A Neural Network Approach for Solving a Class of Fractional Optimal Control Problems

2016 ◽  
Vol 45 (1) ◽  
pp. 59-74 ◽  
Author(s):  
Javad Sabouri K. ◽  
Sohrab Effati ◽  
Morteza Pakdaman
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Network Approach ◽  
Neural Network Approach ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

On fractional optimal control problems with an application in fractional chaotic systems using a Legendre collocation-optimization technique

2020 ◽  
pp. 014233122096958
Author(s):  
Safiye Ghasemi ◽  
Alireza Nazemi ◽  
Raziye Tajik ◽  
Marziyeh Mortezaee
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Optimal Control Problems ◽  
Minimum Principle ◽  
Control Problems ◽  
Back Propagation Algorithm ◽  
Functional Link ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
Following Error

In this paper, an intelligence method based on single layer legendre neural network is proposed to solve fractional optimal control problems where the dynamic control system depends on Caputo fractional derivatives. First, with the help of an approximation, the Caputo derivative is replaced to integer order derivative. According to the Pontryagin minimum principle for optimal control problems and by constructing an error function, an unconstrained minimization problem is then defined. In the optimization problem, trial solutions are used for state, costate and control functions, where these trial solutions are constructed by using Legendre polynomial based functional link artificial neural network. In the following, error back propagation algorithm is used for updating the network parameters (weights). At the end, some illustrative examples are included to demonstrate the validity and capability of the proposed method. Three applicable examples about chaos control of Malkus waterwheel, finance fractional chaotic models and fractional-order geomagnetic field models are also considered.

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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