Fractional Chebyshev functional link neural network‐optimization method for solving delay fractional optimal control problems with Atangana‐Baleanu derivative

2020 ◽  
Vol 41 (3) ◽  
pp. 808-832 ◽  
Author(s):  
Farzaneh Kheyrinataj ◽  
Alireza Nazemi
Keyword(s):  
Neural Network ◽  
Network Optimization ◽  
Optimal Control Problems ◽  
Optimization Method ◽  
Control Problems ◽  
Functional Link ◽  
Neural Network Optimization ◽  
Chebyshev Functional ◽  
Fractional Optimal Control Problems ◽  
Functional Link Neural Network

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.

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