scholarly journals Optimal Control of Pseudoparabolic Variational Inequalities Involving State Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Youjun Xu ◽  
Shu Zhou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Variational Inequalities ◽  
Control Problem ◽  
Control Process ◽  
State Constraint ◽  
Necessary Condition ◽  
Necessary Condition Of Optimality

We establish the necessary condition of optimality for optimal control problem governed by some pseudoparabolic differential equations involving monotone graphs. Some approximating control process and examples are given.

scholarly journals Optimal Control Problem for the Weak Nonlinear Equation of Thin Plate With Control at the Coefficient of Lowest Term

2020 ◽  
Vol 12 (3) ◽  
pp. 31
Author(s):  
Khayala I. Seyfullaeva
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Nonlinear Equation ◽  
Control Problem ◽  
Linear Equation ◽  
Thin Plates ◽  
Necessary Condition ◽  
Necessary Condition Of Optimality ◽  
The Right

The paper deals with an inverse problem of determining the right-hand side of the linear equation of oscillations of thin plates. The problem is reduced to the optimal control problem. Differentiability of the functional is studied. Necessary condition of optimality is derived.

scholarly journals The Problem of the Optimal Control with a Lower Coefficient for Weakly Nonlinear Wave Equation in the Mixed Problem

2020 ◽  
Vol 13 (2) ◽  
pp. 314-322
Author(s):  
Gunay Ismayilova
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Necessary Condition ◽  
Weakly Nonlinear ◽  
Necessary Condition Of Optimality

In this paper, we consider the problem of determining the lowest coefficient of weakly nonlinear wave equation. The problem is reduced to the optimal control problem, in the new problem. In the this existence theorem of the optimal control and, the Fre ́echet differentiability of the functional is proved. Also the necessary condition of optimality is derived in view of variational inequality.

Stochastic optimal control problem of constrained switching system with delay

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 711-720
Author(s):  
Charkaz Aghayeva
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Initial Conditions ◽  
Necessary Condition ◽  
Switching System ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Optimal Control Problem ◽  
Necessary Condition Of Optimality

This paper concerns the stochastic optimal control problem of switching systems with delay. The evolution of the system is governed by the collection of stochastic delay differential equations with initial conditions that depend on its previous state. The restriction on the system is defined by the functional constraint that contains state and time parameters. First, maximum principle for stochastic control problem of delay switching system without constraint is established. Finally, using Ekeland?s variational principle, the necessary condition of optimality for control system with constraint is obtained.

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 OPTIMAL CONTROL FOR ROUGH DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (01) ◽  
pp. 23-33 ◽  
Author(s):  
LAURENT MAZLIAK ◽  
IVAN NOURDIN
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Continuous Function ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence Theorem ◽  
Control Process ◽  
Hölder Continuous ◽  
Regular Functions

In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index β > 1/2. We split our study into two cases. If the coefficient of dgt does not depend on the control process, we prove an existence theorem for a slightly generalized control problem, that is we obtain a literal extension of the corresponding situation for ordinary differential equations. If the coefficient of dgt depends on the control process, we also prove an existence theorem but here we are obliged to restrict the set of controls to sufficiently regular functions.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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