scholarly journals Fractional order optimal control problems with free terminal time

2014 ◽  
Vol 10 (2) ◽  
pp. 363-381 ◽  
Author(s):  
Shakoor Pooseh ◽  
◽  
Ricardo Almeida ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Terminal Time ◽  
Free Terminal Time

scholarly journals A Numerical Scheme to Solve Fractional Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Shakoor Pooseh ◽  
Ricardo Almeida ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Numerical Scheme ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Terminal Time ◽  
Dynamic Constraint ◽  
Fractional Optimal Control Problems ◽  
Free Terminal Time

We review recent results obtained to solve fractional order optimal control problems with free terminal time and a dynamic constraint involving integer and fractional order derivatives. Some particular cases are studied in detail. A numerical scheme is given, based on expansion formulas for the fractional derivative. The efficiency of the method is illustrated through examples.

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.

scholarly journals Solution of Some Types for Composition Fractional Order Differential Equations Corresponding to Optimal Control Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sameer Qasim Hasan ◽  
Moataz Abbas Holel
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Chebyshev Approximation ◽  
Approximate Solutions ◽  
Control Problems ◽  
Fractional Differential ◽  
Working Method

The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document