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Cooperative driving at isolated intersections based on the optimal minimization of the maximum exit time

Jia Wu, Abdeljalil Abbas-Turki, Florent Perronnet (2013)

International Journal of Applied Mathematics and Computer Science

Traditional traffic control systems based on traffic light have achieved a great success in reducing the average delay of vehicles or in improving the traffic capacity. The main idea of these systems is based on the optimization of the cycle time, the phase sequence, and the phase duration. The right-of-ways are assigned to vehicles of one or several movements for a specific time. With the emergence of cooperative driving, an innovative traffic control concept, Autonomous Intersection Management...

Coplanar control of a satellite around the earth

Jean-Baptiste Caillau, Joseph Noailles (2001)

ESAIM: Control, Optimisation and Calculus of Variations

We investigate the minimum time transfer of a satellite around the Earth. Using an optimal control model, we study the controllability of the system and propose a geometrical analysis of the optimal command structure. Furthermore, in order to solve the problem numerically, a new parametric technique is introduced for which convergence properties are established.

Coplanar control of a satellite around the Earth

Jean-Baptiste Caillau, Joseph Noailles (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We investigate the minimum time transfer of a satellite around the Earth. Using an optimal control model, we study the controllability of the system and propose a geometrical analysis of the optimal command structure. Furthermore, in order to solve the problem numerically, a new parametric technique is introduced for which convergence properties are established.

Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

Gilles A. Francfort, Nam Q. Le, Sylvia Serfaty (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.

Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

Gilles A. Francfort, Nam Q. Le, Sylvia Serfaty (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to converge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.

Critical points of the Moser-Trudinger functional on a disk

Andrea Malchiodi, Luca Martinazzi (2014)

Journal of the European Mathematical Society

On the unit disk B 1 ⊂ ℝ 2 we study the Moser-Trudinger functional E ( u ) = ∫ B 1 e u 2 - 1 d x , u ∈ H 0 1 ( B 1 ) and its restrictions E | M Λ , where M Λ : = { u ∈ H 0 1 ( B 1 ) : ∥ u ∥ H 0 1 2 = Λ } for Λ > 0 . We prove that if a sequence u k of positive critical points of E | M Λ k (for some Λ k > 0 ) blows up as k → ∞ , then Λ k → 4 π , and u k → 0 weakly in H 0 1 ( B 1 ) and strongly in C loc 1 ( B ¯ 1 ∖ { 0 } ) . Using this fact we also prove that when Λ is large enough, then E | M Λ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.

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