Necessary condition of optimality in a minimax control problem

1993 ◽  
Vol 28 (4) ◽  
pp. 591-598
Author(s):  
S. Otakulov
Keyword(s):  
Control Problem ◽  
Necessary Condition ◽  
Minimax Control ◽  
Necessary Condition Of Optimality

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.

scholarly journals Reducing the Problem of Minimax Control of Linear non-Stationary Systems to a - Robust One by the Way of Dynamic Game

2020 ◽  
pp. 143-162
Author(s):  
Oleksij Lobok ◽  
◽  
Boris Goncharenko ◽  
Larisa Vihrova ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Initial Conditions ◽  
Dynamic Game ◽  
Quality Criterion ◽  
Necessary Condition ◽  
Search Problem ◽  
Algebraic Equations ◽  
Initial State ◽  
Minimax Control

The problem of synthesis of minimax control for the dynamic, described by the linear system of differential equations (taking into account the state, controls, perturbations and initial conditions, with the given equation of observation inclusive) of objects functioning in accordance with the integral-quadratic quality criterion in uncertainty is solved in the work. External perturbations, errors, and initial conditions were assumed to belong to a number of uncertainties. The task of finding optimal control in the form of a feedback object that minimizes the performance criterion is presented in the form of a minimum maximal uncertainty control problem. In the absence of ready-made solution paths, this problem is reduced to a -control problem under the most unfavorable disturbances, and in addition to a dynamic game problem with zero sum and a certain price for the game, and a strategy for solving it is proposed that offers a way to new results. The problem of finding the optimal control and the initial state that maximize the quality criterion is considered in the framework of the optimization problem solved by the Lagrange multiplier method after introducing the auxiliary scalar function, the Hamiltonian. It is shown that to find the maximum value of the criterion, either the necessary condition of the extremum of the first kind can be used, which depends on the ratio of the first variation of the criterion and the first variations of the control vectors and the initial state, or also the necessary condition of the extremum of the second kind, which depends on the sign of the second variation. For the first and second variations, formulas are given that can be used for calculations. It is suggested to solve the control search problem in two steps: search for an intermediate solution at fixed values of control vectors and errors, and then search for final optimal control. Consideration is also given to solving -optimal control for infinite control time with respect to the signal from the compensator output, as well as solving the corresponding Riccati matrix algebraic equations.

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 CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

2017 ◽  
Vol 2 ◽  
pp. 9-15
Author(s):  
Iryna Svyatovets
Keyword(s):  
Riccati Equation ◽  
Infinite System ◽  
Conservative System ◽  
Coefficient Matrix ◽  
Necessary Condition ◽  
Existence Of A Solution ◽  
Minimax Control ◽  
System Of Matrix Equations ◽  
System A ◽  
The Matrix

The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts. To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations. A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation. An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

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