hull

PURPOSE

SYNOPSIS

DESCRIPTION

HULL Converts vertices/polytope array into an H-representation polytope

 [P,Vconv]=hull(V,Options)
 [P,Vconv]=hull(PA,Options)

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 DESCRIPTION
 ---------------------------------------------------------------------------
 Creates convex hull of vertices or of a polytope array and returns the 
 H-representation of the hull

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 INPUT
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 V                      - matrix containing vertices of the polytope
 PA                     - polytope array
 Options.extreme_solver - which method to use for convex hull computation
                          (see help mpt_init for details)
 Options.abs_tol        - absolute tolerance
 Options.roundat        - if CDD is used, it usually helps to round the
                          V-representation of a polytope to certain number of
                          decimal places. This option defines at which decimal
                          point the representation should be rounded.
                          (Default is Options.roundat=14, which means that the
                          representation will be rounded to 14 decimal points)
                          NOTE! rounding is only used if extreme_solver=3
                          NOTE! set Options.roundat=Inf to disable rounding

 Note: Initial values of the Options variable are given by mptOptions 
       (see help mpt_init)

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 OUTPUT
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 P      - an H-representation polytope P={x | H x <= K}
 Vconv  - extreme points (i.e. points forming the convex hull)

 see also POLYTOPE/HULL, EXTREME, UNION, ENVELOPE

CROSS-REFERENCE INFORMATION

• length LENGTH Returns number of regions over which the explicit control law is defined
• set SET Set a field of MPTCTRL objects
• end END Returns the last element in a given polytope array
• extreme EXTREME Calculates extreme points of a given polytope
• isminrep ISMINREP Checks if a given polytope is in minimal representation
• length LENGTH Returns number of elements in a polytope array
• polytope POLYTOPE Default constructor for the POLYTOPE object
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• set SET Used to modify internal properties of a given polytope object
• size SIZE Returns size of the given polytope object
• unique UNIQUE Removes redundant entries from a polytope array
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• mpt_lrs MPT_LRS Matlab implementation of the LRS algorithm
• mpt_solverInfo MPT_SOLVERINFO returns information about a given solver
• unitbox UNITBOX Creates a unit box centered at origin

• extreme EXTREME Calculates extreme points of a given polytope
• hull HULL Convex hull of n polytopes
• isconvex ISCONVEX Checks if a polytope array forms a convex union
• merge MERGE merges polytopes together
• 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
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• mpt_feasibleStates MPT_FEASIBLESTATES returns equidistantly spaced data points in feasible set
• mpt_randPWASys MPT_RANDPWASYS generates random PWA systems
• mpt_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems
• mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices
• mpt_optMerge ===============================================================================
• mpt_optMergeDivCon ===============================================================================
• mpt_control MPT_CONTROL Main control routine. Computes explicit controller for a given problem
• mpt_init MPT_INIT Initializes the MPT toolbox
• mpt_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law