Displaying similar documents to “Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs”

On the optimal control of coefficients in elliptic problems. Application to the optimization of the head slider

Ionel Ciuperca, Mohamed El Alaoui Talibi, Mohammed Jai (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.

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)...

On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

Denis Pennequin (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed...

Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs

Peter I. Kogut, Günter Leugering (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We are concerned with the asymptotic analysis of optimal control problems for 1 -D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized...