A General Formulation and Solution Scheme for Fractional Optimal Control Problems

2004 ◽  
Vol 38 (1-4) ◽  
pp. 323-337 ◽  
Author(s):  
Om Prakash Agrawal
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Solution Scheme ◽  
Fractional Optimal Control Problems

Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation

2016 ◽  
Vol 24 (9) ◽  
pp. 1741-1756 ◽  
Author(s):  
Seyed Ali Rakhshan ◽  
Sohrab Effati ◽  
Ali Vahidian Kamyad
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Bellman Equation ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Solution Scheme ◽  
Hamilton Jacobi Bellman Equation ◽  
Fractional Optimal Control Problems ◽  
Hamilton Jacobi Bellman

The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional derivative in the Riemann–Liouville sense and explain our method for a fractional derivative of order of [Formula: see text]. Numerical examples are provided to show the effectiveness of the formulation and solution scheme.

Fractional Optimal Control Problems With Specified Final Time

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Raj Kumar Biswas ◽  
Siddhartha Sen
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Optimal Control Problems ◽  
Numerical Solutions ◽  
Order System ◽  
Control Problems ◽  
Final Time ◽  
Fractional Optimal Control ◽  
Solution Scheme ◽  
Fractional Optimal Control Problems

A constrained dynamic optimization problem of a fractional order system with fixed final time has been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The dynamic constraint is described by a fractional differential equation of order less than 1, and the fractional derivative is defined in terms of Riemann–Liouville. The performance index includes the terminal cost function in addition to the integral cost function. A general transversility condition in addition to the optimal conditions has been obtained using the Hamiltonian approach. Both the specified and unspecified final state cases have been considered. A numerical technique using the Grünwald–Letnikov definition is used to solve the resulting equations obtained from the formulation. Numerical examples are provided to show the effectiveness of the formulation and solution scheme. It has been observed that the numerical solutions approach the analytical solutions as the order of the fractional derivatives approach 1.

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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