scholarly journals Optimal control problem of variable-order delay system of advertising procedure: Numerical treatment

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nasser H. Sweilam ◽  
Taghreed A. Assiri ◽  
Muner M. Abou Hasan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Analytic Solutions ◽  
Delay System ◽  
Variable Order ◽  
Delay Model ◽  
Standard Difference ◽  
New Formulation ◽  
Number Of Customers

<p style='text-indent:20px;'>This paper presents an optimal control problem of the general variable-order fractional delay model of advertising procedure. The problem describes the flow of the clients from the unaware people group to the conscious or bought band. The new formulation generalizes the model that proposed by Muller. Two control variables are considered to increase the number of customers who purchased the products. An efficient nonstandard difference approach is used to study numerically the behavior of the solution of the mentioned problem. Properties of the proposed system were introduced analytically and numerically. The proposed difference schema maintains the properties of the analytic solutions as boundedness and the positivity. Numerical examples, for testing the applicability of the utilized method and to show the simplicity, accuracy and efficiency of this approximation approach, are presented with some comprising with standard difference methods.</p>

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.

scholarly journals Stability and Analytic Solutions of an Optimal Control Problem on the Schrödinger Lie Group

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 549-558
Author(s):  
Remus-Daniel Ene ◽  
Camelia Pop ◽  
Camelia Petrişor
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Nonlinear Stability ◽  
Lie Group ◽  
Asymptotic Method ◽  
Analytic Solutions ◽  
Optimal Homotopy Asymptotic Method

AbstractThe nonlinear stability and the existence of the periodic solutions for an optimal control problem on the Schrödinger Lie group are discussed. The analytic solutions via optimal homotopy asymptotic method of the dynamics and numerical simulations are presented, too.

The Tensor Product Based Analytic Solutions of Nonlinear Optimal Control Problem

2014 ◽  
Vol 511-512 ◽  
pp. 1063-1067 ◽  
Author(s):  
Hajer Bouzaouache ◽  
Naceur Benhadj Braiek
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Tensor Product ◽  
Control Problem ◽  
State Feedback ◽  
Numerical Procedure ◽  
Analytic Solutions ◽  
Linear Solution ◽  
Algebraic Laws ◽  
Feedback Optimal Control

In this paper, the attention is focused on the optimization of a particular class of nonlinear systems. The optimum linear solution is not the best one so the problem of determining a nonlinear state feedback optimal control law with quadratic performance index over infinite time horizon is considered. It isn't an easy task and the most discouraging obstacle is the resolution of the Hamilton-Jacobi equation. Thus our contribution, based on the use of the tensor product and its algebraic laws, provide analytic solutions of the studied optimal control problem. The polynomial state feedback solution is computed through a numerical procedure. A numerical example is treated to illustrate the proposed solutions and some conclusions are drawn.

scholarly journals Optimal Control of a Nonlinear Time-Delay System in Batch Fermentation Process

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongsheng Yu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Batch Process ◽  
Delay System ◽  
High Yield ◽  
Time Delay System ◽  
Control Variables ◽  
Terminal Time

The main control goal in batch process is to get a high yield of products. In this paper, to maximize the yield of 1,3-propanediol (1,3-PD) in bioconversion of glycerol to 1,3-PD, we consider an optimal control problem involving a nonlinear time-delay system. The control variables in this problem include the initial concentrations of biomass and glycerol and the terminal time of the batch process. By a time-scaling transformation, we transcribe the optimal control problem into a new one with fixed terminal time, which yields a new nonlinear system with variable time-delay. The gradients of the cost and constraint functionals with respect to the control variables are derived using the costate method. Then, a gradient-based optimization method is developed to solve the optimal control problem. Numerical results show that the yield of 1,3-PD at the terminal time is increased considerably compared with the experimental data.

scholarly journals Solving Linear Optimal Control Problems Using Cubic B-spline Quasi-interpolation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 313-324
Author(s):  
M. Matinfar ◽  
M. Dosti
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Main Idea ◽  
Absolute Error ◽  
Analytic Solutions ◽  
Linear Optimal Control ◽  
B Spline ◽  
Linear Optimal Control Problems ◽  
Made In

In this article, we apply an impressive method for solving linear optimal control problem based on cubic B-spline quasi-interpolation. Hamilton-Jacobi equation are applied to linear optimal control problem convert to systems of first-order equations. The main idea of our scheme is approximation derivative with cubic B-spline quasi-interpolation. This method is straightforward, without restrictive assumptions.The results of scheme are made in pleasant agreement with analytic solutions. The accuracy of the proposed method is demonstrated by absolute error. Our scheme is simple to implement because its algorithm is easy and it's one of the advantages of the proposed method.

Fractional optimal control problem for variable-order differential systems

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Gaber M. Bahaa
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential System ◽  
Time Derivative ◽  
Variable Order ◽  
Fractional Optimal Control Problem ◽  
Fractional Optimal Control ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we apply the classical control theory to a variable order fractional differential system in a bounded domain. The Fractional Optimal Control Problem (FOCP) for variable order differential system is considered. The fractional time derivative is considered in a Caputo sense. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the variable order fractional differential system in a Hilbert space. Then we show that the considered optimal control problem has a unique solution. The performance index of a (FOCP) is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) with variable order. The time horizon is fixed. Finally, we impose some constraints on the boundary control. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Caputo derivative, we obtain an optimality system for the optimal control. Some examples are analyzed in details.

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