scholarly journals Adaptive Method for Solving Optimal Control Problem with State and Control Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Louadj Kahina ◽  
Aidene Mohamed
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Control ◽  
Linear Programming ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Adaptive Method ◽  
Control Variables ◽  
The Right ◽  
And Control

The problem of optimal control with state and control variables is studied. The variables are: a scalar vectorxand the controlu(t); these variables are bonded, that is, the right-hand side of the ordinary differential equation contains both state and control variables in a mixed form. For solution of this problem, we used adaptive method and technology of linear programming.

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.

Optimal Control Problem for a Degenerate Fractional Differential Equation

2021 ◽  
Vol 42 (6) ◽  
pp. 1239-1247
Author(s):  
R. A. Bandaliyev ◽  
I. G. Mamedov ◽  
A. B. Abdullayeva ◽  
K. H. Safarova
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Differential Equation ◽  
Fractional Differential

scholarly journals Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Human Population ◽  
Cost Effective ◽  
Farm Animals ◽  
Effective Control ◽  
Multiple Control ◽  
Control Variables ◽  
Control Functions

Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.

scholarly journals Robust Multi-Objective Singular Optimal Control Ofpenicillin Fermentation Process

2020 ◽  
pp. 23-30
Author(s):  
Gustavo B. Libotte ◽  
Fran S. Lobato ◽  
Gustavo M. Platt ◽  
Francisco D. Moura Neto
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fermentation Process ◽  
Singular Problem ◽  
Fed Batch ◽  
Control Variables ◽  
Singular Optimal Control ◽  
Multi Objective ◽  
Singular Optimal Control Problem

The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi- objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time.

scholarly journals Delayed Stochastic Linear-Quadratic Control Problem and Related Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Li Chen ◽  
Zhen Wu ◽  
Zhiyong Yu
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Delay System ◽  
Linear Quadratic ◽  
Stochastic Linear System ◽  
And Control

We discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with Itô’s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially, we present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.

Sign in / Sign up

Export Citation Format

Share Document