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The H–1-norm of tubular neighbourhoods of curves

Yves van Gennip, Mark A. Peletier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We study the H–1-norm of the function 1 on tubular neighbourhoods of curves in ℝ 2 . We take the limit of small thickness ε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε3), the ends (ε4), and the curvature (ε5). The second result is a Γ-convergence result, in which the central curve may vary along the sequence ε → 0. We prove that a rescaled version of...

The optimization of the stationary heat equation with a variable right-hand side

Ctirad Matyska (1986)

Aplikace matematiky

Solving the stationary heat equation we optimize the temperature on part of the boundary of the domain under investigation. First the Poisson equation is solved; both the Neumann condition on part of the boundary and the Newton condition on the rest are prescribed, the distribution of the heat sources being variable. In the second case, the heat equation also contains a convective term, the distribution of heat sources is specified and the Neumann condition is variable on part of the boundary.

The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch, Stefan Volkwein (2001)

ESAIM: Control, Optimisation and Calculus of Variations

A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...

The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch, Stefan Volkwein (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical examples are...

The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Yannick Privat, Mario Sigalotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...

Time domain decomposition in final value optimal control of the Maxwell system

John E. Lagnese, G. Leugering (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time...

Time Domain Decomposition in Final Value Optimal Control of the Maxwell System

John E. Lagnese, G. Leugering (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a boundary optimal control problem for the Maxwell system with a final value cost criterion. We introduce a time domain decomposition procedure for the corresponding optimality system which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. In the limit full recovery of the coupling conditions is achieved, and, hence, the local solutions and controls converge to the global ones. The process is inherently parallel and is suitable for real-time...

Time-optimal boundary control of a parabolic system with time lags given in integral form

Adam Kowalewski, Anna Krakowiak (2006)

International Journal of Applied Mathematics and Computer Science

In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.

Time-optimal control of infinite order hyperbolic systems with time delays

Adam Kowalewski (2009)

International Journal of Applied Mathematics and Computer Science

In this paper, the time-optimal control problem for infinite order hyperbolic systems in which time delays appear in the integral form both in state equations and in boundary conditions is considered. Optimal controls are characterized in terms of an adjoint system and shown to be unique and bang-bang. These results extend to certain cases of nonlinear control problems. The particular properties of optimal control are discussed.

Topology optimization of quasistatic contact problems

Andrzej Myśliński (2012)

International Journal of Applied Mathematics and Computer Science

This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the...

Transportation flow problems with Radon measure variables

Marcus Wagner (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

For a multidimensional control problem ( P ) K involving controls u ∈ L ∞ , we construct a dual problem ( D ) K in which the variables ν to be paired with u are taken from the measure space rca (Ω,) instead of ( L ∞ ) * . For this purpose, we add to ( P ) K a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.

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