scholarly journals Approximated Solutions of Linear Quadratic Fractional Optimal Control Problems

2016 ◽  
Vol 12 (2) ◽  
pp. 83-94
Author(s):  
S. Soradi Zeid ◽  
M. Yousefi ◽  
M. Yousefi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Linear Quadratic ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems ◽  
The Cost

Abstract In this study we apply the Adomian decomposition method (ADM) to approximate the solution of fractional optimal control problems (FOCPs) where the dynamic of system is a linear control system with constant coefficient and the cost functional is defined in a quadratic form. First we stated the necessary optimality conditions in a form of fractional two point boundary value problem (TPBVP), then the ADM is used to solve the resulting fractional differential equations (FDEs). Some examples are provided to demonstrate the validity and applicability of the proposed method.

Modified Adomian decomposition method for solving fractional optimal control problems

2017 ◽  
Vol 40 (6) ◽  
pp. 2054-2061 ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems

In this study, we use the modified Adomian decomposition method to solve a class of fractional optimal control problems. The performance index of a fractional optimal control problem is considered as a function of both the state and the control variables, and the dynamical system is expressed in terms of a Caputo type fractional derivative. Some properties of fractional derivatives and integrals are used to obtain Euler–Lagrange equations for a linear tracking fractional control problem and then, the modified Adomian decomposition method is used to solve the resulting fractional differential equations. This technique rapidly provides convergent successive approximations of the exact solution to a linear tracking fractional optimal control problem. We compare the proposed technique with some numerical methods to demonstrate the accuracy and efficiency of the modified Adomian decomposition method by examining several illustrative test problems.

Numerical Schemes for Fractional Optimal Control Problems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Decomposition Method ◽  
Optimal Control Problems ◽  
Adomian Decomposition Method ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Variational Iteration ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Optimal Control Problems

In the present study, variational iteration and Adomian decomposition methods (ADMs) are applied for solving a class of fractional optimal control problems (FOCPs). Also, a comparative study between these two methods is presented. The fractional derivative (FD) in these problems is in the Caputo sense. To solve the problem, first the necessary optimality conditions of FOCP are achieved for a linear tracking fractional optimal control problem, and then, these two methods are used to solve the resulting fractional differential equations (FDEs). It is shown that the modified Adomian decomposition method and variational iteration method (VIM) use the same iterative formula for solving linear and nonlinear FOCPs. The convergence of the modified Adomian decomposition method is analytically studied and to illustrate the validity and applicability of the methods, some examples are provided.

Implementation of fractional optimal control problems in real-world applications

2020 ◽  
Vol 23 (6) ◽  
pp. 1783-1796
Author(s):  
Neelam Singha
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Order Model ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Real World Applications ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order model describes the interaction of effector-immune cells and tumor cells, including combined chemo-immunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractional-order optimal control problem. The key motive is to perform numerical simulations that shall facilitate us in understanding the behavior of state and control variables. Further, the graphical interpretation of solutions effectively validates the applicability of the present analysis to investigate the growth of cancer cells in the presence of medical treatment.

An iterative approach for solving fractional optimal control problems

2016 ◽  
Vol 24 (1) ◽  
pp. 18-36 ◽  
Author(s):  
Ali Alizadeh ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Variational Iteration Method ◽  
Successive Approximations ◽  
Classical Solutions ◽  
Control Problems ◽  
Lagrange Equations ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

In this work, the variational iteration method (VIM) is used to solve a class of fractional optimal control problems (FOCPs). New Lagrange multipliers are determined and some new iterative formulas are presented. The fractional derivative (FD) in these problems is in the Caputo sense. The necessary optimality conditions are achieved for FOCPs in terms of associated Euler–Lagrange equations and then the VIM is used to solve the resulting fractional differential equations. This technique rapidly provides the convergent successive approximations of the exact solution and the solutions approach the classical solutions of the problem as the order of the FDs approaches 1. To achieve the solution of the FOCPs using VIM, four illustrative examples are included to demonstrate the validity and applicability of the proposed method.

scholarly journals Numerical Solution of Some Types of Fractional Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nasser Hassan Sweilam ◽  
Tamer Mostafa Al-Ajami ◽  
Ronald H. W. Hoppe
Keyword(s):  
Optimal Control ◽  
Numerical Solution ◽  
Optimal Control Problems ◽  
Ritz Method ◽  
Necessary Optimality Conditions ◽  
State Equation ◽  
The State ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.

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