Optimal control problems for fractional-order dynamical systems with lumped and distributed parameters

2018 ◽  
Author(s):  
Sergey Sergeevich Postnov
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Distributed Parameters

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.

Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures

2012 ◽  
Vol 22 (4) ◽  
pp. 599-629 ◽  
Author(s):  
Kathrin Flaßkamp ◽  
Sina Ober-Blöbaum ◽  
Marin Kobilarov
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Optimal Control Problems ◽  
Control Problems

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.

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

Fractional-order Boubaker functions and their applications in solving delay fractional optimal control problems

2017 ◽  
Vol 24 (15) ◽  
pp. 3370-3383 ◽  
Author(s):  
Kobra Rabiei ◽  
Yadollah Ordokhani ◽  
Esmaeil Babolian
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Operational Matrix ◽  
Nonlinear Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Newton’S Iterative Method ◽  
Quadratic Performance ◽  
Fractional Optimal Control Problems

In this paper, a new set of functions called fractional-order Boubaker functions is defined for solving the delay fractional optimal control problems with a quadratic performance index. To solve the problem, first we obtain the operational matrix of the Caputo fractional derivative of these functions and the operational matrix of multiplication to solve the nonlinear problems for the first time. Also, a general formulation for the delay operational matrix of these functions has been achieved. Then we utilized these matrices to solve delay fractional optimal control problems directly. In fact, the delay fractional optimal control problem converts to an optimization problem, which can then be easily solved with the aid of the Gauss–Legendre integration formula and Newton’s iterative method. Convergence of the algorithm is proved. The applicability of the method is shown by some examples; moreover, a comparison with the existing results shows the preference of this method.

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