Numerical Method for Solving Fractional Optimal Control Problems

2009 ◽  
Author(s):  
Raj Kumar Biswas ◽  
Siddhartha Sen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Numerical Technique ◽  
Control Problems ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Fractional Optimal Control Problems ◽  
The Right

A numerical technique for the solution of a class of fractional optimal control problems has been proposed in this paper. The technique can used for problems defined both in terms of Riemann-Liouville and Caputo fractional derivatives. In this technique a Reflection Operator is used to convert the right Riemann-Liouville derivative into an equivalent left Riemann-Liouville derivative, and then the two point boundary value problem is solved numerically. The proposed method is straightforward and it uses an available numerical technique to solve fractional differential equations resulting from the formulation. Examples considered here show that the numerical results obtained using this and other techniques agree very well.

Research on a collocation approach and three metaheuristic techniques based on MVO, MFO, and WOA for optimal control of fractional differential equation

2021 ◽  
pp. 107754632110514
Author(s):  
Asiyeh Ebrahimzadeh ◽  
Raheleh Khanduzi ◽  
Samaneh P A Beik ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Focal Point ◽  
Control Problems ◽  
Operational Matrices ◽  
State Variables ◽  
Caputo Fractional Derivatives ◽  
Fractional Optimal Control ◽  
Whale Optimization ◽  
Fractional Optimal Control Problems

Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann–Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.

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.

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