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Nonlinear Control Synthesis by Convex Optimization

Prajna, Stephen; Parrilo, Pablo and Rantzer, Anders LU (2004) In IEEE Transactions on Automatic Control 49(2). p.310-314
Abstract
A stability criterion for nonlinear systems, recently derived by thethird author, can be viewed as a dual to Lyapunov's second theorem.The criterion is stated in terms of a function which can beinterpreted as the stationary density of a substance that is generatedall over the state space and flows along the system trajectoriestowards the equilibrium.The new criterion has a remarkable convexity property, which in thispaper is used for controller synthesis via convex optimization. Recentnumerical methods for verification of positivity of multivariatepolynomials are used.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
semidefinite programming relaxation, Density functions, nonlinear control, sum of squares decomposition
in
IEEE Transactions on Automatic Control
volume
49
issue
2
pages
310 - 314
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000189037200023
  • scopus:1442288703
ISSN
0018-9286
DOI
10.1109/TAC.2003.823000
language
English
LU publication?
yes
id
bf54a206-66aa-493a-8722-87edf31e6504 (old id 161414)
date added to LUP
2007-07-10 08:57:03
date last changed
2017-11-19 04:10:32
@article{bf54a206-66aa-493a-8722-87edf31e6504,
  abstract     = {A stability criterion for nonlinear systems, recently derived by thethird author, can be viewed as a dual to Lyapunov's second theorem.The criterion is stated in terms of a function which can beinterpreted as the stationary density of a substance that is generatedall over the state space and flows along the system trajectoriestowards the equilibrium.The new criterion has a remarkable convexity property, which in thispaper is used for controller synthesis via convex optimization. Recentnumerical methods for verification of positivity of multivariatepolynomials are used.},
  author       = {Prajna, Stephen and Parrilo, Pablo and Rantzer, Anders},
  issn         = {0018-9286},
  keyword      = {semidefinite programming
relaxation,Density functions,nonlinear control,sum of squares decomposition},
  language     = {eng},
  number       = {2},
  pages        = {310--314},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Automatic Control},
  title        = {Nonlinear Control Synthesis by Convex Optimization},
  url          = {http://dx.doi.org/10.1109/TAC.2003.823000},
  volume       = {49},
  year         = {2004},
}