A numerical scheme for a class of sweeping processes

Venel, Juliette

doi:10.1007/s00211-010-0329-0

Cited by 50 publications

(79 citation statements)

References 19 publications

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“…2.9) for a result with H = R n under some boundedness assumptions related to the first and second derivatives of the constraints functions g k (t, ·). Our statement, approach and proof of Theorem 9.1 are general and different from those of the aforementioned results in [34,35].…”

Section: This and Proposition 24 Justify The R-prox-regularity Of Thmentioning

confidence: 64%

Discontinuous sweeping process with prox-regular sets

2017

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Abstract. In this paper, we study the well−posedness (in the sense of existence and uniqueness of a solution) of a discontinuous sweeping process involving prox-regular sets in Hilbert spaces. The variation of the moving set is controlled by a positive Radon measure and the perturbation is assumed to satisfy a Lipschitz property. The existence of a solution with bounded variation is achieved thanks to the Moreau's catching-up algorithm adapted to this kind of problem. Various properties and estimates of jumps of the solution are also provided. We give sufficient conditions to ensure the uniform proxregularity when the moving set is described by inequality constraints. As an application, we consider a nonlinear differential complementarity system which is a combination of an ordinary differential equation with a nonlinear complementarily condition. Such problems appear in many areas such as nonsmooth mechanics, nonregular electrical circuits and control systems.Mathematics Subject Classification. 49J52, 49J53, 34A60.

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Section: This and Proposition 24 Justify The R-prox-regularity Of Thmentioning

confidence: 64%

Discontinuous sweeping process with prox-regular sets

2017

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“…31,45 The idea is borrowed from granular flow simulations 26 : we denote by q n the position vector at time t n . The next position vector is q n+1 = q n + τ u n+1 , where τ = t n+1 − t n > 0 is the time step.…”

Section: Numerical Aspectsmentioning

confidence: 99%

Crowd motion from the granular standpoint

Faure

Maury

2014

Math. Models Methods Appl. Sci.

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International audienceFollowing the approach initially proposed in Maury & Venel [30, 31], we consider here crowd motion from the standpoint of granular media, and we investigate how theoretical and numerical tools in non-smooth analysis can help better understanding some paradoxical features. We shall be especially interested in evacuation processes, jams, and we will detail how the granular nature of the flow helps to understand two well-known phenomena, the so-called " Faster is Slower " effect, and " Stop-and-Go " waves

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“…This proof is a modification of a similar proof presented in [38], the first part goes in the same way, yet for the second part we depart from finite-dimensional setting into the infinite-dimensional one and then return back.…”

Section: Remarkmentioning

confidence: 92%

“…This follows from the discretization scheme used in [38]. The main argument is that the points z j will not be far away from the set Z j and thus the projection will retain its single-valued Lipschitzian character, even though the set may be nonconvex.…”

Section: Remarkmentioning

confidence: 99%

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On optimal control of a sweeping process coupled with an ordinary differential equation

Adam¹,

Outrata²

2014

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract. We study a special case of an optimal control problem governed by a differential equation and a differential rate-independent variational inequality, both with given initial conditions. Under certain conditions, the variational inequality can be reformulated as a differential inclusion with discontinuous right-hand side. This inclusion is known as sweeping process.We perform a discretization scheme and prove the convergence of optimal solutions of the discretized problems to the optimal solution of the original problem. For the discretized problems we study the properties of the solution map and compute its coderivative. Employing an appropriate chain rule, this enables us to compute the subdifferential of the objective function and to apply a suitable optimization technique to solve the discretized problems. The investigated problem is used to model a situation arising in the area of queuing theory.

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A numerical scheme for a class of sweeping processes

Cited by 50 publications

References 19 publications

Discontinuous sweeping process with prox-regular sets

Discontinuous sweeping process with prox-regular sets

Crowd motion from the granular standpoint

On optimal control of a sweeping process coupled with an ordinary differential equation

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