Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

Aditya A. Paranjape; Soon Jo Chung

doi:10.1109/CDC.2016.7798459

Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

Aditya A. Paranjape, Soon Jo Chung

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other

2 Citations (Scopus)

Abstract

In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system.

Original language	English
Title of host publication	2016 IEEE 55th Conference on Decision and Control, CDC 2016
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	1382-1387
Number of pages	6
ISBN (Electronic)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7798459
Publication status	Published - 2016
Externally published	Yes
Event	IEEE Conference on Decision and Control 2016 - Las Vegas, United States of America Duration: 12 Dec 2016 → 14 Dec 2016 Conference number: 55th https://ieeexplore.ieee.org/xpl/conhome/7786694/proceeding

Conference

Conference	IEEE Conference on Decision and Control 2016
Abbreviated title	CDC 2016
Country/Territory	United States of America
City	Las Vegas
Period	12/12/16 → 14/12/16
Internet address	https://ieeexplore.ieee.org/xpl/conhome/7786694/proceeding

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10.1109/CDC.2016.7798459

Cite this

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title = "Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer",

abstract = "In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system.",

author = "Paranjape, {Aditya A.} and Chung, {Soon Jo}",

note = "Funding Information: The second author gratefully acknowledges support by the National Science Foundation (IIS-1253758; CMMI-1427111). Publisher Copyright: {\textcopyright} 2016 IEEE.; IEEE Conference on Decision and Control 2016, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

year = "2016",

doi = "10.1109/CDC.2016.7798459",

language = "English",

pages = "1382--1387",

booktitle = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

publisher = "IEEE, Institute of Electrical and Electronics Engineers",

address = "United States of America",

url = "https://ieeexplore.ieee.org/xpl/conhome/7786694/proceeding",

}

Paranjape, AA & Chung, SJ 2016, Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 779845, IEEE, Institute of Electrical and Electronics Engineers, pp. 1382-1387, IEEE Conference on Decision and Control 2016, Las Vegas, Nevada, United States of America, 12/12/16. https://doi.org/10.1109/CDC.2016.7798459

TY - GEN

T1 - Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

AU - Paranjape, Aditya A.

AU - Chung, Soon Jo

N1 - Conference code: 55th

PY - 2016

Y1 - 2016

N2 - In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system.

AB - In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system.

UR - http://www.scopus.com/inward/record.url?scp=85010716253&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7798459

DO - 10.1109/CDC.2016.7798459

M3 - Conference Paper

AN - SCOPUS:85010716253

SP - 1382

EP - 1387

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - IEEE, Institute of Electrical and Electronics Engineers

T2 - IEEE Conference on Decision and Control 2016

Y2 - 12 December 2016 through 14 December 2016

ER -

Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

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