Optimal Trajectory Tracking Solution: Fractional Order Viewpoint

Abolhassan Razminia, Mehdi Asadizadehshiraz, Hamid Reza Shaker*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper, a generalized trajectory tracking problem for a closed-loop control
system is formulated in the optimal control context. A linear time varying plant is considered to track a closed-loop desired trajectory generated by a given mechanism.
The theoretical results are obtained based on the Hamilton-Jacobi-Bellman theory in which some generalized semi-quadratic value functions are employed as the Lagrangian.
In addition, we employ a non-integer order integral of Riemann-Liouville type as the cost functional, so that the trajectory tracking process can be evaluated in an extended optimum manner wherein the fractionality plays the main role. By
selecting a suitable fractional order of the integral, a satisfactory optimal control
system can be deduced in which least concentration on selecting the weighting matrices is needed. To show the effectiveness of the results, some numerical examples illustrate the potentials.
Original languageEnglish
JournalJournal of The Franklin Institute
Volume356
Issue number3
Pages (from-to)1590-1603
ISSN0016-0032
DOIs
Publication statusPublished - Feb 2019

Fingerprint

Optimal Trajectory
Trajectory Tracking
Fractional Order
Closed-loop
Trajectories
Hamilton-Jacobi
Quadratic Function
Value Function
Weighting
Linear Time
Time-varying
Optimal Control
Trajectory
Numerical Examples
Costs
Context

Cite this

Razminia, Abolhassan ; Asadizadehshiraz, Mehdi ; Shaker, Hamid Reza. / Optimal Trajectory Tracking Solution : Fractional Order Viewpoint. In: Journal of The Franklin Institute. 2019 ; Vol. 356, No. 3. pp. 1590-1603.
@article{74185c95f9154b6697dbb34cfd09ea19,
title = "Optimal Trajectory Tracking Solution: Fractional Order Viewpoint",
abstract = "In this paper, a generalized trajectory tracking problem for a closed-loop controlsystem is formulated in the optimal control context. A linear time varying plant is considered to track a closed-loop desired trajectory generated by a given mechanism.The theoretical results are obtained based on the Hamilton-Jacobi-Bellman theory in which some generalized semi-quadratic value functions are employed as the Lagrangian.In addition, we employ a non-integer order integral of Riemann-Liouville type as the cost functional, so that the trajectory tracking process can be evaluated in an extended optimum manner wherein the fractionality plays the main role. Byselecting a suitable fractional order of the integral, a satisfactory optimal controlsystem can be deduced in which least concentration on selecting the weighting matrices is needed. To show the effectiveness of the results, some numerical examples illustrate the potentials.",
author = "Abolhassan Razminia and Mehdi Asadizadehshiraz and Shaker, {Hamid Reza}",
year = "2019",
month = "2",
doi = "10.1016/j.jfranklin.2018.11.024",
language = "English",
volume = "356",
pages = "1590--1603",
journal = "Journal of The Franklin Institute",
issn = "0016-0032",
publisher = "Pergamon Press",
number = "3",

}

Optimal Trajectory Tracking Solution : Fractional Order Viewpoint. / Razminia, Abolhassan ; Asadizadehshiraz, Mehdi ; Shaker, Hamid Reza.

In: Journal of The Franklin Institute, Vol. 356, No. 3, 02.2019, p. 1590-1603.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Optimal Trajectory Tracking Solution

T2 - Fractional Order Viewpoint

AU - Razminia, Abolhassan

AU - Asadizadehshiraz, Mehdi

AU - Shaker, Hamid Reza

PY - 2019/2

Y1 - 2019/2

N2 - In this paper, a generalized trajectory tracking problem for a closed-loop controlsystem is formulated in the optimal control context. A linear time varying plant is considered to track a closed-loop desired trajectory generated by a given mechanism.The theoretical results are obtained based on the Hamilton-Jacobi-Bellman theory in which some generalized semi-quadratic value functions are employed as the Lagrangian.In addition, we employ a non-integer order integral of Riemann-Liouville type as the cost functional, so that the trajectory tracking process can be evaluated in an extended optimum manner wherein the fractionality plays the main role. Byselecting a suitable fractional order of the integral, a satisfactory optimal controlsystem can be deduced in which least concentration on selecting the weighting matrices is needed. To show the effectiveness of the results, some numerical examples illustrate the potentials.

AB - In this paper, a generalized trajectory tracking problem for a closed-loop controlsystem is formulated in the optimal control context. A linear time varying plant is considered to track a closed-loop desired trajectory generated by a given mechanism.The theoretical results are obtained based on the Hamilton-Jacobi-Bellman theory in which some generalized semi-quadratic value functions are employed as the Lagrangian.In addition, we employ a non-integer order integral of Riemann-Liouville type as the cost functional, so that the trajectory tracking process can be evaluated in an extended optimum manner wherein the fractionality plays the main role. Byselecting a suitable fractional order of the integral, a satisfactory optimal controlsystem can be deduced in which least concentration on selecting the weighting matrices is needed. To show the effectiveness of the results, some numerical examples illustrate the potentials.

U2 - 10.1016/j.jfranklin.2018.11.024

DO - 10.1016/j.jfranklin.2018.11.024

M3 - Journal article

VL - 356

SP - 1590

EP - 1603

JO - Journal of The Franklin Institute

JF - Journal of The Franklin Institute

SN - 0016-0032

IS - 3

ER -