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

Mohammad Ghanaatpishe, Hosam K. 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

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    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