scholarly journals An Optimal Control Problem for A Viscoelastic Plate in a Dynamic Contact with an Obstacle

2018 ◽  
Vol 71 (1) ◽  
pp. 27-37
Author(s):  
Igor Bock ◽  
Mária Kečkemétyová
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Variable ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dynamic Contact ◽  
Viscoelastic Plate ◽  
Initial Boundary Value ◽  
Thickness Function

Abstract We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a simply supported anisotropic viscoelastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. We verify the existence of an optimal thickness function.

scholarly journals Regularized optimal control problem for a beam vibrating against an elastic foundation

2015 ◽  
Vol 63 (1) ◽  
pp. 53-71
Author(s):  
Igor Bock ◽  
Mária Kečkemétyová
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elastic Foundation ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value

Abstract We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a clamped beam against a u elastic foundation. A variable thickness of a beam plays the role of a control variable. The original equation for the deflection is regularized in order to derive necessary optimality conditions

Optimal control problem for the equation of vibrations of an elastic plate

2018 ◽  
Vol 25 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Hamlet F. Guliyev ◽  
Khayala I. Seyfullaeva
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elastic Plate ◽  
Control Function ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Necessary Condition ◽  
Necessary Condition Of Optimality ◽  
Initial Boundary Value

AbstractAn optimal control problem for the vibration equation of an elastic plate is considered when the control function is included in the coefficient of the highest order derivative and the right-hand side of the equation. The solvability of the initial boundary value problem is shown, the theorem on the existence of an optimal control is proved and a necessary condition of optimality in the form of an integral equation is obtained.

scholarly journals Multi-Term Fractional Degenerate Evolution Equations and Optimal Control Problems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 483
Author(s):  
Marina Plekhanova ◽  
Guzel Baybulatova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Evolution Equations ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fractional Equations ◽  
Initial Boundary Value ◽  
Degenerate Evolution Equations

A theorem on unique solvability in the sense of the strong solutions is proved for a class of degenerate multi-term fractional equations in Banach spaces. It applies to the deriving of the conditions on unique solution existence for an optimal control problem to the corresponding equation. Obtained results are used to an optimal control problem study for a model system which is described by an initial-boundary value problem for a partial differential equation.

Optimal control of thermal processes with phase transitions

2021 ◽  
Author(s):  
Yury Evtushenko ◽  
Vladimir Zubov ◽  
Anna Albu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Crystallization Process ◽  
Automatic Differentiation ◽  
Phase Interface ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Phase ◽  
Metal Solidification

The optimal control of the metal solidification process in casting is considered. Quality of the obtained detail greatly depends on how the crystallization process proceeds. It is known that to obtain a model of a good quality it is desirable that the phase interface would be as close as possible to a plane and that the speed of its motion would be close to prescribed. The proposed mathematical model of the crystallization process is based on a three dimensional two phase initial-boundary value problem of the Stefan type. The velocity of the mold in the furnace is used as the control. The control satisfying the technological requirements is determined by solving the posed optimal control problem. The optimal control problem was solved numerically using gradient optimization methods. The effective method is proposed for calculation of the cost functional gradient. It is based on the fast automatic differentiation technique and produces the exact gradient for the chosen approximation of the optimal control problem.

Mixed Control Problem for the Linearized Quasi-Stationary Phase Field System of Equations

2016 ◽  
Vol 845 ◽  
pp. 170-173 ◽  
Author(s):  
Marina Plekhanova
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Phase Field ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Operator Differential Equation ◽  
Field Equations ◽  
Mixed Control ◽  
Phase Field Equations

Conditions are obtained for unique solution existence of a mixed control problem without taking in account control expenses for a system that described by an initial-boundary value problem for the linearized quasi-stationary system of phase field equations. The problem is reduced to an optimal control problem for operator differential equation of first order in abstract space with degenerate operator at derivative using start and distributed controls simultaneously. The theorem on the unique solvability of this problem is applied to studying of optimal control problem for the phase field equations system.

On the Dynamic Contact Problem for a Viscoelastic Plate

2010 ◽  
Author(s):  
Igor Bock
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dynamic Contact ◽  
Viscoelastic Plate ◽  
Weak Formulation ◽  
Priori Estimates ◽  
Elliptic Variational Inequalities ◽  
Initial Boundary Value

We deal with an initial-boundary value problem describing the perpendicular vibrations of an anisotropic viscoelastic plate free on its boundary and with a rigid inner obstacle. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the discretizing the time variable. The elliptic variational inequalities for every time level are uniquely solved. We derive the a priori estimates and the convergence of the sequence of segment line functions to a variational solution of the considered problem.

Inverse extremum problem for a model of endovenous laser ablation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrey Kovtanyuk ◽  
Alexander Chebotarev ◽  
Alena Astrakhantseva
Keyword(s):  
Optimal Control ◽  
Laser Ablation ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Extremum Problem ◽  
Transfer Model ◽  
Conductive Heat ◽  
Endovenous Laser Ablation

AbstractAn inverse extremum problem (optimal control problem) for a quasi-linear radiative-conductive heat transfer model of endovenous laser ablation is considered. The problem is to find the powers of the source spending on heating the fiber tip and on radiation. As a result, it provides a given temperature distribution in some part of the model domain. The unique solvability of the initial-boundary value problem is proved, on the basis of which the solvability of the optimal control problem is shown. An iterative algorithm for solving the optimal control problem is proposed. Its efficiency is illustrated by a numerical example.

Dynamical Behavior of a Malaria Model with Discrete Delay and Optimal Insecticide Control

2017 ◽  
Vol 12 (01) ◽  
pp. 19-38 ◽  
Author(s):  
Tuhin Kumar Kar ◽  
Soovoojeet Jana
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Reproduction Number ◽  
Dynamical Behavior ◽  
Control Variable ◽  
Discrete Delay ◽  
Insecticide Control

In this paper we have proposed and analyzed a simple three-dimensional mathematical model related to malaria disease. We consider three state variables associated with susceptible human population, infected human population and infected mosquitoes, respectively. A discrete delay parameter has been incorporated to take account of the time of incubation period with infected mosquitoes. We consider the effect of insecticide control, which is applied to the mosquitoes. Basic reproduction number is figured out for the proposed model and it is shown that when this threshold is less than unity then the system moves to the disease-free state whereas for higher values other than unity, the system would tend to an endemic state. On the other hand if we consider the system with delay, then there may exist some cases where the endemic equilibrium would be unstable although the numerical value of basic reproduction number may be greater than one. We formulate and solve the optimal control problem by considering insecticide as the control variable. Optimal control problem assures to obtain better result than the noncontrol situation. Numerical illustrations are provided in support of the theoretical results.

scholarly journals Ana posteriorierror analysis for an optimal control problem with point sources

2018 ◽  
Vol 52 (5) ◽  
pp. 1617-1650 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weighted Sobolev Spaces ◽  
Control Variable ◽  
The State ◽  
Point Sources ◽  
Adjoint Equations ◽  
Error Estimator ◽  
A Posteriori

We propose and analyze a reliable and efficienta posteriorierror estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposeda posteriorierror estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the deviseda posteriorierror estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform.

scholarly journals Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

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