Design of 'softer' robust nonlinear control laws

R. A. Freeman; P. V. Kokotovic

doi:10.1016/0005-1098(93)90007-G

Design of 'softer' robust nonlinear control laws

R. A. Freeman, P. V. Kokotovic^*

^*Corresponding author for this work

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

106 Scopus citations

Abstract

We show that the Lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily 'hard' control laws having undesirable high-gain properties. We present a new Lyapunov function and use it to design 'softer' control laws which exhibit the high-gain properties to a much lesser extent. We show that the 'soft' designs eliminate the chattering exhibited by the 'hard' designs and achieve the same or better performance with less control effort.

Original language	English (US)
Pages (from-to)	1425-1437
Number of pages	13
Journal	Automatica
Volume	29
Issue number	6
DOIs	https://doi.org/10.1016/0005-1098(93)90007-G
State	Published - Nov 1993

Keywords

Backstepping
mismatched uncertainties
nonlinear systems
robust control

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/0005-1098(93)90007-G

Cite this

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title = "Design of 'softer' robust nonlinear control laws",

abstract = "We show that the Lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily 'hard' control laws having undesirable high-gain properties. We present a new Lyapunov function and use it to design 'softer' control laws which exhibit the high-gain properties to a much lesser extent. We show that the 'soft' designs eliminate the chattering exhibited by the 'hard' designs and achieve the same or better performance with less control effort.",

keywords = "Backstepping, mismatched uncertainties, nonlinear systems, robust control",

author = "Freeman, {R. A.} and Kokotovic, {P. V.}",

note = "Funding Information: Acknowledgementv--The authors would like to thank Riccardo Marino and Laurent Praly for their helpful comments. This research was supported in part by the U.S. Department of Energy under Grant DE-FG-02-88-ER-13939, in part by Air Force Office of Scientific Research under Grant AFOSR F49620-92-J-0004, and in part by the National Science Foundation under an NSF Graduate Fellowship.",

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doi = "10.1016/0005-1098(93)90007-G",

language = "English (US)",

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T1 - Design of 'softer' robust nonlinear control laws

AU - Freeman, R. A.

AU - Kokotovic, P. V.

N1 - Funding Information: Acknowledgementv--The authors would like to thank Riccardo Marino and Laurent Praly for their helpful comments. This research was supported in part by the U.S. Department of Energy under Grant DE-FG-02-88-ER-13939, in part by Air Force Office of Scientific Research under Grant AFOSR F49620-92-J-0004, and in part by the National Science Foundation under an NSF Graduate Fellowship.

PY - 1993/11

Y1 - 1993/11

N2 - We show that the Lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily 'hard' control laws having undesirable high-gain properties. We present a new Lyapunov function and use it to design 'softer' control laws which exhibit the high-gain properties to a much lesser extent. We show that the 'soft' designs eliminate the chattering exhibited by the 'hard' designs and achieve the same or better performance with less control effort.

AB - We show that the Lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily 'hard' control laws having undesirable high-gain properties. We present a new Lyapunov function and use it to design 'softer' control laws which exhibit the high-gain properties to a much lesser extent. We show that the 'soft' designs eliminate the chattering exhibited by the 'hard' designs and achieve the same or better performance with less control effort.

KW - Backstepping

KW - mismatched uncertainties

KW - nonlinear systems

KW - robust control

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JO - Automatica

JF - Automatica

IS - 6

ER -

Design of 'softer' robust nonlinear control laws

Abstract

Keywords

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