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自动化学报 2007
线性离散奇异系统的不定二次最优控制问题:Krein空间方法DOI: 10.1360/aas-007-0635, PP. 635-640 Keywords: Singularlineardiscrete-timesystem,LQoptimalcontrol,finitetimehorizon,Riccatidifferenceequation,Kalmanfilter Abstract: ？Thefinitetimehorizonindefinitelinearquadratic(LQ)optimalcontrolproblemforsingularlineardiscretetime-varyingsystemsisdiscussed.IndefiniteLQoptimalcontrolproblemforsingularsystemscanbetransformedtothatforstandardstate-spacesystemsunderareasonableassumption.ItisshownthattheindefiniteLQoptimalcontrolproblemisdualtothatofprojectionforbackwardstochasticsystems.Thus,theoptimalLQcontrollercanbeobtainedbycomputingthegainmatricesofKalmanfilter.NecessaryandsufficientconditionsguaranteeingauniquesolutionfortheindefiniteLQproblemaregiven.AnexplicitsolutionfortheproblemisobtainedintermsofthesolutionofRiccatidifferenceequations.
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