7,379 research outputs found
On Optimal Control Problem for Conservation Law Modelling One Class of Highly Re-Entrant Production Systems
No full textWe discuss the optimal control problem stated as the minimization in the L2-sense of the mismatch between the actual out-flux
and a demand forecast for a hyperbolic conservation law that models a highly re-entrant production system. The output of the factory is
described as a function of the work in progress and the position of the so-called push-pull point (PPP) where we separate the beginning of
the factory employing a push policy from the end of the factory, which uses a pull policy
Qualitative Analysis of an Optimal Sparse Control Problem for Quasi Linear Parabolic Equation with Variable Order of Nonlinearity
No full textAsymptotic Analysis of an Optimal Boundary Control Problem for Ill-Posed Elliptic Equation in Domains with Rugous Boundary
No full textWe study an optimal control problem for the mixed Dirichlet-Neumann boundary value problem for
the strongly non-linear elliptic equation with exponential nonlinearity in a domain with
rugous boundary. A density of surface traction acting on a part of rugous boundary is taken as a control. The optimal control problem is to minimize the
discrepancy between a given distribution and the
current system state. We deal with such case of nonlinearity when we cannot expect to have a solution of the state equation for a given control.
After having defined a suitable
class of the weak solutions, we provide asymptotic analysis of the above mentioned optimal control problem posed in a family of perturbed domains and give the characterization of the limiting behavior of its optimal solutions
On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations
No full textWe discuss the existence issue to an optimal control problem for one class of nonlinear elliptic equations with an exponential type of nonlinearity. We deal with the control object when we cannot expect to have a solution of the corresponding boundary value problem in the standard functional space for all admissible controls. To overcome this difficulty, we make use of a variant of the classical Tikhonov regularization scheme. In particular, we eliminate the PDE constraints between control and state and allow such pairs run freely by introducing an additional variable which plays the role of “compensator” that appears in the original state equation. We show that this fictitious variable can be determined in a unique way. In order to provide an approximation of the original optimal control problem, we define a special family of regularized optimization problems. We show that each of these problems is consistent, well-posed, and their solutions allow to attain an optimal solution of the original problem as the parameter of regularization tends to zero. As a consequence, we prove the existence of optimal solutions to the original problem and propose a way for their approximation
On Optimal Control of Quasi-Linear Elliptic Equation with Variable p(x)-Laplacian
No full textWe consider an optimal control problem for quasilinear
elliptic equation containing the p-Laplacian with variable
exponent p = p(x). The exponent p(x) are used as the controls
in L^1(Ω). The optimal control problem is to minimize the
discrepancy between a given distribution yd and the
current system state y, by choosing an appropriate
exponent p(x)
Weak Optimal Controls in Coefficients for Linear Elliptic Problems
No full textSUMMARY In this paper we study an optimal control problem associated to a linear
degenerate elliptic equation with mixed boundary conditions. The equations of
this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak
solutions. We adopt the weight function as a control in . Using
the direct method in the Calculus of variations, we discuss the solvability of
this optimal control problem in the class of weak admissible solutions
An Indirect Approach to the Existence of Quasi-optimal Controls in Coefficients for Multi-dimensional Thermistor Problem
No full textThe paper studies a problem of an optimal control in coefficients for the system of two coupled elliptic equations also known as thermistor problem which provides a simultaneous description of the electric field and temperature . The coefficient of operator is used as the control in with q>N. The optimal control problem is to minimize the discrepancy between a given distribution and the temperature of thermistor by choosing an appropriate anisotropic heat conductivity . Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an extquotedblleft approximation approach extquotedblright and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem
Variational Model with Nonstandard Growth Conditions for Restoration of Satellite Optical Images Using Synthetic Aperture Radar
No full textIn this paper, the problem of restoration of cloud contaminated optical images is studied in the
case when we have no information about brightness of such images in the damage region. We
propose a new variational approach for exact restoration of optical multi-band images utilising Synthetic Aperture Radar (EOS – Spatial Data Analytics, GIS Software, Satellite Imagery – is a
cloud-based platform to derive remote sensing data and analyse satellite imagery for business and
science purposes) images of the same regions. We prove existence of solutions, propose an alternating minimisation method for computing them, prove convergence of this method to weak solutions
of the original problem and derive optimality conditions
Computational aspects of the crop field segmentation problem based on anisotropic active contour mode
No full textIn this paper, we analyse the numerical aspects of the practical implementation of the generalized active contour model, that has been recently proposed in the literature, for extracting agricultural crop fields with a high level of inhomogeneity from satellite data. We also derive the corresponding Euler-Lagrange equation and discuss its relaxation method
A two-level variational algorithm in the Sobolev–Orlicz space to predict daily surface reflectance at LANDSAT high spatial resolution and MODIS temporal frequency
No full textWe propose a new two-level variational model in Sobolev-Orlicz spaces with nonstandard growth conditions
of the objective functional and discuss its applications to the spatiotemporal interpolation of multispectral satellite images. At the firrst level, we deal with the temporal interpolation problem that can be cast as a state constrained optimal control problem for anisotropic convection-diffusion equation, whereas at the second level we solve a constrained minimization problem with a nonstandard growth energy functional that lives in variable Sobolev-Orlicz spaces. The characteristic feature of the proposed model is the fact that the variable exponent, which is associated with non-standard growth in spatial interpolation problem, is unknown a priori and it depends on the solution of the first-level optimal control problem. It makes this spatiotemporal interpolation problem rather challenging. In view of this, we discuss the consistency of the proposed model, study the existence of optimal solutions, and derive the corresponding optimality systems. In particular, we apply this approach to the well-known prediction problem of the Daily MODIS Surface Reflectance at the Landsat-Like Resolution
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