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Conformal mapping and inverse conductivity problem with one measurement

Marc Dambrine, Djalil Kateb (2007)

ESAIM: Control, Optimisation and Calculus of Variations

This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series...

Continuity of solutions to a basic problem in the calculus of variations

Francis Clarke (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the problem of minimizing ∫ Ω F ( D u ( x ) ) d x over the functions u ∈ W 1 , 1 ( Ω ) that assume given boundary values φ on Γ : = ∂ Ω . The lagrangian F and the domain Ω are assumed convex. A new type of hypothesis on the boundary function φ is introduced: thelower (or upper) bounded slope condition. This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary...

Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem

Claudio Marchi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space  [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.

Continuous-time periodic systems in H 2 and H ∞ . Part I: Theoretical aspects

Patrizio Colaneri (2000)

Kybernetika

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of H 2 and H ∞ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in H 2 and H ∞ are introduced and solved.

Continuous-time periodic systems in H 2 and H ∞ . Part II: State feedback problems

Patrizio Colaneri (2000)

Kybernetika

This paper deals with some state-feedback H 2 / H ∞ control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in H 2 , H ∞ and mixed H 2 / H ∞ are introduced and solved.

Controllability, observability and optimal control of continuous-time 2-D systems

Gerhard Jank (2002)

International Journal of Applied Mathematics and Computer Science

We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data....

Convergence and regularization results for optimal control problems with sparsity functional

Gerd Wachsmuth, Daniel Wachsmuth (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical...

Convergence and regularization results for optimal control problems with sparsity functional

Gerd Wachsmuth, Daniel Wachsmuth (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Optimization problems with convex but non-smooth cost functional subject to an elliptic partial differential equation are considered. The non-smoothness arises from a L1-norm in the objective functional. The problem is regularized to permit the use of the semi-smooth Newton method. Error estimates with respect to the regularization parameter are provided. Moreover, finite element approximations are studied. A-priori as well as a-posteriori error estimates are developed and confirmed by numerical...

Deadbeat control, pole placement, and LQ regulation

Vladimír Kučera (1999)

Kybernetika

Deadbeat control, a typical example of linear control strategies in discrete- time systems, is shown to be a special case of the linear-quadratic regulation. This result is obtained by drawing on the parallels between the state-space and the transfer-function design techniques.

Design of predictive LQ controller

Miroslav Fikar, Sebastian Engell, Petr Dostál (1999)

Kybernetika

A single variable controller is developed in the predictive control framework based upon minimisation of the LQ criterion with infinite output and control horizons. The infinite version of the predictive cost function results in better stability properties of the controller and still enables to incorporate constraints into the control design. The constrained controller consists of two parts: time-invariant nominal LQ controller and time-variant part given by Youla–Kučera parametrisation of all stabilising...

Currently displaying 101 – 120 of 597