简介:Basedonthenotionofmaximalabsoluteobservabilityanditsnormalforms,anewmethodforstudyingthelocalstabilizationforakindofnonlinearcontrolsystemsisestablished.DifferentfromthepreviousresultsgivenbyByrnes-Isitoriandothers,thisnewmethodcandealwithmoregeneralsystems,andhasmuchsimplerwaytoprovethestabilizationconditionsandtodesignthefeedbacklaws.
简介:Thispaperstudiesafamilyofthelocalconvergenceoftheimprovedsecantmethodsforsolvingthenonlinearequalityconstrainedoptimizationsubjecttoboundsonvariables.TheHessianoftheLagrangianisapproximatedusingtheDFPortheBFGSsecantupdates.Theimprovedsecantmethodsareusedtogenerateasearchdirection.Combiningwithasuitablestepsize,eachiterateswitchestotrialstepofstrictinteriorfeasibility.WhentheHessianisonlypositivedefiniteinanaffinenullsubspace,oneshowsthatthealgorithmsgeneratethesequencesconvergingq-linearlyandtwo-stepq-superlinearly.Furthermore,undersomesuitableassumptions,somesequencesgeneratedbythealgorithmsconvergelocallyone-stepq-superlinearly.Finally,somenumericalresultsarepresentedtoillustratetheeffectivenessoftheproposedalgorithms.