length
PURPOSE 
LENGTH Returns number of elements in a polytope array
SYNOPSIS
function len = length(P)
DESCRIPTION
CROSS-REFERENCE INFORMATION
This function calls:
- length LENGTH Returns number of regions over which the explicit control law is defined
- end END Returns the last element in a given polytope array
- isfulldim ISFULLDIM Checks if a polytope is full dimensional
- length LENGTH Returns number of elements in a polytope array
This function is called by:
- char CHAR Provides textual description of a given controller
- info INFO Displays more detailed information a given MPT controller
- length LENGTH Returns number of regions over which the explicit control law is defined
- modify MODIFY Modifies an MPTCTRL object
- mptctrl MPTCTRL Constructor for the MPT controller object
- addMLDconstraints ADDMLDCONSTRAINTS Adds state and output constraints to MLD matrices
- copyvalidfields COPYVALIDFIELDS copies only fields listed in 'allowedfields' from ctrlStruct to ctrl
- subsref SUBSREF Indexed referencing for MPTCTRL object
- and AND Intersection of n polytopes
- bounding_box BOUNDING_BOX Compute a bounding box for a given polytope
- chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
- dimension DIMENSION Returns dimension of the given polytope
- display DISPLAY Displays details about the given polytope
- distance DISTANCE Distance between two sets
- dointersect DOINTERSECT Checks if two polytopes / polyarrays intersect
- domain DOMAIN Computes polytope that is mapped to an another polytope using affine map
- double DOUBLE Function used to access internal properties of the given polytope
- end END Returns the last element in a given polytope array
- envelope ENVELOPE Computes envelope of n polytopes
- eq EQ Checks if two polytopes are equal
- extreme EXTREME Calculates extreme points of a given polytope
- facetcircle FACETCIRCLE Returns largest circle inside facet 'ind' of polytope P
- facetvoronoi FACETVORONOI Computes an equivalent of voronoi diagrams for facets
- fliplr FLIPLR Flips array of polytopes
- getInnerEllipsoid GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
- horzcat HORZCAT Concatenates polytopes into a polytope array
- hull HULL Convex hull of n polytopes
- intersect INTERSECT Intersection of 2 polytopes or polytope arrays
- isbounded ISBOUNDED Checks if a polytope is bounded
- isfulldim ISFULLDIM Checks if a polytope is full dimensional
- isinside ISINSIDE Checks if a given point lies in the interior of a given polytope
- isminrep ISMINREP Checks if a given polytope is in minimal representation
- isnormal ISNORMAL Checks if a given polytope is in normalized description
- isredundant ISREDUNDANT Check if a constraint is redundant
- le LE Checks if polytope P is a subset of polytope Q
- length LENGTH Returns number of elements in a polytope array
- lt LT Checks if polytope P is a strict subset of polytope Q
- merge MERGE merges polytopes together
- minus MINUS Pontryagin difference
- mldivide MLDIVIDE Set difference
- mtimes MTIMES Polytope multiplication
- nconstr NCONSTR Returns number of constraints that form an H-representation of a polytope
- normalize NORMALIZE Normalizes a given polytope
- pelemfun PELEMFUN Execute the specified function on each element of a polytope array
- plot PLOT Plots polytopes in 2D or 3D
- plus PLUS Minkowski sum of two polytopes
- polytope POLYTOPE Default constructor for the POLYTOPE object
- chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
- uniquerows2 UNIQUEROWS1 Fast method to obtain indices of unique rows of a given matrix
- projection PROJECTION Projection of a polytope or a polytope array
- range RANGE Affine transformation of a polytope
- reduce REDUCE Reduces the polytope by removing redundant inequalities
- reduceunion REDUCEUNION Removes redundant elements from a polytope array
- regiondiff REGIONDIFF Region difference
- regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space
- size SIZE Returns size of the given polytope object
- slice SLICE cuts a polytope (polytope array) at prespecified values
- subsasgn SUBSASGN Indexed assignments for polytope objects
- subsref SUBSREF Indexed referencing for polytope objects
- triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
- uminus UMINUS Unary minus for a polytope
- union UNION convex union computation
- unique UNIQUE Removes redundant entries from a polytope array
- uplus UPLUS Unary plus for a polytope
- vertcat VERTCAT Concatenates polytopes into a polytope array
- volume VOLUME Calculates volume of a polytope
- mpt_demo3 MPT_DEMO3 Explains control routines for LTI systems
- ownmpc10
- ownmpc4
- ownmpc7
- ownmpc8
- reachdemo2 reachability computation demo
- mpt_buildAdjacency MPT_BUILDADJACENCY Builds adjacency information
- mpt_checkLyapFct MPT_CHECKLYAPFCT Checks if a function is a Lyapunov function for a given ctrlStruct
- mpt_computePWATset MPT_COMPUTEPWATSET Computes a stabilizing control invariant set (+ controllers) around the origin
- mpt_dlyap_infnorm Lyapunov equation with inf-norm for discrete-time LTI systems
- mpt_getCommonSOSLyapFct MPT_GETCOMMONSOSLYAPFCT Calculates Common SOS Lyapunov function for system with additive disturbance
- mpt_getPWALyapFct MPT_GETPWALYAPFCT Calculates PWA Lyapunov function
- mpt_getPWPLyapFct MPT_GETPWPLYAPFCT Calculates Piecewise Polynomial (sum of squares) Lyapunov function
- mpt_getPWQLyapFct MPT_GETPWQLYAPFCT Calculates PWQ Lyapunov function
- mpt_getQuadLyapFct MPT_GETQUADLYAPFCT Computes common Lyapunov function for PWA system
- mpt_getReachSubset MPT_GETREACHSUBSET Computes a subset of P which enters Pfin
- mpt_infset MPT_INFSET Calculates the maximal positively invariant set for an LTI system
- mpt_infsetPWA MPT_INFSETPWA Computes (robust) positive invariant subset for PWA systems
- mpt_isPWAbigger MPT_ISPWABIGGER Test if one PWA function is bigger than a second PWA function
- mpt_maxCtrlSet MPT_MAXCTRLSET Computes the maximal robust control invariant set C_inf
- mpt_reachSets MPT_REACHSETS Computes sets of reachable states for a given system / controller
- mpt_removeOverlaps MPT_REMOVEOVERLAPS Removes overlaps from (a set of) polyhedral partitions with associated linear cost
- mpt_searchTree MPT_SEARCHTREE Computes a search-tree for a given explicit solution
- mpt_transmap MPT_TRANSMAP Computes transition map
- mpt_verify MPT_VERIFY Verifies if states enter a given set in a given number of steps
- display DISPLAY Display information about a HASHTABLE object
- subsasgn SUBSREF Subreferencing operator for HASHTABLE objects
- subsref SUBSREF Subreferencing operator for HASHTABLE objects
- identifyRegion IDENTIFYREGION plots the number of the polytopes into the current figure
- mpt_allcombs MPT_ALLCOMBS All combinations of discrete-valued inputs
- mpt_defaultOptions MPT_DEFAULTOPTIONS Sets default values of undefined fields of Options structure
- mpt_dummyCS MPT_DUMMYCS Returns a dummy controller structure
- mpt_evalPWA MPT_EVALPWA Evaluates a PWA function at a given location
- mpt_feasibleStates MPT_FEASIBLESTATES returns equidistantly spaced data points in feasible set
- mpt_getCommonLyapFct MPT_GETCOMMONLYAPFCT Computes common Lyapunov function for PWA system
- mpt_greedyMerging MPT_GREEDYMERGING Greedy merging of polyhedra
- mpt_isValidCS MPT_ISVALIDCS Checks if input argument is a valid controller structure
- mpt_lrs MPT_LRS Matlab implementation of the LRS algorithm
- mpt_mergeCS MPT_GLUECS Merges a cell array of ctrlStruct structures
- mpt_mldsim MPT_MLDSIM Simulates an MLD system for one time step
- mpt_mplp_ver1 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mplp_ver2 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mplp_ver3 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mplp_ver4 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mplp_ver5 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mplp_ver6 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mplp_ver7 MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mpsol2ctrl MPT_MPSOL2CTRL Convert solution of multi-parametric program into a controller structure
- mpt_norm2pwa MPT_NORM2PWA transformes a linear norm into an equivalent PWA fcn representation
- mpt_optControlPWAold MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
- mpt_options MPT_OPTIONS Read / modify solver settings for MPT
- mpt_performance MPT_PERFORMANCE Computes performance (i.e. sum of closed-loop costs) associated to a given controller
- mpt_prepareDU MPT_PREPAREDU Extends system and problem matrices to deal with deltaU constraints
- mpt_prepareTracking MPT_PREPARETRACKING Extends system and problem matrices to deal with tracking
- mpt_pwa2hys MPT_PWA2HYS Converts a PWA system described in sysStruct into a HYSDEL model
- mpt_randPWASys MPT_RANDPWASYS generates random PWA systems
- mpt_solveLPi MPT_SOLVELPi Interface to various LP solvers (version without errorchecks)
- mpt_solveLPs MPT_SOLVELPS Interface to various LP solvers ("safe" version)
- mpt_sysStructInfo MPT_SYSSTRUCTINFO Returns information about system structure
- mpt_update MPT_UPDATE Checks for updates of the Multi-Parametric Toolbox
- mpt_verifyProbStruct MPT_VERIFYPROBSTRUCT Verifies the probStruct structure
- mpt_verifySysProb MPT_VERIFYSYSPROB Verifies system and problem structures
- mpt_verifySysStruct MPT_VERIFYSYSSTRUCT Verifies the sysStruct structure
- mpt_yalmipDU MPT_YALMIPDU Augmentes the system to cope with deltaU constraints
- mpt_yalmipTracking MPT_YALMIPTRACKING Extends system and problem matrices to deal with tracking
- sub_computeTrajectory sub_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
- PWAwelldefined 1.) check if the polyhedral partition covers the whole xr-ur space defined
- findFAS ===============================================================================
- hys2pwa HYS2PWA Transformation of HYSDEL model into PWA model
- mpt_hyparr ===============================================================================
- mpt_pwa2mld MPT_PWA2MLD Converts a PWA system into the MLD representation
- mpt_pwa2sys MPT_PWA2SYS Converts structure generated by hys2pwa.m to a sysStruct structure
- remAL ===============================================================================
- gen_log ===============================================================================
- mpc_buildmatFAST ===============================================================================
- mpc_checkSysWeight ===============================================================================
- mpc_mip ===============================================================================
- mpt_blockingMatrices MPT_BLOCKINGMATRICES Constructs matrices for the CFTOC problem for move blocking strategies
- mpt_boolMinTime MPT_BOOLMINTIME Computes minimum time controller for systems with discrete inputs
- mpt_constructMatrices MPT_CONSTRUCTMATRICES Constructs matrices for the finite time constrained optimal control problem
- mpt_getInputXU MPT_GETINPUTXU For a given state, extracts the an output from an XUset
- mpt_getStabFeedback MPT_GETSTABFEEDBACK Computes a stabilizing feedback law for a PWA system
- mpt_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems
- mpt_iterativePWA MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems
- mpt_mixedMinTime MPT_MIXEDMINTIME Computes minimum time controller for systems with discrete and continuous inputs
- mpt_optBoolCtrl MPT_OPTBOOLCTRL Computes optimal controller for systems with discrete inputs
- mpt_optControl MPT_OPTCONTROL Solves the CFTOC problem for a given LTI system
- mpt_optControlPWA MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
- mpt_optInfControl MPT_OPTINFCONTROL Solves the infinite-time constrained optimal control problem for LTI systems
- mpt_optInfControlPWA MPT_OPTINFCONTROLPWA Solves the infinite-time constrained optimal control problem for PWA systems
- mpt_optMixedCtrl MPT_OPTMIXEDCTRL Computes optimal controller for systems discrete and continuous inputs
- mpt_optQuadCtrl MPT_OPTQUADCTRL CFTOC of PWA systems with quadratic cost
- mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices
- mpt_solveMPC MPT_SOLVEMPC Solves the on line optimization MPC problem
- mpt_yalmipcftoc MPT_YALMIPCFTOC CFTOC of PWA systems
- mpt_exHyperAdv ===============================================================================
- mpt_hyparr2 ===============================================================================
- mpt_merge5 ===============================================================================
- mpt_optMerge ===============================================================================
- mpt_optMergeDivCon ===============================================================================
- polyinnerball CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
- tg_polyreduce
- hull HULL Converts vertices/polytope array into an H-representation polytope
- mpt_delaunay MPT_DELAUNAY Computes the delaunay triangulation of a polytope
- mpt_voronoi MPT_VORONOI Computes the voronoi diagram via mpLP
- mpt_getInnerEllipsoid MPT_GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
- mpt_plotArrangement MPT_PLOTARRANGEMENT Plots hyperplane arrangement of a polytope in H-representation
- mpt_plotJ MPT_PLOTJ Plots value function associated to a given controller
- mpt_plotLyapunov MPT_PLOTLYAPUNOV Plots lyapunov function stored in a controlle
- mpt_plotPWA MPT_PLOTPWA Plots a PWA function defined over a given polyhedral partition
- mpt_plotPWQ MPT_PLOTPWQ Plots a PWQ function defined over polyhedral partition
- mpt_plotPartition MPT_PLOTPARTITION Plots a polyhedral partition obtained by mpt_control
- mpt_plotSysStruct MPT_PLOTSYSSTRUCT Plots the system partitions of a PWA system
- mpt_plotTimeTrajectory MPT_PLOTTIMETRAJECTORY Plots trajectories of states, inputs, outputs and disturbances
- mpt_plotTrajectory MPT_PLOTTRAJECTORY Graphical interface for piloting trajectories for LTI and PWA systems subject to control
- mpt_plotU MPT_PLOTU For a given explicit controller, plots value of the control action
- mpt_computeTrajectory MPT_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
- mpt_control MPT_CONTROL Main control routine. Computes explicit controller for a given problem
- mpt_getInput MPT_GETINPUT For a given state, extracts the (optimal) output from a controller structure
- mpt_init MPT_INIT Initializes the MPT toolbox
- mpt_invariantSet MPT_INVARIANTSET Computes (robust) positive invariant subset of an explicit controller
- mpt_ownmpc MPT_OWNMPC The "Design your own MPC" function
- mpt_simSys MPT_SIMSYS Simulates evolution of a given system
- mpt_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law
- mpt_sys MPT_SYS Converts an object to sysStruct structure
- runExample RUNEXAMPLE Demonstrates MPT control routines
- mpt_mplp MPT_MPLP Explicitly solves the given linear program (LP)
- mpt_mpmilp MPT_MPMILP Multi-Parametric Mixed-Integer LP solver
- mpt_mpmiqp MPT_MPMIQP Multi-Parametric Mixed-Integer QP solver
- mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)
- mpt_solveLP MPT_SOLVELP Interface to various LP solvers
- mpt_solveMILP MPT_SOLVEMILP Interface to various MILP solvers
- mpt_solveMIQP MPT_SOLVEMIQP Interface to various MIQP solvers
- mpt_solveQP MPT_SOLVEQP Interface to various QP solvers
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