An Efficient Finite Difference Method for The Time-Delay Optimal Control Problems With Time-Varying Delay

2016 ◽  
Vol 19 (2) ◽  
pp. 554-563 ◽  
Author(s):  
Amin Jajarmi ◽  
Mojtaba Hajipour
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

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.

A new approach for the optimal control of time-varying delay systems with external persistent matched disturbances

2017 ◽  
Vol 24 (19) ◽  
pp. 4505-4512 ◽  
Author(s):  
Amin Jajarmi ◽  
Mojtaba Hajipour ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Necessary Optimality Conditions ◽  
Delay Systems ◽  
Time Varying ◽  
Time Varying Delay ◽  
Augmented System ◽  
Varying Delay

The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results.

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