sponsored by: bosch, ford, and toyota compression...
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CompressionAlgorithmsforEnablingHigh-DimensionalMotionPlanning
ABSTRACT:Autonomoussystemsthatoperateinrealtimeposeuniquechallengesforreliable,accurate,andoptimaluncertaintyquantificationandcontrol.Manyalgorithmswithstrongoptimalityguaranteesencounterthecurse-of-dimensionality;theircomputationalexpensegrowsexponentiallywiththesizeofthestatespace.Inthistalk,wedescribenewdevelopmentsinlow-rankmultilinearalgebrathatenablefoundationalalgorithmswithinautonomyforhigh-dimensionalsystems.WedemonstratehowcompressiontechniquesbasedonacontinuousextensionoftensordecompositionscanbeusedtosolveMarkovdecisionsprocesses(MDPs)thatariseinsystemsdescribedbystochasticdifferentialequations.Theresultingdynamicprogrammingalgorithmsscalepolynomiallywithdimensionwithguaranteedconvergence.Applicationstostochasticoptimalcontrol,differentialgames,andlineartemporallogicarediscussed.Experimentalresultsareshownforanagilequadcoptersystem,whereweachieve7ordersofmagnitudecompressionofadiscretizedspacewith$10^12$states.Finally,newresearchdirectionsaimedtowardsembeddingsuchschemesforonlinelearningaredescribed.
BIO:AlexGorodetskyisanAssistantProfessorinAerospaceEngineeringattheUniversityofMichigan.Hisresearchinterestsincludeusingappliedmathematicsandcomputationalsciencetoenableautonomousdecisionmakingunderuncertainty.Heisespeciallyinterestedincontrollingsystemsthatmustactincomplexenvironmentsthatcanbesimulatedusingalargeamountofcomputationalresources.Towardthisgoal,hepursuesresearchinwide-rangingareasincludinguncertaintyquantification,statisticalinferenceandmachinelearning,numericalanalysis,functionapproximation,control,andoptimization.PriortoreturningtotheUniversityofMichigan,AlexwastheJohnvonNeumannPostdoctoralResearchFellowatSandiaNationalLaboratoriesinAlbuquerque,NewMexico.AtSandia,AlexworkedintheOptimizationandUncertaintyQuantificationGrouponalgorithmsforpropagatinguncertaintythroughcomplexphysicalsystems.AlexcompletedhisPh.D.(2016)andS.M.(2012)intheDepartmentofAeronauticsandAstronauticsattheMassachusettsInstituteofTechnology,whereheworkedonalgorithmsforstochasticoptimalcontrolandestimationindynamicalsystems.HereceivedhisB.S.E(2010)inAerospaceEngineeringfromtheUniversityofMichigan.
AlexGorodetskyUniversityofMichigan
DepartmentofAerospaceEngineering
Friday,January19,2018
3:30–4:30pm•1500EECS
Sponsoredby:Bosch,Ford,andToyota