The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Didier Henrion - One of the best experts on this subject based on the ideXlab platform.
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Parabolic Set Simulation for Reachability Analysis of Linear Time Invariant Systems with Integral Quadratic Constraint
European Journal of Control, 2021Co-Authors: Paul Rousse, Pierreloic Garoche, Didier HenrionAbstract:This work extends reachability analyses based on ellipsoidal techniques to Linear Time Invariant (LTI) systems subject to an integral quadratic constraint (IQC) between the past state and disturbance signals , interpreted as an input-output energetic constraint. To compute the reachable set, the LTI system is augmented with a state corresponding to the amount of energy still available before the constraint is violated. For a given parabolic set of initial states, the reachable set of the augmented system is overapproximated with a time-varying parabolic set. Parameters of this Paraboloid are expressed as the solution of an Initial Value Problem (IVP) and the overapproximation relationship with the reachable set is proved. This Paraboloid is actually supported by the reachable set on so-called touching trajectories. Finally , we describe a method to generate all the supporting Paraboloids and prove that their intersection is an exact characterization of the reachable set. This work provides new practical means to compute overapproximation of reachable sets for a wide variety of systems such as delayed systems, rate limiters or energy-bounded linear systems.
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parabolic set simulation for reachability analysis of linear time invariant systems with integral quadratic constraint
European Journal of Control, 2020Co-Authors: Paul Rousse, Pierreloic Garoche, Didier HenrionAbstract:Abstract This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of Paraboloidal overapproximations. These Paraboloids are supported by the reachable tube on touching trajectories. Parameters of each Paraboloid are expressed as a solution to an initial value problem. Compared to previous methods based on the classical linear quadratic regulator, our approach can be applied to unstable systems as well. We tested our approach on large scale systems.
Paul Rousse - One of the best experts on this subject based on the ideXlab platform.
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Parabolic Set Simulation for Reachability Analysis of Linear Time Invariant Systems with Integral Quadratic Constraint
European Journal of Control, 2021Co-Authors: Paul Rousse, Pierreloic Garoche, Didier HenrionAbstract:This work extends reachability analyses based on ellipsoidal techniques to Linear Time Invariant (LTI) systems subject to an integral quadratic constraint (IQC) between the past state and disturbance signals , interpreted as an input-output energetic constraint. To compute the reachable set, the LTI system is augmented with a state corresponding to the amount of energy still available before the constraint is violated. For a given parabolic set of initial states, the reachable set of the augmented system is overapproximated with a time-varying parabolic set. Parameters of this Paraboloid are expressed as the solution of an Initial Value Problem (IVP) and the overapproximation relationship with the reachable set is proved. This Paraboloid is actually supported by the reachable set on so-called touching trajectories. Finally , we describe a method to generate all the supporting Paraboloids and prove that their intersection is an exact characterization of the reachable set. This work provides new practical means to compute overapproximation of reachable sets for a wide variety of systems such as delayed systems, rate limiters or energy-bounded linear systems.
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parabolic set simulation for reachability analysis of linear time invariant systems with integral quadratic constraint
European Journal of Control, 2020Co-Authors: Paul Rousse, Pierreloic Garoche, Didier HenrionAbstract:Abstract This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of Paraboloidal overapproximations. These Paraboloids are supported by the reachable tube on touching trajectories. Parameters of each Paraboloid are expressed as a solution to an initial value problem. Compared to previous methods based on the classical linear quadratic regulator, our approach can be applied to unstable systems as well. We tested our approach on large scale systems.
Jiři Neustupa - One of the best experts on this subject based on the ideXlab platform.
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a refinement of the local serrin type regularity criterion for a suitable weak solution to the navier stokes equations
Archive for Rational Mechanics and Analysis, 2014Co-Authors: Jiři NeustupaAbstract:We formulate a new criterion for regularity of a suitable weak solution v to the Navier–Stokes equations at the space-time point (x0, t0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of (x0, t0), intersected with the exterior of a certain space-time Paraboloid with vertex at point (x0, t0). We make no special assumptions on the solution in the interior of the Paraboloid.
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a refinement of the local serrin type regularity a refinement of the local serrin type regularity criterion for a suitable weak solution to the navier stokes equations
arXiv: Analysis of PDEs, 2013Co-Authors: Jiři NeustupaAbstract:We formulate a new criterion for regularity of a suitable weak solution v to the Navier-Stokes equations at the space-time point (x_0,t_0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of (x_0,t_0), intersected with the exterior of a certain space-time Paraboloid with vertex at point (x_0,t_0). We make no special assumptions on the solution in the interior of the Paraboloid.
Pierreloic Garoche - One of the best experts on this subject based on the ideXlab platform.
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Parabolic Set Simulation for Reachability Analysis of Linear Time Invariant Systems with Integral Quadratic Constraint
European Journal of Control, 2021Co-Authors: Paul Rousse, Pierreloic Garoche, Didier HenrionAbstract:This work extends reachability analyses based on ellipsoidal techniques to Linear Time Invariant (LTI) systems subject to an integral quadratic constraint (IQC) between the past state and disturbance signals , interpreted as an input-output energetic constraint. To compute the reachable set, the LTI system is augmented with a state corresponding to the amount of energy still available before the constraint is violated. For a given parabolic set of initial states, the reachable set of the augmented system is overapproximated with a time-varying parabolic set. Parameters of this Paraboloid are expressed as the solution of an Initial Value Problem (IVP) and the overapproximation relationship with the reachable set is proved. This Paraboloid is actually supported by the reachable set on so-called touching trajectories. Finally , we describe a method to generate all the supporting Paraboloids and prove that their intersection is an exact characterization of the reachable set. This work provides new practical means to compute overapproximation of reachable sets for a wide variety of systems such as delayed systems, rate limiters or energy-bounded linear systems.
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parabolic set simulation for reachability analysis of linear time invariant systems with integral quadratic constraint
European Journal of Control, 2020Co-Authors: Paul Rousse, Pierreloic Garoche, Didier HenrionAbstract:Abstract This paper describes the computation of reachable sets and tubes for linear time-invariant systems with an unknown input bounded by integral quadratic constraints, modeling e.g. delay, rate limiter, or energy bounds. We define a family of Paraboloidal overapproximations. These Paraboloids are supported by the reachable tube on touching trajectories. Parameters of each Paraboloid are expressed as a solution to an initial value problem. Compared to previous methods based on the classical linear quadratic regulator, our approach can be applied to unstable systems as well. We tested our approach on large scale systems.
Yang Heng - One of the best experts on this subject based on the ideXlab platform.
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Fully nonlinear investigation on water entry of a rigid Paraboloid
Engineering Analysis with Boundary Elements, 2020Co-Authors: Sun Shili, Chen Yuhang, Yang HengAbstract:Abstract Oblique water entry of a rigid Paraboloid is investigated by fully nonlinear boundary element method. The deadrise angle of the Paraboloid increases gradually from zero at the bottom tip and a slenderness coefficient is introduced to symbolize the shape of the Paraboloid. Convergence study with respect to time step and element size is carried on to assure the numerical procedure. The free surface elevation and pressure distribution are depicted in time domain. The present solution is compared with the linearized Wagner method and the composite solution with spray jets to investigate the influence of exact fully nonlinear boundary conditions. As there is no sharp edge or tip around the Paraboloid, the water flows over the body both from lateral side and down side in oblique entry, the stagnation point relative to the body moves towards the flow-coming direction, and the negative pressure can be observed on both lateral side and down side of the Paraboloid. The horizontal speed has great influence on horizontal total force and little influence on vertical total force, while the effect of the slenderness coefficient just has the opposite effect.
