Displaying similar documents to “On the modelling and management of traffic”

On the modelling and management of traffic

Rinaldo M. Colombo, Paola Goatin, Massimiliano D. Rosini (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Several realistic situations in vehicular traffic that give rise to queues can be modeled through conservation laws with boundary and unilateral constraints on the flux. This paper provides a rigorous analytical framework for these descriptions, comprising stability with respect to the initial data, to the boundary inflow and to the constraint. We present a framework to rigorously state optimal management problems and prove the existence of the corresponding optimal controls. Specific...

Mean-Field Optimal Control

Massimo Fornasier, Francesco Solombrino (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We introduce the concept of which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. While in the classical mean-field theory one studies the behavior of a large number of small individuals with each other, by simplifying...

A set oriented approach to global optimal control

Oliver Junge, Hinke M. Osinga (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination)...

Relaxation of optimal control problems in L-SPACES

Nadir Arada (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space ( < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows

Max D. Gunzburger, O. Yu. Imanuvilov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem for a model for stationary, low Mach number, highly nonisothermal, viscous flows is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. The existence of solutions of a boundary value problem for the model equations is established as is the existence of solutions of the optimal control problem. Then, a derivation of an optimality system, , a boundary value problem...