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Adiabatic passage and ensemble control of quantum systems ; Sarlette, Alain ; in Journal of Physics : B Atomic Molecular & Optical Physics (2011), 44(15), 154017 This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be ... [more ▼] This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol—chirped pulse—practised by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude-shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with unknown coupling strengths. These adiabatic control protocols are illustrated by simulations on a four-level ladder. [less ▲] Detailed reference viewed: 50 (2 ULg)Voltage control in an HVDC system to share primary frequency reserves between non-synchronous areas ; ; Sarlette, Alain et al in Proceedings of the 17th Power Systems Computation Conference (PSCC-11) (2011) This paper addresses the problem of frequency control for non-synchronous AC areas connected by a multi-terminal HVDC grid. It proposes a decentralized control scheme for the DC voltages of the HVDC ... [more ▼] This paper addresses the problem of frequency control for non-synchronous AC areas connected by a multi-terminal HVDC grid. It proposes a decentralized control scheme for the DC voltages of the HVDC converters aimed to make the AC areas collectively react to power imbalances. A theoretical study shows that, by using local information only, the control scheme allows to signiﬁcantly reduce the impact of a power imbalance by distributing the associated frequency deviation over all areas. A secondary frequency control strategy that can be combined with this control scheme is also proposed so as to restore the frequencies and the power exchanges to their nominal values in the aftermath of a power imbalance. Simulation results on a benchmark system with ﬁve AC areas illustrate the good performance of the control scheme. [less ▲] Detailed reference viewed: 239 (7 ULg)Synchronization on the circle Sarlette, Alain ; Sepulchre, Rodolphe in Dubbeldam; Green; Lenstra (Eds.) "The complexity of dynamical systems: a multi-disciplinary perspective" (2011) Detailed reference viewed: 71 (3 ULg)Stabilization of Nonclassical States of the Radiation Field in a Cavity by Reservoir Engineering Sarlette, Alain ; ; et al in Physical Review Letters (2011), 107 We propose an engineered reservoir inducing the relaxation of a cavity field towards nonclassical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity interaction ... [more ▼] We propose an engineered reservoir inducing the relaxation of a cavity field towards nonclassical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity interaction is first dispersive, then resonant, then dispersive again. The reservoir pointer states are those produced by an effective Kerr Hamiltonian acting on a coherent field. We thereby stabilize squeezed states and quantum superpositions of multiple coherent components in a cavity having a finite damping time. This robust decoherence protection method could be implemented in state-of-the-art experiments. [less ▲] Detailed reference viewed: 12 (0 ULg)Real-time synchronization feedbacks for single-atom frequency standards: V- and Lambda-structure systems ; Sarlette, Alain ; in Proceedings of the 49th IEEE Conference on Decision and Control (2010, December) This paper proposes simple feedback loops, inspired from extremum-seeking, that use the photon emission times of a single quantum system following quantum Monte-Carlo trajectories in order to lock in real ... [more ▼] This paper proposes simple feedback loops, inspired from extremum-seeking, that use the photon emission times of a single quantum system following quantum Monte-Carlo trajectories in order to lock in real time a probe frequency to the system’s transition frequency. Two specific settings are addressed: a 3-level system coupling one ground to two excited states (one highly unstable and one metastable) and a 3-level system coupling one excited to two ground states (both metastable). Analytical proofs and simulations show the accurate and robust convergence of probe frequency to system-transition frequency in the two cases. [less ▲] Detailed reference viewed: 29 (3 ULg)Consensus in non-commutative spaces Sepulchre, Rodolphe ; Sarlette, Alain ; in Proceedings of the 49th IEEE Conference on Decision and Control (2010, December) 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 ... [more ▼] 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 in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. [less ▲] Detailed reference viewed: 64 (5 ULg)Impact of delays on a consensus-based primary frequency control scheme for AC systems connected by a multi-terminal HVDC grid ; ; Sarlette, Alain et al in Proceedings of the 2010 IREP Symposium - Bulk Power Systems Dynamics and Control - VIII (2010, August) This paper addresses the problem of sharing primary frequency control reserves among nonsynchronous AC systems connected by a multi-terminal HVDC grid. We focus on a control scheme that modifies the power ... [more ▼] This paper addresses the problem of sharing primary frequency control reserves among nonsynchronous AC systems connected by a multi-terminal HVDC grid. We focus on a control scheme that modifies the power injections from the different areas into the DC grid based on remote measurements of the other areas’ frequencies. This scheme is proposed and applied to a simplified system in a previous work by the authors. The current paper investigates the effects of delays on the control scheme’s effectiveness. The study shows that there generally exists a maximum acceptable delay, beyond which the areas’ frequency deviations fail to converge to an equilibrium point. This constraint should be taken into account when commissioning such a control scheme. [less ▲] Detailed reference viewed: 67 (9 ULg)The planar optics phase sensor: a study for the VLTI 2nd generation fringe tracker ; ; Absil, Olivier et al in Danchi, W. C.; Delplancke, F.; Rajagopal, J. K. (Eds.) Optical and Infrared Interferometry II (2010, July) In a few years, the second generation instruments of the Very Large Telescope Interferometer (VLTI) will routinely provide observations with 4 to 6 telescopes simultaneously. To reach their ultimate ... [more ▼] In a few years, the second generation instruments of the Very Large Telescope Interferometer (VLTI) will routinely provide observations with 4 to 6 telescopes simultaneously. To reach their ultimate performance, they will need a fringe sensor capable to measure in real time the randomly varying optical paths differences. A collaboration between LAOG (PI institute), IAGL, OCA and GIPSA-Lab has proposed the Planar Optics Phase Sensor concept to ESO for the 2[SUP]nd[/SUP] Generation Fringe Tracker. This concept is based on the integrated optics technologies, enabling the conception of extremely compact interferometric instruments naturally providing single-mode spatial filtering. It allows operations with 4 and 6 telescopes by measuring the fringes position thanks to a spectrally dispersed ABCD method. We present here the main analysis which led to the current concept as well as the expected on-sky performance and the proposed design. [less ▲] Detailed reference viewed: 51 (12 ULg)Coordinated motion design on Lie groups Sarlette, Alain ; ; Sepulchre, Rodolphe in IEEE Transactions on Automatic Control (2010), 55(5), 1047-1058 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 ... [more ▼] 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 introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3) , SE(2) and SE(3). [less ▲] Detailed reference viewed: 70 (19 ULg)Synchronization with partial state feedback on SO(n), ; Sarlette, Alain ; Sepulchre, Rodolphe in Proceedings of the 48th IEEE Conference on Decision and Control (2009, December) 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 ... [more ▼] 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 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. [less ▲] Detailed reference viewed: 35 (6 ULg)Consensus on homogeneous manifolds Sarlette, Alain ; Sepulchre, Rodolphe in Proceedings of the 48th IEEE Conference on Decision and Control (2009, December) 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 ... [more ▼] 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 according to an interconnection graph. The paper first formalizes the consensus problem for synchronization (i.e. maximizing the consensus) and balancing (i.e. minimizing the consensus); it thereby introduces the induced arithmetic mean, an easily computable mean position on CCH manifolds. Then it proposes and analyzes various consensus algorithms on manifolds: natural gradient algorithms which reach local consensus equilibria; an adaptation using auxiliary variables for almost-global synchronization or balancing; and a stochastic gossip setting for global synchronization. It closes by investigating the dependence of synchronization properties on the attraction function between interacting agents on the circle. The theory is also illustrated on SO(n) and on the Grassmann manifolds. [less ▲] Detailed reference viewed: 41 (7 ULg)A PDE viewpoint on basic properties of coordination algorithms with symmetries Sarlette, Alain ; Sepulchre, Rodolphe in Proceedings of the 48th IEEE Conference on Decision and Control (2009, December) 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 ... [more ▼] 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 of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. [less ▲] Detailed reference viewed: 22 (4 ULg)An application of distributed control: segmented primary mirror for the European Extremely Large Telescope Bastin, Christian ; Sarlette, Alain ; Sepulchre, Rodolphe Conference (2009, March) Detailed reference viewed: 47 (20 ULg)Autonomous rigid body attitude synchronization Sarlette, Alain ; Sepulchre, Rodolphe ; in Automatica (2009), 45(2), 572-577 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 ... [more ▼] 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". In 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. [less ▲] Detailed reference viewed: 67 (12 ULg)Consensus optimization on manifolds Sarlette, Alain ; Sepulchre, Rodolphe in SIAM Journal on Control & Optimization (2009), 48(1), 56-76 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 ... [more ▼] 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 state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to eﬃcient gradient algorithms to synchronize (i.e., maximizing the consensus) or balance (i.e., minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a speciﬁc centroid deﬁnition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) and the Grassmann manifold Grass(p,n) are treated as original examples. A link is also drawn with the many existing results on the circle. [less ▲] Detailed reference viewed: 61 (8 ULg)Geometry and Symmetries in Coordination Control Sarlette, Alain Doctoral thesis (2009) 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 ... [more ▼] 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 somewhere between control algorithm design and system analysis, as algorithms are derived from simple principles — often retrieving existing models — to highlight speciﬁc behaviors. With a fair amount of approximation, the objective of the dissertation can be summarized by the following question: Given a swarm of identical agents evolving on a nonlinear, nonconvex conﬁguration space with high symmetry, how can you deﬁne speciﬁc collective behavior, and how can you design individual agent control laws to get a collective behavior, without introducing hierarchy nor external reference points that would break the symmetry of the conﬁguration space? Maintaining the basic symmetries of the coordination problem lies at the heart of the contributions. The main focus is on the global geometric invariance of the conﬁguration space. This contrasts with most existing work on coordination, where either the agents evolve on vector spaces — which, to some extent, can cover local behavior on manifolds — or coordination is coupled to external reference tracking such that the reference can serve as a beacon around which the geometry is distorted towards vector space-like properties. A second, more standard symmetry is to treat all agents identically. Another basic ingredient of the coordination problem that has important implications in this dissertation is the reduced agent interconnectivity: each agent only gets information from a limited set of other agents, which can be varying. In order to focus on issues related to geometry / symmetry and reduced interconnectivity, individual agent dynamics are drastically simpliﬁed to simple integrators. This is justiﬁed at a “planning” level. Making the step towards realistic dynamics is illustrated for the speciﬁc case of rigid body attitude synchronization. The main contributions of this dissertation are I. an extensive study of synchronization on the circle, (a) highlighting diﬃculties encountered for coordination and (b) proposing simple strategies to overcome these diﬃculties; II. (a) a geometric deﬁnition and related control law for “consensus” conﬁgurations on compact homogeneous manifolds, of which synchronization — all agents at the same point — is a special case, and (b) control laws to (almost) globally reach synchronization and “balancing”, its opposite, under general interconnectivity conditions; III. several propositions for rigid body attitude synchronization under mechanical dynamics; IV. a geometric framework for “coordinated motion” on Lie groups, (a) giving a geometric deﬁnition of coordinated motion and investigating its implications, and (b) providing systematic methods to design control laws for coordinated motion. Examples treated for illustration of the theoretical concepts are the circle S^1 (sometimes the sphere S^n ), the rotation group SO(n), the rigid-body motion groups SE(2) and SE(3) and the Grassmann manifolds Grass(p,n). The developments in this dissertation remain at a rather theoretical level; potential applications are brieﬂy discussed. [less ▲] Detailed reference viewed: 283 (24 ULg)Coordination on Lie groups Sarlette, Alain ; ; Sepulchre, Rodolphe in Proceedings of the 47th IEEE Conference on Decision and Control (2008, December) 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 ... [more ▼] 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 relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2). [less ▲] Detailed reference viewed: 42 (16 ULg)Global synchronization on the circle Sarlette, Alain ; ; et al in Proceedings of the 17th IFAC World Congress (2008, July) 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 ... [more ▼] 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 for (almost-)global synchronization on the circle are either restricted to speciﬁc interconnection topologies or use auxiliary variables. The present paper ﬁrst illustrates this problem by showing that weighted, directed interconnection topologies can be designed to make any reasonably chosen conﬁguration of the agents on the circle a stable equilibrium of a basic continuous-time consensus algorithm. Then it proposes a so-called “gossip algorithm”, which achieves global asymptotic synchronization on the circle with probability 1 for a large class of interconnections, without using auxiliary variables, thanks to the introduction of randomness in the system. [less ▲] Detailed reference viewed: 147 (7 ULg)Geometric framework for coordination on Lie groups Sarlette, Alain ; Bonnabel, Silvère ; Sepulchre, Rodolphe Conference (2008, March) Detailed reference viewed: 35 (11 ULg)Autonomous rigid body attitude synchronization Sarlette, Alain ; Sepulchre, Rodolphe ; in Proceedings of the 46th IEEE Conference on Decision and Control (2007, December) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 37 (9 ULg) |
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