The Experts below are selected from a list of 210 Experts worldwide ranked by ideXlab platform
Emmanuel Trélat - One of the best experts on this subject based on the ideXlab platform.
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Characterization by observability inequalities of Controllability and stabilization properties
Pure and Applied Analysis, 2020Co-Authors: Emmanuel Trélat, Gengsheng WangAbstract:Given a Linear Control System in a Hilbert space with a bounded Control operator, we establish a characterization of exponential stabilizability in terms of an observability inequality. Such dual characterizations are well known for exact (null) Controllability. Our approach exploits classical Fenchel duality arguments and, in turn, leads to characterizations in terms of observability inequalities of approximately null Controllability and of α-null Controllability. We comment on the relationships between those various concepts, at the light of the observability inequalities that characterize them.
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Linear-quadratic optimal sampled-data Control problems: convergence result and Riccati theory
Automatica, 2017Co-Authors: Loïc Bourdin, Emmanuel TrélatAbstract:We consider a general Linear Control System and a general quadratic cost, where the state evolves continuously in time and the Control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of a Linear-quadratic optimal sampled-data Control problem. As a first result, we prove that, as the sampling periods tend to zero, the optimal sampled-data Controls converge pointwise to the optimal permanent Control. Then, we extend the classical Riccati theory to the sampled-data Control framework, by developing two different approaches: the first one uses a recently established version of the Pontryagin maximum principle for optimal sampled-data Control problems, and the second one uses an adequate version of the dynamic programming principle. In turn, we obtain a closed-loop expression for optimal sampled-data Controls of Linear-quadratic problems.
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Control and stabilization of steady-states in a finite-length ferromagnetic nanowire
ESAIM: Control Optimisation and Calculus of Variations, 2015Co-Authors: Yannick Privat, Emmanuel TrélatAbstract:We consider a finite-length ferromagnetic nanowire, in which the evolution of the magnetization vector is governed by the Landau-Lishitz equation. We first compute all steady-states of this equation, and prove that they share a quantization property in terms of a certain energy. We study their local stability properties. Then we address the problem of Controlling and stabilizing steady-states by means of an external magnetic field induced by a solenoid rolling around the nanowire. We prove that, for a generic placement of the solenoid, any steady-state can be locally exponentially stabilized with a feedback Control. Moreover we design this feedback Control in an explicit way by considering a finite-dimensional Linear Control System resulting from a spectral analysis. Finally, we prove that we can steer approximately the System from any steady-state to any other one, provided that they have the same energy level.
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Uniform Controllability of semidiscrete approximations of parabolic Control Systems
Systems and Control Letters, 2006Co-Authors: Stéphane Labbé, Emmanuel TrélatAbstract:Controlling an approximation model of a Controllable infinite dimensional Linear Control System does not necessarily yield a good approximation of the Control needed for the continuous model. In the present paper, under the main assumptions that the discretized semigroup is uniformly analytic, and that the Control operator is mildly unbounded, we prove that the semidiscrete approximation models are uniformly Controllable. Moreover, we provide a computationally efficient way to compute the approximation Controls. An example of application is implemented for the one- and two-dimensional heat equation with Neumann boundary Control.
Daniel Liberzon - One of the best experts on this subject based on the ideXlab platform.
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Finite data-rate feedback stabilization of switched and hybrid Linear Systems
Automatica, 2014Co-Authors: Daniel LiberzonAbstract:We study the problem of asymptotically stabilizing a switched Linear Control System using sampled and quantized measurements of its state. The switching is assumed to be slow enough in the sense of combined dwell time and average dwell time, each individual mode is assumed to be stabilizable, and the available data rate is assumed to be large enough but finite. Our encoding and Control strategy is rooted in the one proposed in our earlier work on non-switched Systems, and in particular the data-rate bound used here is the data-rate bound from that earlier work maximized over the individual modes. The main technical step that enables the extension to switched Systems concerns propagating over-approximations of reachable sets through sampling intervals, during which the switching signal is not known; a novel algorithm is developed for this purpose. Our primary focus is on Systems with time-dependent switching (switched Systems) but the setting of state-dependent switching (hybrid Systems) is also discussed.
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CDC-ECE - Stabilizing a switched Linear System by sampled-data quantized feedback
IEEE Conference on Decision and Control and European Control Conference, 2011Co-Authors: Daniel LiberzonAbstract:We study the problem of asymptotically stabilizing a switched Linear Control System using sampled and quantized measurements of its state. The switching is assumed to be slow enough in the sense of combined dwell time and average dwell time, each individual mode is assumed to be stabilizable, and the available data rate is assumed to be large enough. Our encoding and Control strategy is rooted in the one proposed in our earlier work on non-switched Systems, and in particular the data-rate bound used here is the data-rate bound from that earlier work maximized over the individual modes. The main technical step that enables the extension to switched Systems concerns propagating over-approximations of reachable sets through sampling intervals, during which the switching signal is unknown.
Vsevolod M. Kuntsevich - One of the best experts on this subject based on the ideXlab platform.
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Linear adaptive Control for nonstationary uncertain Systems under bounded noise
Systems & Control Letters, 1997Co-Authors: Alexi V. Kuntsevich, Vsevolod M. KuntsevichAbstract:A discrete-time nonstationary Linear Control System is considered to be given by the algebraic difference equation in the state space. The Control System is subject to a bounded additive noise. Uncertain parameters of the System take their values on the given polytopes which evolve in time. The objective is to generate a Linear feedback, which provides the minimization of a given performance criterion in adaptive way. In general, the Control problem is reduced to the convex programming one of an insignificant computational complexity. Therewith, the Control problem can be solved analytically in the case of interval set-valued parameter estimates.
Adriano Da Silva - One of the best experts on this subject based on the ideXlab platform.
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The Control set of a Linear Control System on the two dimensional Lie group
Journal of Differential Equations, 2020Co-Authors: Víctor Ayala, Adriano Da SilvaAbstract:Abstract In this paper we explicitly calculate the Control sets associated with a Linear Control System on the two dimensional solvable Lie group. We show that a Linear Control System of such kind admits exactly one Control set or infinite Control sets depending on some algebraic conditions.
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ITW - On the continuity of the invariance entropy for hyperbolic Linear Control Systems on Lie groups
2019 IEEE Information Theory Workshop (ITW), 2019Co-Authors: Adriano Da SilvaAbstract:In this paper we show that the invariance entropy of the chain Control set associated with a hyperbolic Linear Control System on a connected Lie group is continuous with relation to the System parameters.
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On the characterization of the Controllability property for Linear Control Systems on nonnilpotent, solvable three-dimensional Lie groups
Journal of Differential Equations, 2019Co-Authors: Víctor Ayala, Adriano Da SilvaAbstract:Abstract In this paper we show that a complete characterization of the Controllability property for Linear Control System on three-dimensional solvable nonnilpotent Lie groups is possible by the LARC and the knowledge of the eigenvalues of the derivation associated with the drift of the System.
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Control sets of Linear Systems on Lie groups
Nodea-nonlinear Differential Equations and Applications, 2017Co-Authors: Víctor Ayala, Adriano Da Silva, Guilherme ZsigmondAbstract:Like in the classical Linear Euclidean System, we would like to characterize for a Linear Control System on a connected Lie group G its Control set with nonempty interior that contains the identity of G. We show that many topological properties of this Control set are intrinsically connected with the eigenvalues of a derivation associated to the drift of the System. In particular, we prove that if G is a decomposable Lie group there exists only one Control set with nonempty interior for the whole Linear System. Furthermore, for nilpotent Lie groups we characterize when this set is bounded.
Loïc Bourdin - One of the best experts on this subject based on the ideXlab platform.
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Linear-quadratic optimal sampled-data Control problems: convergence result and Riccati theory
Automatica, 2017Co-Authors: Loïc Bourdin, Emmanuel TrélatAbstract:We consider a general Linear Control System and a general quadratic cost, where the state evolves continuously in time and the Control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of a Linear-quadratic optimal sampled-data Control problem. As a first result, we prove that, as the sampling periods tend to zero, the optimal sampled-data Controls converge pointwise to the optimal permanent Control. Then, we extend the classical Riccati theory to the sampled-data Control framework, by developing two different approaches: the first one uses a recently established version of the Pontryagin maximum principle for optimal sampled-data Control problems, and the second one uses an adequate version of the dynamic programming principle. In turn, we obtain a closed-loop expression for optimal sampled-data Controls of Linear-quadratic problems.
