1 Ola Härkegård Backstepping: From simple designs to take-off Internal seminar January 27, 2005 AUTOMATIC CONTROL LINKÖPINGS UNIVERSITET COMMUNICATION SYSTEMS Backstepping From simple designs to take-off Ola Härkegård Control & Communication Linköpings universitet Ola Härkegård Backstepping: From simple designs to take-off Internal seminar January 27, 2005 AUTOMATIC CONTROL LINKÖPINGS UNIVERSITET COMMUNICATION SYSTEMS Backstepping Constructive (=systematic) control design for nonlinear systems ( 29 ( 29 ( 29 u , x , , x , x , x f x x , x , x f x x , x f x n 3 2 1 n n 3 2 1 2 2 2 1 1 1 K & M & & = = = (essentially same as for feedback linearization) Applies to systems of lower triangular form Can be used to avoid cancellation of "useful nonlinearities" (unlike feedback linearization) Different flavours: adaptive, robust and observer backstepping
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1
Ola HärkegårdBackstepping: From simple designs to take-off
Internal seminarJanuary 27, 2005
AUTOMATIC CONTROL
LINKÖPINGS UNIVERSITETCOMMUNICATION SYSTEMS
BacksteppingFrom simple designs to take-off
Ola HärkegårdControl & Communication
Linköpings universitet
Ola HärkegårdBackstepping: From simple designs to take-off
Internal seminarJanuary 27, 2005
AUTOMATIC CONTROL
LINKÖPINGS UNIVERSITETCOMMUNICATION SYSTEMS
Backstepping
� Constructive (=systematic) control design for nonlinear systems
( )( )
( )u,x,,x,x,xfx
x,x,xfx
x,xfx
n321nn
32122
2111
K&
M
&
&
=
==
(essentially same as forfeedback linearization)
� Applies to systems of lower triangular form
� Can be used to avoid cancellation of "useful nonlinearities"(unlike feedback linearization)
� Different flavours: adaptive, robust and observer backstepping
2
Ola HärkegårdBackstepping: From simple designs to take-off
Internal seminarJanuary 27, 2005
AUTOMATIC CONTROL
LINKÖPINGS UNIVERSITETCOMMUNICATION SYSTEMS
Paper statistics
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92 93 94 95 96 97 98 99 00 01 02 03
Conference papersJournal papers
� Conference papers: 194
� Not adaptive: 108
� Applied 2003: 16 of 25
IEEE Explore 1990-2003Backstepping in title
Ola HärkegårdBackstepping: From simple designs to take-off
Internal seminarJanuary 27, 2005
AUTOMATIC CONTROL
LINKÖPINGS UNIVERSITETCOMMUNICATION SYSTEMS
References
� Booksì Nonlinear and Adaptive Control Design, 1995 (Krstic,