Conditions for the Existence of Optimal Control for Some Classes of Differential Equations on Time Scales

2017 ◽  
Vol 222 (3) ◽  
pp. 276-295 ◽  
Author(s):  
O. E. Lavrova
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Time Scales ◽  
Existence Of Optimal Control

scholarly journals Application of the averaging method to the problems of optimal control of the impulse systems

2020 ◽  
Vol 12 (2) ◽  
pp. 504-521
Author(s):  
T.V. Koval'chuk ◽  
V.V. Mogylova ◽  
O.M. Stanzhytskyi ◽  
T.V. Shovkoplyas
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Finite Time ◽  
Averaging Method ◽  
Optimal Synthesis ◽  
Time Interval ◽  
Finite Time Interval ◽  
System Of Differential Equations ◽  
Existence Of Optimal Control

The problem of optimal control at finite time interval for a system of differential equations with impulse action at fixed moments of time as well as the corresponding averaged system of ordinary differential equations are considered. It is proved the existence of optimal control of exact and averaged problems. Also, it is established that optimal control of averaged problem realize the approximate optimal synthesis of exact problem. The main result of the article is a theorem, where it is proved that optimal contol of an averaged problem is almost optimal for exact problem. Substantiation of proximity of solutions of exact and averaged problems is obtained.

scholarly journals On the Linear Quadratic Optimal Control for Systems Described by Singularly Perturbed Itô Differential Equations with Two Fast Time Scales

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 30
Author(s):  
Vasile Dragan
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Time Scales ◽  
Performance Criterion ◽  
Singularly Perturbed ◽  
Algebraic Riccati Equation ◽  
Fast Time ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Stabilizing Solution

In this paper a stochastic optimal control problem described by a quadratic performance criterion and a linear controlled system modeled by a system of singularly perturbed Itô differential equations with two fast time scales is considered. The asymptotic structure of the stabilizing solution (satisfying a prescribed sign condition) to the corresponding stochastic algebraic Riccati equation is derived. Furthermore, a near optimal control whose gain matrices do not depend upon small parameters is discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document