├── Figures ├── desktop.ini ├── paper │ ├── cost 20pt.eps │ ├── cost.eps │ ├── cost_more_noise.eps │ ├── upred_uref.eps │ ├── upred_uref_more_noise.eps │ ├── y1y2.eps │ ├── y1y2_more_noise.eps │ ├── y1y2_overN.eps │ ├── y1y2y3.eps │ ├── y1y2y3_more_noise.eps │ ├── y2_not_robust.eps │ ├── y2_robust.eps │ ├── y2_robust_more_noise.eps │ ├── y3y4.eps │ ├── y3y4_more_noise.eps │ ├── y3y4_overN.eps │ ├── y3y4y5.eps │ ├── y3y4y5_more_noise.eps │ ├── y4y5.eps │ ├── y4y5_more_noise.eps │ ├── y4y5_overN.eps │ ├── ys_ypreds.eps │ ├── ys_ypreds_more_noise.eps │ ├── yt2red 20pt.eps │ ├── yt2red.eps │ └── yt2red_more_noise.eps └── reachmpc.png ├── NZPC.m ├── README.md ├── Robust_MPC_polytopes.m ├── ZPC.m ├── contDynamics ├── @contDynamics │ ├── checkOptionsSimulate.m │ ├── contDynamics.m │ ├── copyOptions.m │ ├── derivatives.m │ ├── dimension.m │ ├── display.m │ ├── linReach.m │ ├── private │ │ ├── abstrerr_lin.m │ │ ├── abstrerr_poly.m │ │ ├── create3rdOrderTensorFile.m │ │ ├── createHessianTensorFile.m │ │ ├── createHigherOrderTensorFiles.m │ │ ├── createJacobianFile.m │ │ ├── createJacobianFile_freeParam.m │ │ ├── createParametricDynamicFile.m │ │ ├── linError.m │ │ ├── linError_higherOrder.m │ │ ├── linError_mixed_noInt.m │ │ ├── linError_thirdOrder.m │ │ ├── precompStatError.m │ │ ├── reportReachError.m │ │ └── select.m │ ├── pruneDynamics.m │ ├── reach.m │ ├── simulateRRT.m │ ├── simulateRandom.m │ └── symVariables.m ├── @linParamSys │ ├── LinParamWrapper_initReach.m │ ├── checkOptionsReach.m │ ├── coreReach.m │ ├── display.m │ ├── errorSolution.m │ ├── getfcn.m │ ├── initReach.m │ ├── initReach_inputDependence.m │ ├── linParamSys.m │ ├── post.m │ ├── postReach.m │ ├── preReach.m │ ├── private │ │ ├── apprSquare.m │ │ ├── dependentHomSol.m │ │ ├── dependentInputSol.m │ │ ├── expMap.m │ │ ├── highOrderMappingMatrix.m │ │ ├── inputSolution.m │ │ ├── inputTie.m │ │ ├── mappingMatrix.m │ │ ├── nonlinMap.m │ │ └── tie.m │ └── simulate.m ├── @linProbSys │ ├── checkOptionsReach.m │ ├── display.m │ ├── getfcn.m │ ├── initReach.m │ ├── linProbSys.m │ ├── plot.m │ ├── post.m │ ├── private │ │ ├── exactTerms.m │ │ ├── infNorm.m │ │ ├── inputSolution.m │ │ ├── pexpm.m │ │ ├── sample.m │ │ └── tie.m │ ├── reachAlternative.m │ └── simulate.m ├── @linearSys │ ├── checkOptionsReach.m │ ├── coreReach.m │ ├── deltaReach.m │ ├── display.m │ ├── errorSolution.m │ ├── exponentialMatrices.m │ ├── getfcn.m │ ├── initReach.m │ ├── initReach_Euclidean.m │ ├── linError.m │ ├── linearSys.m │ ├── post.m │ ├── postReach.m │ ├── post_Euclidean.m │ ├── preReach.m │ ├── private │ │ ├── constInputSolution.m │ │ ├── exponential.m │ │ ├── exponential_Krylov.m │ │ ├── exponential_Krylov_precomputed.m │ │ ├── exponential_Krylov_projected.m │ │ ├── initOutputEquation.m │ │ ├── initReach_Decomp.m │ │ ├── initReach_Krylov.m │ │ ├── initReach_Krylov_nonProjected.m │ │ ├── inputInducedUpdates.m │ │ ├── inputSolution.m │ │ ├── inputSolution_Krylov.m │ │ ├── inputTie.m │ │ ├── outputSet.m │ │ ├── post_Krylov.m │ │ ├── post_Krylov_nonProjected.m │ │ ├── rA_initReach.m │ │ ├── rA_initTimeStepTaylorTerms.m │ │ ├── rA_inputTie.m │ │ ├── rA_post.m │ │ ├── rA_postTSTT_bloatings.m │ │ ├── rA_postTSTT_checkTimeStep.m │ │ ├── rA_postTSTT_savedSets.m │ │ ├── rA_postTimeStepTaylorTerms.m │ │ ├── rA_propInhom.m │ │ ├── reach_adaptive.m │ │ ├── reach_decomp.m │ │ ├── reach_fromStart.m │ │ ├── reach_krylov.m │ │ ├── reach_standard.m │ │ ├── reach_wrappingfree.m │ │ ├── subspace_Krylov.m │ │ ├── subspace_Krylov_individual.m │ │ ├── subspace_Krylov_individual_Wang.m │ │ └── tie.m │ ├── reach.m │ ├── reach_fromStart_tVec.m │ ├── simulate.m │ └── trajectoryError.m ├── @linearSysDT │ ├── checkOptionsObserve.m │ ├── checkOptionsReach.m │ ├── display.m │ ├── initOutputEquation.m │ ├── linearSysDT.m │ ├── observe.m │ ├── post.m │ ├── private │ │ ├── arnoldi.m │ │ ├── constInputSolution.m │ │ ├── determineKrylovOrder.m │ │ ├── exponential.m │ │ ├── exponential_Krylov.m │ │ ├── exponential_Krylov_precomputed.m │ │ ├── exponential_Krylov_projected.m │ │ ├── inputSolution.m │ │ ├── inputSolution_Krylov.m │ │ ├── inputTie.m │ │ ├── observe │ │ │ ├── SMA_SISO_Zonotope.m │ │ │ └── observe_setMembership.m │ │ ├── outputSet.m │ │ ├── subspace_Krylov.m │ │ ├── subspace_Krylov_individual.m │ │ ├── subspace_Krylov_individual_Wang.m │ │ └── tie.m │ ├── reach.m │ └── simulate.m ├── @nonlinDASys │ ├── checkOptionsReach.m │ ├── consistentInitialState.m │ ├── display.m │ ├── getfcn.m │ ├── initReach.m │ ├── linReach.m │ ├── nonlinDASys.m │ ├── post.m │ ├── private │ │ ├── createHessianTensorFile_powSys.m │ │ ├── linError.m │ │ ├── linError_mixed_noInt.m │ │ ├── linError_thirdOrder.m │ │ └── linearize.m │ ├── simulate.m │ ├── simulateRRT.m │ └── simulateRRT_det.m ├── @nonlinParamSys │ ├── checkOptionsReach.m │ ├── display.m │ ├── getfcn.m │ ├── initReach.m │ ├── linearize.m │ ├── nonlinParamSys.m │ ├── post.m │ ├── private │ │ └── symbolicDerivation.m │ └── simulate.m ├── @nonlinearSys │ ├── checkOptionsReach.m │ ├── createRemainderFile_certainInput.m │ ├── display.m │ ├── getfcn.m │ ├── initReach.m │ ├── linearize.m │ ├── nonlinearSys.m │ ├── post.m │ ├── private │ │ ├── allowedError.m │ │ ├── createTaylorFile.m │ │ └── errorEval.m │ ├── reachInner.m │ ├── simulate.m │ └── taylor.m └── @nonlinearSysDT │ ├── checkOptionsReach.m │ ├── display.m │ ├── linReach.m │ ├── nonlinearSysDT.m │ ├── private │ ├── linError_mixed_noInt.m │ ├── linError_thirdOrder.m │ └── linearize.m │ ├── reach.m │ └── simulate.m ├── contSet ├── @conZonotope │ ├── and.m │ ├── boundDir.m │ ├── cartesianProduct.m │ ├── center.m │ ├── conZonotope.m │ ├── display.m │ ├── enclose.m │ ├── interval.m │ ├── intervalMultiplication.m │ ├── isempty.m │ ├── mixedMultiplication.m │ ├── mptPolytope.m │ ├── mtimes.m │ ├── plot.m │ ├── plotFilled.m │ ├── plotFilledSplit.m │ ├── plotFilledTemplate.m │ ├── plotTemplate.m │ ├── plotZono.m │ ├── plus.m │ ├── private │ │ ├── ksi_iterative.m │ │ ├── ksi_optimizer.m │ │ ├── potVertices.m │ │ └── removeZeroConstraints.m │ ├── project.m │ ├── quadraticMultiplication.m │ ├── reduce.m │ ├── rescale.m │ ├── split.m │ ├── vertices.m │ └── zonotope.m ├── @contSet │ ├── contSet.m │ └── display.m ├── @generalSet │ ├── display.m │ ├── generalSet.m │ └── parallelotope.m ├── @halfspace │ ├── commonPoint.m │ ├── display.m │ ├── eventFcn.m │ ├── get.m │ ├── halfspace.m │ ├── in.m │ ├── intersectionTime_oneDirection.m │ ├── isIntersecting.m │ ├── isIntersectingApprox.m │ ├── maps.m │ ├── mapsCubic.m │ ├── mapsQuad.m │ ├── mapsQuad_06Sep2013.m │ ├── mapsQuad_old.m │ ├── mapsQuad_test06Sep2013.m │ ├── mapsQuad_unc.m │ ├── mtimes.m │ ├── partialGuardProjection.m │ ├── plot.m │ ├── plus.m │ ├── polytope.m │ ├── private │ │ └── rotationMatrix.m │ ├── project.m │ ├── projectHighDim.m │ ├── rotate.m │ ├── zonoIn.m │ ├── zonoIntersect.m │ └── zonoPartiallyIn.m ├── @interval │ ├── abs.m │ ├── acos.m │ ├── acosh.m │ ├── and.m │ ├── asin.m │ ├── asinh.m │ ├── atan.m │ ├── atanh.m │ ├── cos.m │ ├── cosh.m │ ├── ctranspose.m │ ├── diag.m │ ├── display.m │ ├── enclosingRadius.m │ ├── enlarge.m │ ├── eq.m │ ├── eventFcn.m │ ├── exp.m │ ├── get.m │ ├── gridPoints.m │ ├── horzcat.m │ ├── hull.m │ ├── in.m │ ├── infimum.m │ ├── interval.m │ ├── isIntersecting.m │ ├── isIntersectingApprox.m │ ├── isempty.m │ ├── isscalar.m │ ├── le.m │ ├── length.m │ ├── log.m │ ├── lt.m │ ├── mid.m │ ├── minus.m │ ├── mpower.m │ ├── mrdivide.m │ ├── mtimes.m │ ├── ne.m │ ├── plot.m │ ├── plotFilled.m │ ├── plus.m │ ├── polytope.m │ ├── power.m │ ├── prod.m │ ├── projectHighDim.m │ ├── rad.m │ ├── rdivide.m │ ├── reshape.m │ ├── sin.m │ ├── sinh.m │ ├── size.m │ ├── sqrt.m │ ├── subsasgn.m │ ├── subsref.m │ ├── sum.m │ ├── supremum.m │ ├── tan.m │ ├── tanh.m │ ├── times.m │ ├── transpose.m │ ├── uminus.m │ ├── uplus.m │ ├── vertcat.m │ ├── vertices.m │ ├── volume.m │ └── zonotope.m ├── @vertices │ ├── collect.m │ ├── dirPolytope.m │ ├── dirPolytope2.m │ ├── dirPolytopeBoth.m │ ├── dirPolytopeNew.m │ ├── display.m │ ├── enclosingZonotope3.m │ ├── enclosingZonotope4.m │ ├── get.m │ ├── interval.m │ ├── isempty.m │ ├── mtimes.m │ ├── parallelotope.m │ ├── plot.m │ ├── plot3d.m │ ├── plotFilled.m │ ├── plus.m │ ├── polygon.m │ ├── rotate.m │ ├── subsref.m │ ├── vertices.m │ └── zonotope.m ├── @zonotope │ ├── abs.m │ ├── and.m │ ├── appVolume.m │ ├── box.m │ ├── cartesianProduct.m │ ├── center.m │ ├── conZonotope.m │ ├── constrSat.m │ ├── containsPoint.m │ ├── cubicMultiplication.m │ ├── cubicMultiplication_interval.m │ ├── cubicMultiplication_old.m │ ├── cubicMultiplication_simple.m │ ├── deleteAligned.m │ ├── deleteZeros.m │ ├── dim.m │ ├── dirPolytopeNew.m │ ├── display.m │ ├── dominantDirections.m │ ├── enclose.m │ ├── encloseMany.m │ ├── enclosingPolytope.m │ ├── enclosingZonotope.m │ ├── enlarge.m │ ├── eventFcn.m │ ├── exactPlus.m │ ├── filterOut.m │ ├── generatorLength.m │ ├── generators.m │ ├── get.m │ ├── guardProjection.m │ ├── guardProjection_09Sep2013.m │ ├── guardProjection_constFlow.m │ ├── halfspace.m │ ├── in.m │ ├── inORH.m │ ├── inParallelotope.m │ ├── inViaProj.m │ ├── intersection.m │ ├── interval.m │ ├── intervalMultiplication.m │ ├── isIntersecting.m │ ├── isIntersectingApprox.m │ ├── isempty.m │ ├── minus.m │ ├── mixedCubicMultiplication.m │ ├── mixedMultiplication.m │ ├── mptPolytope.m │ ├── mtimes.m │ ├── multiPolytope.m │ ├── norm.m │ ├── or.m │ ├── orthVectors.m │ ├── partialGuardProjection.m │ ├── partialGuardProjection_forward.m │ ├── plot.m │ ├── plotAsText.m │ ├── plotFilled.m │ ├── plus.m │ ├── polygon.m │ ├── polytope.m │ ├── private │ │ ├── andAveraging.m │ │ ├── evaluateRotations.m │ │ ├── generatorVolumeFilter.m │ │ ├── kmeansFilter.m │ │ ├── lengthFilter.m │ │ ├── ndimCross.m │ │ ├── nonzeroFilter.m │ │ ├── pickedGenerators.m │ │ ├── reduceCluster.m │ │ ├── reduceCombastel.m │ │ ├── reduceConstOpt.m │ │ ├── reduceGirard.m │ │ ├── reduceMethA.m │ │ ├── reduceMethB.m │ │ ├── reduceMethC.m │ │ ├── reduceMethE.m │ │ ├── reduceMethF.m │ │ ├── reducePCA.m │ │ ├── reduceRedistribute.m │ │ ├── reduceScott.m │ │ ├── reorderingFilter.m │ │ └── volumeFilter.m │ ├── project.m │ ├── quadZonotope.m │ ├── quadraticMultiplication.m │ ├── quadraticMultiplication_interval.m │ ├── quadraticMultiplication_parallel.m │ ├── quadraticMultiplication_zono.m │ ├── quadraticProgramming_interval.m │ ├── radius.m │ ├── randPoint.m │ ├── randPointExtreme.m │ ├── reduce.m │ ├── reduceUnderApprox.m │ ├── rotate.m │ ├── set.m │ ├── split.m │ ├── splitFirstGen.m │ ├── tensorMultiplication.m │ ├── tensorMultiplication_zono.m │ ├── underapproximate.m │ ├── unify.m │ ├── vertices.m │ ├── volume.m │ ├── volumeRatio.m │ └── zonotope.m ├── gramSchmidt.m ├── plotPolytope3D.m ├── randProbZonotope.m └── readPlotOptions.m ├── matrixSet ├── @intervalMatrix │ ├── abs.m │ ├── changeLog_intervalMatrix.txt │ ├── dependentTerms.m │ ├── display.m │ ├── dominantVertices.m │ ├── exactSquare.m │ ├── expm.m │ ├── expmAbsoluteBound.m │ ├── expmInd.m │ ├── expmIndMixed.m │ ├── expmMixed.m │ ├── expmNormInf.m │ ├── expmVertex.m │ ├── exponentialRemainder.m │ ├── interval.m │ ├── intervalMatrix.m │ ├── matPolytope.m │ ├── matZonotope.m │ ├── mpower.m │ ├── mtimes.m │ ├── norm.m │ ├── plot.m │ ├── plus.m │ ├── powers.m │ ├── randomIntervalMatrix.m │ ├── randomSampling.m │ ├── subsref.m │ ├── vertices.m │ └── volume.m ├── @matZonotope │ ├── changeLog_matZonotope.txt │ ├── concatenate.m │ ├── dependentTerms.m │ ├── display.m │ ├── dominantVertices.m │ ├── expmInd.m │ ├── expmIndMixed.m │ ├── expmMixed.m │ ├── expmOneParam.m │ ├── expmVertex.m │ ├── get.m │ ├── intervalMatrix.m │ ├── matPolytope.m │ ├── matZonotope.m │ ├── mpower.m │ ├── mtimes.m │ ├── norm.m │ ├── plot.m │ ├── plus.m │ ├── powers.m │ ├── randomSampling.m │ ├── reduce.m │ ├── set.m │ ├── subsref.m │ ├── vertices.m │ ├── volume.m │ └── zonotope.m ├── changeLog_matrixSet.txt ├── mat2vec.m ├── randomDelta.m └── vec2mat.m ├── models 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