isfulldim

PURPOSE

SYNOPSIS

DESCRIPTION

ISFULLDIM Checks if a polytope is full dimensional

 status = isfulldim(P,Options)

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 DESCRIPTION
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 STATUS = ISFULLDIM(P) returns TRUE (1) if P is a full dimensional polytope

 Note that full dimensionality of a polytope does not imply that it is also
 bounded!

 USAGE:
   isfulldim(P)
   isfulldim(P,Options)

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 INPUT
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 P                - polytope
 Options.abs_tol  - absolute tolerance

 Note: If Options is missing or some of the fields are not defined, the default
       values from mptOptions will be used

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 OUTPUT                                                                                                    
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 status           - Logical statement

 see also ISBOUNDED

CROSS-REFERENCE INFORMATION

• length LENGTH Returns number of regions over which the explicit control law is defined
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array

• char CHAR Provides textual description of a given controller
• length LENGTH Returns number of regions over which the explicit control law is defined
• mptctrl MPTCTRL Constructor for the MPT controller object
• analyticCenter ANALYTICCENTER Computes an analytic center of a polytope
• and AND Intersection of n polytopes
• bounding_box BOUNDING_BOX Compute a bounding box for a given polytope
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• 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
• envelope ENVELOPE Computes envelope of n polytopes
• eq EQ Checks if two polytopes are equal
• extreme EXTREME Calculates extreme points of a given polytope
• facetvoronoi FACETVORONOI Computes an equivalent of voronoi diagrams for facets
• horzcat HORZCAT Concatenates polytopes into a polytope array
• intersect INTERSECT Intersection of 2 polytopes or polytope arrays
• isconvex ISCONVEX Checks if a polytope array forms a convex union
• isinside ISINSIDE Checks if a given point lies in the interior of a given polytope
• 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
• plus PLUS Minkowski sum of two polytopes
• polytope POLYTOPE Default constructor for the POLYTOPE object
• projection PROJECTION Projection of a polytope or a polytope array
• reduceunion REDUCEUNION Removes redundant elements from a polytope array
• regiondiff REGIONDIFF Region difference
• regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space
• slice SLICE cuts a polytope (polytope array) at prespecified values
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• union UNION convex union computation
• vertcat VERTCAT Concatenates polytopes into a polytope array
• 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_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_reachXU MPT_REACHXU One-step reachability computation for an affine system
• mpt_removeOverlaps MPT_REMOVEOVERLAPS Removes overlaps from (a set of) polyhedral partitions with associated linear cost
• mpt_verify MPT_VERIFY Verifies if states enter a given set in a given number of steps
• mpt_addTset MPT_ADDTSET Adds terminal set constraint to Matrices
• mpt_feasibleStates MPT_FEASIBLESTATES returns equidistantly spaced data points in feasible set
• mpt_isnoise MPT_ISNOISE Checks if noise object is not empty
• 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_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_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_sysStructInfo MPT_SYSSTRUCTINFO Returns information about system structure
• mpt_verifyProbStruct MPT_VERIFYPROBSTRUCT Verifies the probStruct 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
• hys2pwa HYS2PWA Transformation of HYSDEL model into PWA model
• 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_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_oneStepCtrl MPT_ONESTEPCTRL Computes low complexity controller for LTI systems
• mpt_optBoolCtrl MPT_OPTBOOLCTRL Computes optimal controller for systems with discrete inputs
• 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_yalmipcftoc MPT_YALMIPCFTOC CFTOC of PWA systems
• mpt_optMerge ===============================================================================
• mpt_optMergeDivCon ===============================================================================
• tg_polyreduce
• mpt_plotSysStruct MPT_PLOTSYSSTRUCT Plots the system partitions of a PWA system
• 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_invariantSet MPT_INVARIANTSET Computes (robust) positive invariant subset of an explicit controller
• mpt_mplp MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)