The finite-difference method in optimal control problems

Cybernetics ◽  
1970 ◽  
Vol 3 (3) ◽  
pp. 1-16 ◽  
Author(s):  
Yu. M. Ermol'ev ◽  
V. P. Gulenko
Keyword(s):  
Optimal Control ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
The Finite Difference Method

A research note on the nonstandard finite difference method for solving variable-order fractional optimal control problems

2018 ◽  
Vol 24 (11) ◽  
pp. 2109-2111 ◽  
Author(s):  
Mahmoud A Zaky
Keyword(s):  
Optimal Control ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Variable Order ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems ◽  
Nonstandard Finite Difference

Zahra and Hikal recently proposed a nonstandard finite difference method for solving a class of variable-order fractional optimal control problems. They presented a system of variable-order fractional differential equations, and they claimed that its solution provides the optimal profiles for the state and control variables. In this note, we prove that this system does not give the necessary conditions of optimality for the variable-order fractional optimal control problems. Consequently, one cannot construct an indirect approach for the variable-order fractional optimal control problems using the Euler–Lagrange equations proposed by Zahra and Hikal.

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