations and this within a Liapunov approach. The stability criteria are ...

Jankovic, M., Sepulchre, R., & Kokotovic, P. V. (1997). Global adaptive stabilization of cascade nonlinear systems.

*Automatica, 33*(2), 263-368.Peer reviewed (verified by ORBi)

An adaptive controller is developed for a class of nonlinear systems for which other approaches (e.g. backstepping) may fail to be applicable. The new design employs feedback passivation and an explicit ...

Magni, L., & Sepulchre, R. (1997). Stability margins of nonlinear receding horizon control via inverse optimality.

*Systems & Control Letters, 32*(4), 241-245.Peer reviewed (verified by ORBi)

Using the nonlinear analog of the Fake Riccati equation developed for linear systems, we derive an inverse optimality result for several receding horizon control schemes. This inverse optimality result ...

Sepulchre, R., Jankovic, M., & Kokotovic, P. V. (1997). Integrator forwarding : a new recursive nonlinear robust design.

*Automatica, 33*(5), 979-984.Peer reviewed (verified by ORBi)

We consider the global stabilization of nonlinear systems in strict feedforward form. We show that these systems, while not feedback linearizable, can be (globally) transformed by feedback and diffeomorphism ...

Sepulchre, R., & Aeyels, D. (1996). Homogeneous Lyapunov Functions and Necessary Conditions for Stabilization.

*Journal of mathematics for control, signal and systems, 9*(1), 34-58.Peer reviewed

We provide necessary conditions for the stabilization of nonlinear
control systems with the additional requirement that a time-invariant homogeneous
Lyapunov function exists for the closed-loop system.