Linear parameter-varying control of nonlinear systems based on incremental stability

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Abstract

The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the L2-gain concept. However, recent research has pointed out that current L2-gain based LPV synthesis methods can fail to guarantee these requirements if stabilization of a non-zero operating condition (e.g. reference tracking, constant disturbance rejection, etc.) is required. In this paper, an LPV based synthesis method is proposed which is able to guarantee incremental performance and stability of an NL system even with reference and disturbance rejection objectives. The developed approach and the current L2 LPV synthesis method are compared in a simulation study of the position control problem of a Duffing oscillator, showing performance improvements of the proposed method compared to the current L2-based approach for tracking and disturbance rejection.
Original languageEnglish
Title of host publication3rd IFAC Workshop on Linear Parameter-Varying Systems
PublisherIFAC
Publication statusAccepted/In press - 2019
Event3rd IFAC Workshop on Linear Parameter-Varying Systems - Eindhoven, Netherlands
Duration: 4 Nov 20196 Nov 2019

Workshop

Workshop3rd IFAC Workshop on Linear Parameter-Varying Systems
Abbreviated titleLPVS'19
CountryNetherlands
CityEindhoven
Period4/11/196/11/19

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Disturbance rejection
Nonlinear systems
Position control
Stabilization

Cite this

Koelewijn, P., Toth, R., & Nijmeijer, H. (Accepted/In press). Linear parameter-varying control of nonlinear systems based on incremental stability. In 3rd IFAC Workshop on Linear Parameter-Varying Systems [MoB1.1] IFAC.
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title = "Linear parameter-varying control of nonlinear systems based on incremental stability",
abstract = "The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the L2-gain concept. However, recent research has pointed out that current L2-gain based LPV synthesis methods can fail to guarantee these requirements if stabilization of a non-zero operating condition (e.g. reference tracking, constant disturbance rejection, etc.) is required. In this paper, an LPV based synthesis method is proposed which is able to guarantee incremental performance and stability of an NL system even with reference and disturbance rejection objectives. The developed approach and the current L2 LPV synthesis method are compared in a simulation study of the position control problem of a Duffing oscillator, showing performance improvements of the proposed method compared to the current L2-based approach for tracking and disturbance rejection.",
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booktitle = "3rd IFAC Workshop on Linear Parameter-Varying Systems",
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Koelewijn, P, Toth, R & Nijmeijer, H 2019, Linear parameter-varying control of nonlinear systems based on incremental stability. in 3rd IFAC Workshop on Linear Parameter-Varying Systems., MoB1.1, IFAC, 3rd IFAC Workshop on Linear Parameter-Varying Systems, Eindhoven, Netherlands, 4/11/19.

Linear parameter-varying control of nonlinear systems based on incremental stability. / Koelewijn, Patrick; Toth, Roland; Nijmeijer, Henk.

3rd IFAC Workshop on Linear Parameter-Varying Systems. IFAC, 2019. MoB1.1.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

TY - GEN

T1 - Linear parameter-varying control of nonlinear systems based on incremental stability

AU - Koelewijn, Patrick

AU - Toth, Roland

AU - Nijmeijer, Henk

PY - 2019

Y1 - 2019

N2 - The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the L2-gain concept. However, recent research has pointed out that current L2-gain based LPV synthesis methods can fail to guarantee these requirements if stabilization of a non-zero operating condition (e.g. reference tracking, constant disturbance rejection, etc.) is required. In this paper, an LPV based synthesis method is proposed which is able to guarantee incremental performance and stability of an NL system even with reference and disturbance rejection objectives. The developed approach and the current L2 LPV synthesis method are compared in a simulation study of the position control problem of a Duffing oscillator, showing performance improvements of the proposed method compared to the current L2-based approach for tracking and disturbance rejection.

AB - The Linear Parameter-Varying (LPV) framework has long been used to guarantee performance and stability requirements of nonlinear (NL) systems mainly through the L2-gain concept. However, recent research has pointed out that current L2-gain based LPV synthesis methods can fail to guarantee these requirements if stabilization of a non-zero operating condition (e.g. reference tracking, constant disturbance rejection, etc.) is required. In this paper, an LPV based synthesis method is proposed which is able to guarantee incremental performance and stability of an NL system even with reference and disturbance rejection objectives. The developed approach and the current L2 LPV synthesis method are compared in a simulation study of the position control problem of a Duffing oscillator, showing performance improvements of the proposed method compared to the current L2-based approach for tracking and disturbance rejection.

M3 - Conference contribution

BT - 3rd IFAC Workshop on Linear Parameter-Varying Systems

PB - IFAC

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Koelewijn P, Toth R, Nijmeijer H. Linear parameter-varying control of nonlinear systems based on incremental stability. In 3rd IFAC Workshop on Linear Parameter-Varying Systems. IFAC. 2019. MoB1.1