A New Approach for Solving Fractional Optimal Control Problems Using Shifted Ultraspherical Polynomials

2018 ◽  
Vol 4 (3) ◽  
pp. 179-195
Author(s):  
Hoda F. Ahmed ◽  
Marina B. Melad
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
New Approach ◽  
Fractional Optimal Control ◽  
Ultraspherical Polynomials ◽  
Fractional Optimal Control Problems

scholarly journals Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohamed Abdelhakem ◽  
Doha Mahmoud ◽  
Dumitru Baleanu ◽  
Mamdouh El-kady
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Approximate Solutions ◽  
Collocation Methods ◽  
Control Problems ◽  
Algebraic Equations ◽  
Fractional Optimal Control ◽  
Ultraspherical Polynomials ◽  
Fractional Optimal Control Problems

AbstractIn this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods. Also, this method can be extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified Galerkin spectral method has been used to create direct approximate solutions of linear/nonlinear ordinary fractional differential equations, a system of ordinary fraction differential equations, fractional integro-differential equations, or fractional optimal control problems. The aim is to transform those problems into a system of algebraic equations. That system will be efficiently solved by any solver. Three spaces of collocation nodes have been used through that transformation. Finally, numerical examples show the accuracy and efficiency of the investigated 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.

Shifted Chebyshev schemes for solving fractional optimal control problems

2019 ◽  
Vol 25 (15) ◽  
pp. 2143-2150 ◽  
Author(s):  
M Abdelhakem ◽  
H Moussa ◽  
D Baleanu ◽  
M El-Kady
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Numerical Examples ◽  
Fractional Optimal Control ◽  
Functional Approximation ◽  
Fractional Optimal Control Problems

Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.

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