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Description
  • We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and compact semialgebraic state and control constraints, we describe a hierarchy of finite-dimensional linear matrix inequality (LMI) relaxations whose optimal values converge to the volume of the MCI set; dual to these LMI relaxations are sum-of-squares (SOS) problems providing a converging sequence of outer approximations to the MCI set. The approach is simple and readily applicable in the sense that the approximations are the outcome of a single semidefinite program with no additional input apart from the problem description. A number of numerical examples illustrate the approach.
  • We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and compact semialgebraic state and control constraints, we describe a hierarchy of finite-dimensional linear matrix inequality (LMI) relaxations whose optimal values converge to the volume of the MCI set; dual to these LMI relaxations are sum-of-squares (SOS) problems providing a converging sequence of outer approximations to the MCI set. The approach is simple and readily applicable in the sense that the approximations are the outcome of a single semidefinite program with no additional input apart from the problem description. A number of numerical examples illustrate the approach. (en)
Title
  • CONVEX COMPUTATION OF THE MAXIMUM CONTROLLED INVARIANT SET FOR POLYNOMIAL CONTROL SYSTEMS
  • CONVEX COMPUTATION OF THE MAXIMUM CONTROLLED INVARIANT SET FOR POLYNOMIAL CONTROL SYSTEMS (en)
skos:prefLabel
  • CONVEX COMPUTATION OF THE MAXIMUM CONTROLLED INVARIANT SET FOR POLYNOMIAL CONTROL SYSTEMS
  • CONVEX COMPUTATION OF THE MAXIMUM CONTROLLED INVARIANT SET FOR POLYNOMIAL CONTROL SYSTEMS (en)
skos:notation
  • RIV/68407700:21230/14:00220940!RIV15-GA0-21230___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA13-06894S)
http://linked.open...iv/cisloPeriodika
  • 5
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
  • Henrion, Didier
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 8912
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21230/14:00220940
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • maximum controlled invariant set; region of attraction; optimal control; nonlinear control; sum of squares; occupation measure; moments; semidefinite programming (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [CE98219D13BD]
http://linked.open...i/riv/nazevZdroje
  • SIAM Journal on Control and Optimization
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 52
http://linked.open...iv/tvurceVysledku
  • Henrion, Didier
  • Korda, Milan
  • Jones, C.N.
http://linked.open...ain/vavai/riv/wos
  • 000344748000012
issn
  • 0363-0129
number of pages
http://bibframe.org/vocab/doi
  • 10.1137/130914565
http://localhost/t...ganizacniJednotka
  • 21230
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