An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters

Mohammad Ghanaatpishe, Hosam Kadry Fathy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper proposes an online adaptive control framework for tracking Optimal Periodic Control (OPC) trajectories of feedback linearizable plants with unknown parameters. The literature already offers different online solution algorithms for solving OPC problems. However, the existing algorithms either assume perfectly known plant models or allow for the appearance of unknown parameters in the plant model, but rely on the plant's open-loop stability for implementation of the optimal solution. This paper, in contrast, develops an adaptive feedback linearizing algorithm to simultaneously estimate and track the optimal OPC orbit. Using Lyapunov analysis, the paper shows that the system trajectories always remain bounded and asymptotically approach the periodic solution corresponding to an estimate of the unknown plant parameter vector. Furthermore, when the regressor vector of the parameter estimation law is persistently exciting, global convergence to the true periodic solution trajectory is guaranteed. The paper concludes with a numerical implementation of its adaptive optimal control algorithm for a periodic drug delivery application, commonly used as a benchmark in the OPC literature.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1819-1826
Number of pages8
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

Fingerprint

Feedback
Trajectories
Drug delivery
Parameter estimation
Orbits

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Ghanaatpishe, M., & Fathy, H. K. (2018). An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters. In 2018 Annual American Control Conference, ACC 2018 (pp. 1819-1826). [8431571] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431571
Ghanaatpishe, Mohammad ; Fathy, Hosam Kadry. / An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters. 2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1819-1826 (Proceedings of the American Control Conference).
@inproceedings{47e9ebcf077f4183a4f18f59e427128d,
title = "An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters",
abstract = "This paper proposes an online adaptive control framework for tracking Optimal Periodic Control (OPC) trajectories of feedback linearizable plants with unknown parameters. The literature already offers different online solution algorithms for solving OPC problems. However, the existing algorithms either assume perfectly known plant models or allow for the appearance of unknown parameters in the plant model, but rely on the plant's open-loop stability for implementation of the optimal solution. This paper, in contrast, develops an adaptive feedback linearizing algorithm to simultaneously estimate and track the optimal OPC orbit. Using Lyapunov analysis, the paper shows that the system trajectories always remain bounded and asymptotically approach the periodic solution corresponding to an estimate of the unknown plant parameter vector. Furthermore, when the regressor vector of the parameter estimation law is persistently exciting, global convergence to the true periodic solution trajectory is guaranteed. The paper concludes with a numerical implementation of its adaptive optimal control algorithm for a periodic drug delivery application, commonly used as a benchmark in the OPC literature.",
author = "Mohammad Ghanaatpishe and Fathy, {Hosam Kadry}",
year = "2018",
month = "8",
day = "9",
doi = "10.23919/ACC.2018.8431571",
language = "English (US)",
isbn = "9781538654286",
series = "Proceedings of the American Control Conference",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1819--1826",
booktitle = "2018 Annual American Control Conference, ACC 2018",
address = "United States",

}

Ghanaatpishe, M & Fathy, HK 2018, An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters. in 2018 Annual American Control Conference, ACC 2018., 8431571, Proceedings of the American Control Conference, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 1819-1826, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431571

An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters. / Ghanaatpishe, Mohammad; Fathy, Hosam Kadry.

2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1819-1826 8431571 (Proceedings of the American Control Conference; Vol. 2018-June).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters

AU - Ghanaatpishe, Mohammad

AU - Fathy, Hosam Kadry

PY - 2018/8/9

Y1 - 2018/8/9

N2 - This paper proposes an online adaptive control framework for tracking Optimal Periodic Control (OPC) trajectories of feedback linearizable plants with unknown parameters. The literature already offers different online solution algorithms for solving OPC problems. However, the existing algorithms either assume perfectly known plant models or allow for the appearance of unknown parameters in the plant model, but rely on the plant's open-loop stability for implementation of the optimal solution. This paper, in contrast, develops an adaptive feedback linearizing algorithm to simultaneously estimate and track the optimal OPC orbit. Using Lyapunov analysis, the paper shows that the system trajectories always remain bounded and asymptotically approach the periodic solution corresponding to an estimate of the unknown plant parameter vector. Furthermore, when the regressor vector of the parameter estimation law is persistently exciting, global convergence to the true periodic solution trajectory is guaranteed. The paper concludes with a numerical implementation of its adaptive optimal control algorithm for a periodic drug delivery application, commonly used as a benchmark in the OPC literature.

AB - This paper proposes an online adaptive control framework for tracking Optimal Periodic Control (OPC) trajectories of feedback linearizable plants with unknown parameters. The literature already offers different online solution algorithms for solving OPC problems. However, the existing algorithms either assume perfectly known plant models or allow for the appearance of unknown parameters in the plant model, but rely on the plant's open-loop stability for implementation of the optimal solution. This paper, in contrast, develops an adaptive feedback linearizing algorithm to simultaneously estimate and track the optimal OPC orbit. Using Lyapunov analysis, the paper shows that the system trajectories always remain bounded and asymptotically approach the periodic solution corresponding to an estimate of the unknown plant parameter vector. Furthermore, when the regressor vector of the parameter estimation law is persistently exciting, global convergence to the true periodic solution trajectory is guaranteed. The paper concludes with a numerical implementation of its adaptive optimal control algorithm for a periodic drug delivery application, commonly used as a benchmark in the OPC literature.

UR - http://www.scopus.com/inward/record.url?scp=85052589488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052589488&partnerID=8YFLogxK

U2 - 10.23919/ACC.2018.8431571

DO - 10.23919/ACC.2018.8431571

M3 - Conference contribution

AN - SCOPUS:85052589488

SN - 9781538654286

T3 - Proceedings of the American Control Conference

SP - 1819

EP - 1826

BT - 2018 Annual American Control Conference, ACC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -

Ghanaatpishe M, Fathy HK. An Adaptive Framework for the Online Optimal Periodic Control of Feedback Linearizable Systems with Unknown Parameters. In 2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1819-1826. 8431571. (Proceedings of the American Control Conference). https://doi.org/10.23919/ACC.2018.8431571