简介：InthispaperweanalyzetheoptimalcontrolproblemforaclassofaffinenonlinearsystemsundertheassumptionthattheassociatedLiealgebraisnilpotent.TheLiebracketsgeneratedbythevectorfieldswhichdefinethenonlinearsystemrepresentaremarkablemathematicalinstrumentforthecontrolofaffinesystems.Wedeterminetheoptimalcontrolwhichcorrespondstothenilpotentoperatorofthefirstorder.Inparticular,weobtainthecontrolthatminimizestheenergyofthegivennonlinearsystem.Applicationsofthiscontroltobilinearsystemswithfirstordernilpotentoperatorareconsidered.
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