Home > mpt > @polytope > dimension.m

# dimension

## PURPOSE

DIMENSION Returns dimension of the given polytope

## SYNOPSIS

function nx = dimension(P)

## DESCRIPTION

```DIMENSION Returns dimension of the given polytope

nx = dimension(P)

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DESCRIPTION
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Returns dimension of the polytope P

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INPUT
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P   - Polytope

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OUTPUT
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nx  - dimension of the given polytope P (or polyarray)

## 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
• length LENGTH Returns number of elements in a polytope array
• size SIZE Returns size of the given polytope object
This function is called by:
• char CHAR Provides textual description of a given controller
• and AND Intersection of n polytopes
• bounding_box BOUNDING_BOX Compute a bounding box for a given polytope
• distance DISTANCE Distance between two sets
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• dointersect DOINTERSECT Checks if two polytopes / polyarrays intersect
• envelope ENVELOPE Computes envelope of n polytopes
• eq EQ Checks if two polytopes are equal
• intersect INTERSECT Intersection of 2 polytopes or polytope arrays
• 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
• lt LT Checks if polytope P is a strict subset of polytope Q
• minus MINUS Pontryagin difference
• plot PLOT Plots polytopes in 2D or 3D
• plus PLUS Minkowski sum of two polytopes
• projection PROJECTION Projection of a polytope or a polytope array
• regiondiff REGIONDIFF Region difference
• slice SLICE cuts a polytope (polytope array) at prespecified values
• subsasgn SUBSASGN Indexed assignments for polytope objects
• mpt_checkLyapFct MPT_CHECKLYAPFCT Checks if a function is a Lyapunov function for a given ctrlStruct
• 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_isPWAbigger MPT_ISPWABIGGER Test if one PWA function is bigger than a second PWA function
• 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_searchTree MPT_SEARCHTREE Computes a search-tree for a given explicit solution
• mpt_transmap MPT_TRANSMAP Computes transition map
• identifyRegion IDENTIFYREGION plots the number of the polytopes into the current figure
• mpt_dummyCS MPT_DUMMYCS Returns a dummy controller structure
• mpt_evalPWA MPT_EVALPWA Evaluates a PWA function at a given location
• 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_verifySysProb MPT_VERIFYSYSPROB Verifies system and problem structures
• mpt_verifySysStruct MPT_VERIFYSYSSTRUCT Verifies the sysStruct structure
• sub_computeTrajectory sub_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
• unitbox UNITBOX Creates a unit box centered at origin
• 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_optControlPWA MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
• mpt_optMergeDivCon ===============================================================================
• mpt_voronoi MPT_VORONOI Computes the voronoi diagram via mpLP
• 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_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_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law

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