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The COntinuous Reachability Analyzer (CORA) is a collection of MATLAB classes for the formal verification of cyber-physical systems using reachability analysis. CORA integrates various vector and matrix set representations and operations on them as well as reachability algorithms of various dynamic system classes. The software is designed such that set representations can be exchanged without having to modify the code for reachability analysis. CORA is designed using the object oriented paradigm, such that users can safely use methods without concerning themselves with detailed information hidden inside the object. Since the toolbox is written in MATLAB, the installation and use is platform independent. From Release 2018 on, the direct import of SpaceEx models into CORA is also supported.
Cite As
Matthias Althoff (2023). CORA (https://github.com/TUMcps/CORA), GitHub. Retrieved .
Requires
MPT toolbox (see http://people.ee.ethz.ch/~mpt/3/)
MATLAB Release Compatibility
Created with
R2021a
Compatible with R2017b to R2021a
Platform Compatibility
Windows macOS LinuxCategories
- Signal Processing > Signal Processing Toolbox > Digital and Analog Filters > Digital Filter Analysis >
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Acknowledgements
Inspired: AROC
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app
app/auxiliary
contDynamics/@contDynamics
- contDynamics
- derivatives
- display
- isemptyobject
- isequal
- linReach
- observe
- observe_stripBased
- outputSet
- pruneDynamics
- reach
- simulateRandom
- symVariables
contDynamics/@contDynamics/private
- abstrerr_lin
- abstrerr_poly
- checkRequiredFiles
- create3rdOrderTensorFile
- createHessianTensorFile
- createHigherOrderTensorFiles
- createJacobianFile
- createJacobianFile_freeParam
- createParametricDynamicFile
- linError
- linError_higherOrder
- linError_mixed_noInt
- linError_thirdOrder.m
- observe_intersectionMethod_I
- observe_intersectionMethod_II
- precompStatError
- reportReachError
- select
- simulateGaussian
- simulateGaussian_old
- simulateRRT
- simulateStandard
- simulateStandard_old
contDynamics/@linParamSys
- coreReach
- display
- errorSolution
- getfcn
- initReach
- initReach_inputDependence
- linParamSys
- LinParamWrapper_initReach
- post
- postReach
- preReach
- simulate
contDynamics/@linParamSys/private
- apprSquare
- dependentHomSol
- dependentInputSol
- expMap
- highOrderMappingMatrix
- inputSolution
- inputTie
- mappingMatrix
- nonlinMap
- tie
contDynamics/@linProbSys
contDynamics/@linProbSys/private
contDynamics/@linearSys
- coreReach
- deltaReach
- deltaReach_adaptive
- display
- eq
- errorSolution
- errorSolution_adaptive
- exponentialMatrices
- generateRandom
- getfcn
- initReach
- initReach_adaptive
- initReach_Euclidean
- isequal
- linearSys
- linearSysDT
- linError
- ne
- nonlinearSys
- outputSet
- post
- postReach
- post_Euclidean
- preReach
- reach
- reachInner
- simulate
- trajectoryError
- verify
contDynamics/@linearSys/private
- checkSpecification
- constInputSolution
- expmtie_adaptive
- exponential
- exponential_Krylov
- exponential_Krylov_precomputed
- exponential_Krylov_projected
- initReach_Decomp
- initReach_Krylov
- inputInducedUpdates
- inputSolution
- inputSolution_Krylov
- inputTie
- post_Krylov
- post_Krylov_nonProjected
- reach_adaptive
- reach_decomp
- reach_fromStart
- reach_krylov
- reach_standard
- reach_wrappingfree
- subspace_Krylov
- subspace_Krylov_individual
- subspace_Krylov_individual_Wang
- tie
contDynamics/@linearSysDT
contDynamics/@linearSysDT/private
- observe_CZN_A
- observe_CZN_B
- observe_ESO_A
- observe_ESO_B
- observe_ESO_C
- observe_ESO_D
- observe_FRadA
- observe_FRadB
- observe_FRadC
- observe_gain_ESO_C
- observe_gain_ESO_D
- observe_gain_HinfG
- observe_gain_NomG
- observe_gain_PRadA
- observe_gain_PRadB
- observe_gain_PRadC
- observe_gain_PRadD
- observe_gain_PRadE
- observe_HinfG
- observe_intersectionFree
- observe_intersectionFreeAdaptive
- observe_interval
- observe_NomG
- observe_PRadA
- observe_PRadB
- observe_PRadC
- observe_PRadD
- observe_PRadE
- observe_ROPO
- observe_volMinA
- observe_volMinB
contDynamics/@neurNetContrSys
contDynamics/@nonlinDASys
- consistentInitialState
- display
- getfcn
- initReach
- linReach
- linReach_adaptive
- nonlinDASys
- outputSet
- post
- reach_adaptive
- simulate
- steadyState
contDynamics/@nonlinDASys/private
- checkIfHessianConst
- createHessianTensorFile_powSys
- linearize
- linError
- linError_mixed_noInt
- linError_mixed_noInt_comp.m
- linError_thirdOrder
- select
- simulateRRT
- simulateRRT_det
contDynamics/@nonlinParamSys
contDynamics/@nonlinearSys
- createRemainderFile_certainInput
- display
- eq
- getfcn
- initReach
- initReach_adaptive
- isequal
- linearize
- linReach_adaptive
- linReach_adaptive_old
- ne
- nonlinearSys
- post
- reachInner
- reach_adaptive
- simulate
- taylor
contDynamics/@nonlinearSys/private
- abstractionError_adaptive
- allowedError
- errorEval
- precompStatError_adaptive
- reachInnerParallelotope
- reachInnerProjection
- reachInnerScaling
contDynamics/@nonlinearSysDT
contDynamics/@nonlinearSysDT/private
- linearize
- linError_mixed_noInt
- linError_thirdOrder
- observe_FRadA
- observe_FRadB
- observe_FRadC
- observe_intersectionFreeAdaptive
- observe_volMinA
- observe_volMinB
contSet/@affine
contSet/@capsule
- capsule
- center
- conPolyZono
- contains_
- convHull
- dim
- display
- ellipsoid
- enclose
- enclosePoints
- enlarge
- eq
- generateRandom
- interval
- isempty
- isequal
- isFullDim
- isIntersecting_
- isInterval
- isnan
- isZero
- mtimes
- ne
- plot
- plus
- polygon
- polyZonotope
- project
- radius
- randPoint_
- reduce
- supportFunc_
- volume_
- zonotope
contSet/@capsule/private
contSet/@conHyperplane
- and_
- conHyperplane
- contains_
- dim
- display
- distance
- eq
- generateRandom
- isempty
- isequal
- isHyperplane
- isIntersecting_
- isnan
- levelSet
- mptPolytope
- ne
- plot
- projectHighDim
- projectOnHyperplane
- randPoint_
- supportFunc_
contSet/@conHyperplane/private
contSet/@conPolyZono
- and_
- cartProd_
- center
- compact
- conPolyZono
- contains_
- convHull
- conZonotope
- dim
- display
- ellipsoid
- enclose
- eq
- exactPlus
- generateRandom
- getSubset
- interval
- isempty
- isequal
- isFullDim
- isIntersecting_
- linComb
- minkDiff
- mptPolytope
- mtimes
- ne
- or
- plot
- plus
- polygon
- polyZonotope
- project
- quadMap
- randPoint_
- reduce
- reduceConstraints
- rescale
- split
- splitDepFactor
- splitLongestGen
- supportFunc_
- zonotope
contSet/@conPolyZono/private
contSet/@conZonotope
- and_
- cartProd_
- center
- conIntersect
- conPolyZono
- contains_
- convHull
- conZonotope
- cubMap
- deleteZeros
- dim
- display
- enclose
- eq
- generateRandom
- generators
- intersectStrip
- interval
- intervalMultiplication
- isempty
- isequal
- isFullDim
- isIntersecting_
- isInterval
- isZero
- minkDiff
- mptPolytope
- mtimes
- ne
- or
- plot
- plotZono
- plus
- polyZonotope
- project
- quadMap
- randPoint_
- reduce
- reduceConstraints
- rescale
- split
- supportFunc_
- vertices_
- zonoBundle
- zonotope
contSet/@conZonotope/private
contSet/@contSet
- and
- cartProd
- contains
- contSet
- dim
- display
- generateRandom
- in
- isemptyobject
- isIntersecting
- minkDiff
- minus
- norm
- plot
- plotRandPoint
- projVertices
- randPoint
- supportFunc
- times
- uminus
- uplus
- vertices
- volume
contSet/@ellipsoid
- and_
- array
- cartProd_
- center
- conPolyZono
- contains_
- convHull
- dim
- display
- distance
- ellipsoid
- ellipsoidNorm
- enclose
- enclosePoints
- enlarge
- eq
- generateRandom
- intersectStrip
- interval
- isBadDir
- isBigger
- isempty
- isequal
- isFullDim
- isIntersecting_
- isInterval
- isnan
- isZero
- minkDiff
- mtimes
- ne
- norm_
- or
- plot
- plus
- polyZonotope
- project
- radius
- randPoint_
- rank
- reduce
- supportFunc_
- volume_
- zonotope
contSet/@ellipsoid/private
- andEllipsoidIA
- andEllipsoidOA
- andHalfspace
- andHyperplane
- andMptPolytope
- boundary
- compIntersectionParam
- containsEllipsoid
- distanceEllipsoid
- distanceHyperplane
- distanceMptPolytope
- distancePoint
- enc_parallelotope
- enc_zonotope
- insc_parallelotope
- insc_zonotope
- isIntersectingMixed
- lminkDiff
- lplus
- minkDiffEllipsoid
- orEllipsoidOA
- plusEllipsoid
- plusEllipsoidOA
- plusEllipsoidOA_halder
- rootfnc
contSet/@emptySet
- and_
- center
- contains_
- dim
- display
- emptySet
- eq
- generateRandom
- isempty
- isequal
- isFullDim
- isIntersecting_
- mtimes
- ne
- not
- plot
- plus
- project
- projectHighDim
- radius
- randPoint_
- supportFunc_
- volume_
contSet/@fullspace
- and_
- box
- center
- contains_
- dim
- display
- enclosePoints
- eq
- fullspace
- generateRandom
- interval
- isempty
- isequal
- isFullDim
- isIntersecting_
- mtimes
- ne
- not
- plot
- plus
- project
- projectHighDim
- radius
- randPoint_
- supportFunc_
- vertices_
- volume_
contSet/@halfspace
- and_
- commonPoint
- contains_
- dim
- display
- eq
- generateRandom
- halfspace
- isempty
- isequal
- isIntersecting_
- isnan
- mptPolytope
- mtimes
- ne
- plot
- plus
- projectHighDim
- rotate
contSet/@halfspace/private
contSet/@interval
- abs
- acos
- acosh
- and_
- asin
- asinh
- atan
- atanh
- capsule
- cartProd_
- center
- conPolyZono
- contains_
- convHull
- conZonotope
- cos
- cosh
- ctranspose
- diag
- dim
- display
- ellipsoid
- enclosePoints
- enlarge
- eq
- exp
- generateRandom
- gridPoints
- horzcat
- infimum
- interval
- isempty
- isequal
- isFullDim
- isIntersecting_
- isnan
- isscalar
- issparse
- isZero
- kron
- le
- length
- log
- lt
- minkDiff
- minus
- mpower
- mptPolytope
- mrdivide
- mtimes
- ne
- norm_
- or
- partition
- plot
- plus
- polyZonotope
- power
- prod
- project
- quadMap
- rad
- radius
- randPoint_
- rdivide
- reduce
- reshape
- sin
- sinh
- size
- split
- sqrt
- string
- subsasgn
- subsref
- sum
- supportFunc_
- supremum
- tan
- tanh
- times
- transpose
- tril
- triu
- uminus
- uplus
- vertcat
- vertices_
- volume_
- zonoBundle
- zonotope
contSet/@interval/private
contSet/@levelSet
- and_
- compact
- contains_
- dim
- display
- eq
- eventFcn
- generateRandom
- isequal
- isIntersecting_
- levelSet
- ne
- not
- plot
- projectHighDim
- tightenDomain
contSet/@mptPolytope
- and_
- cartProd_
- center
- conPolyZono
- contains_
- convHull
- conZonotope
- dim
- display
- distance
- ellipsoid
- enclose
- enclosePoints
- eq
- eventFcn
- generateRandom
- get
- halfspace
- hausdorffDist
- interval
- isConHyperplane
- isempty
- isFullDim
- isIntersecting_
- isInterval
- isZero
- le
- levelSet
- minkDiff
- mldivide
- mptPolytope
- mtimes
- ne
- normalizeConstraints
- normalizedRep
- not
- or
- plot
- plus
- polyZonotope
- project
- projectHighDim
- randPoint_
- removedHalfspaces
- removeRedundancies
- supportFunc_
- vertices_
- volume_
- zonoBundle
contSet/@polyZonotope
- addedTermsHessian
- approxVolumeRatio
- cartProd_
- center
- compact
- conPolyZono
- containsPointSet
- contains_
- convHull
- cubMap
- deleteZeros
- dim
- display
- ellipsoid
- enclose
- eq
- exactPlus
- fhandle
- generateRandom
- getSubset
- hausdorffDist
- hessianHandle
- innerApprox
- interval
- isempty
- isequal
- isFullDim
- isIntersecting_
- isInterval
- isPolytope
- isZero
- isZonotope
- jacobian
- jacobianHandle
- linComb
- mptPolytope
- mtimes
- ne
- noIndep
- onlyId
- outerApprox
- partZonotope
- plot
- plus
- polygon
- polyZonotope
- project
- quadMap
- randPoint_
- reduce
- replaceId
- resolve
- restoreId
- restructure
- rmId
- split
- splitDepFactor
- splitLongestGen
- stack
- subs
- sum
- supportFunc_
- taylm
- zonotope
contSet/@polyZonotope/private
- checkDiffParamIds
- multiply
- reduceAdaptive
- removeZeroExponents
- restructureReduce
- restructureReduceDI
- restructureReduceFull
- restructureReducePart
- restructureZono
contSet/@probZonotope
- abs
- center
- dim
- display
- enclose
- enclosingPolytope
- enclosingProbability
- generateRandom
- generators
- interval
- max
- mean
- mtimes
- plot
- plus
- probReduce
- probZonotope
- project
- pyramid
- randPoint_
- reduce
- sigma
- singleGenPlot
- sup
- vertices_
- zonotope
contSet/@probZonotope/private
contSet/@taylm
- acos
- asin
- atan
- conPolyZono
- cos
- cosh
- det
- dim
- display
- exp
- generateRandom
- getCoef
- getRem
- getSyms
- interval
- log
- minus
- mpower
- mrdivide
- mtimes
- optBernstein
- optBnb
- optBnbAdv
- optLinQuad
- plus
- polyZonotope
- power
- prod
- rdivide
- reexpand
- set
- setName
- sin
- sinh
- sqrt
- subsasgn
- subsref
- sum
- supportFunc_
- tan
- tanh
- taylm
- times
- trace
- uminus
- uplus
contSet/@taylm/private
contSet/@zonoBundle
- and_
- cartProd_
- center
- conPolyZono
- contains_
- convHull
- conZonotope
- dim
- display
- enclose
- encloseTight
- enlarge
- eq
- generateRandom
- interval
- isempty
- isequal
- isFullDim
- isIntersecting_
- isInterval
- isZero
- mptPolytope
- mtimes
- ne
- or
- plot
- plus
- polyZonotope
- project
- quadMap
- randPoint_
- reduce
- reduceCombined
- replace
- shrink
- split
- supportFunc_
- vertices_
- volume_
- zonoBundle
- zonotope
contSet/@zonoBundle/private
contSet/@zonotope
- abs
- and_
- box
- capsule
- cartProd_
- center
- conPolyZono
- constrSat
- contains_
- convHull
- conZonotope
- cubMap
- deleteAligned
- deleteZeros
- dH2box
- dim
- display
- dominantDirections
- ellipsoid
- enclose
- encloseMany
- enclosePoints
- enlarge
- eq
- exactPlus
- filterOut
- generateRandom
- generatorLength
- generators
- halfspace
- intersectStrip
- interval
- intervalMultiplication
- isempty
- isequal
- isFullDim
- isIntersecting_
- isInterval
- isParallelotope
- isZero
- minkDiff
- minnorm
- mptPolytope
- mtimes
- ne
- norm_
- or
- orthVectors
- plot
- plus
- polygon
- polyZonotope
- project
- projectHighDim
- quadMap
- quadMap_parallel
- radius
- randPoint_
- rank
- reduce
- reduceUnderApprox
- rotate
- sampleBox
- simplex
- split
- splitFirstGen
- splitLongestGen
- supportFunc_
- taylm
- tensorMultiplication
- tensorMultiplication_zono
- underapproximate
- vertices_
- volumeRatio
- volume_
- zonoBundle
- zonotope
- zonotopeNorm
contSet/@zonotope/private
- andAveraging
- enc_ellipsoid
- evaluateRotations
- generatorVolumeFilter
- insc_ellipsoid
- kmeansFilter
- lengthFilter
- MVEE
- MVIE
- norm_exact
- norm_ub
- reduceAdaptive
- reduceCluster
- reduceCombastel
- reduceConstOpt
- reduceGirard
- reduceIdx
- reduceMethA
- reduceMethB
- reduceMethC
- reduceMethE
- reduceMethF
- reducePCA
- reduceRedistribute
- reduceScott
- reduceValero
- reorderingFilter
- volumeFilter
contSet/@zoo
contSet/@zoo/private
converter/commonroad2cora
converter/cora2spaceex
converter/cora2spaceex/private
- assignment_cora2spaceex
- conHyperplane_cora2spaceex
- flow_cora2spaceex
- guard_cora2spaceex
- headline_cora2spaceex
- hybrid_cora2spaceex
- invariant_cora2spaceex
- levelSet_cora2spaceex
- location_cora2spaceex
- mptPolytope_cora2spaceex
- parameter_cora2spaceex
- transition_cora2spaceex
converter/neuralnetwork2cora
converter/powerSystem2cora
converter/powerSystem2cora/private
- createFileFromFunction
- generateConstraintEquations
- generateDynamicEquations
- reorderBuses
- symPowerVariables
converter/spaceex2cora
converter/spaceex2cora/phase1
converter/spaceex2cora/phase1/auxiliary
converter/spaceex2cora/phase1/step1
converter/spaceex2cora/phase1/step2
- AssignTemplate
- CollectVariables
- ComputeBaseComponent
- ComputeNetworkComponent
- parseCondition
- ParseTemplates
converter/spaceex2cora/phase1/step3
- applyMappingToCondition
- applyMappingToEquation
- applyRenames
- InstantiateBC
- InstantiateComponents
- InstantiateNC
- resolveBinds
converter/spaceex2cora/phase1/step4
converter/spaceex2cora/phase1/step5
- applySymMapping
- classifyVariablesFlat
- classifyVariablesParallel
- eq2linSys.m
- eq2linSysFlat.m
- eq2set
- FormalizeBaseComponent
- outputMatrices.m
- outputMatricesComp2Comp
converter/spaceex2cora/phase2
converter/spaceex2cora/phase3
converter/spaceex2cora/phase3/auxiliary
discrDynamics/@markovchain
- build
- build4road
- build4road_reach
- build_reach
- convertTransitionMatrix
- get
- markovchain
- plot
- plotP
- plot_reach
- set
- stretch
discrDynamics/@markovchain/private
discrDynamics/@partition
- cellCenter
- cellIndices
- cellIntervals
- cellPolytopes
- cellSegments
- cellZonotopes
- display
- exactIntersectingSegments
- intersectingCells
- nrOfCells
- partition
- plot
discrDynamics/ProbOccupancyPrediction
- calculateCrashProbability
- Car
- carReach
- carReach_reach
- getPolytopeForSegment
- getSegmentsForManeuver
- getSegmentsForPath
- initBicycle
- initCar
- plotHisto
- plotHistobars
- plotPositionDistribution
- segmentCenter
- segmentData
- start_carReach
- start_carReach_reach
- vehicleBodyDistribution
discrDynamics/ProbOccupancyPrediction/@road
- createPath
- deviationProbability
- display
- intersection
- intersectionAlexander
- intersection_database
- plot
- plot3Lanes
- plotCrossing
- plotPath
- plotVehSeg
- road
- segCenter
- segData
- segPolytope
discrDynamics/ProbOccupancyPrediction/@simulation
discrDynamics/ProbOccupancyPrediction/@simulation/private
- autonomousDriving
- autonomousDrivingOptimized
- autonomousDrivingOptimizedPosOnly
- avgVelocityOnPath
- combine
- combineOptimized
- driving
- drivingOptimized
- drivingOptimized
- drivingOptimized_noInteraction
- freeDriving
- freeDrivingOptimized
- gammaMatrix
- gammaMatrix
- generalProject
- inputDist
- inputDistOptimized
- laneChangeEvolution
- laneChangeProbability
- laneChangeProbabilityOptimized
- laneChanging
- laneChangingOptimized
- motivation
- motivationOptimized
- normalize
- potChange
- project
- reachableSet
- roadCrossing
- roadCrossingOptimized
- simulateCar
- singleStepDriving
- singleStepDrivingOptimized
- speedRestriction
- speedRestrictionOptimized
- vehicleFollowing
- vehicleFollowingOptimized
discrDynamics/ProbOccupancyPrediction/interaction
discrDynamics/ProbOccupancyPrediction/intersection
discrDynamics/ProbOccupancyPrediction/scenarios
- braking
- intersectionCrossing
- knownBehavior
- laneChange
- merging
- motivationPlot
- overtaking
- straightVScurved
- xIntegration