Description of mpt

DESCRIPTION

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 function [PAmer, colorMer] = mpt_optMerge(PA, Opt)
 
 Title:        mpt_optMerge
                                                             
 Project:      Optimal merging of a set of polyhedra 

 Input:        PA: polyhedral array
               Opt: Options with the following fields
                 .color: color of polyhedra
                         this is an integer 1,2,... 
                         the algorithm will merge polyhedra with the same color 
                         if color is not specified, it is assumed to be 1
                         for all polyhedra.
                 .PAdom: the set of polyhedra (the so called domain) the problem 
                         is defined in. If not given, the algorithm assumes the 
                         domain is given by the hull (or envelope if the hull 
                         computation fails) of PA.
                 .PAcompl:  polyhedral array that is within the domain and not 
                            in PA - it is the so called complement. If not specified, 
                            the algorithm assumes PAcompl is empty. Then the 
                            complement is filled up optimally by the merging algorithm.
                            Refer also to the second remark below.
                 .verbose: 0: silent (=default)
                           1: verbose only important information
                           2: verbose everything
                 .algo: 0:        overlapping merging (boolean minimization)
                        [1, inf]: optimal merging, with the given upper bound on nodes
                                  (default is inf)

 Output:       PAmer: merged polyhedra array
               colorMer: colors with the following fields
                 .Reg:   color of each region
                 .Table: regions with the same color 

 Authors:      Tobias Geyer <geyer@control.ee.ethz.ch>, Fabio D. Torrisi

CROSS-REFERENCE INFORMATION

horzcat HORZCAT Concatenation of MPTCTRL objects

length LENGTH Returns number of regions over which the explicit control law is defined

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

horzcat HORZCAT Concatenates polytopes into a polytope array

hull HULL Convex hull of n polytopes

isfulldim ISFULLDIM Checks if a polytope is full dimensional

length LENGTH Returns number of elements in a polytope array

or OR Convex union of n polytopes

polytope POLYTOPE Default constructor for the POLYTOPE object

size SIZE Returns size of the given polytope object

unique UNIQUE Removes redundant entries from a polytope array

mpt_exHyperAdv ===============================================================================

mpt_hyparr2 ===============================================================================

mpt_merge5 ===============================================================================

readEspressoOne ===============================================================================

writeEspressoOnOff ===============================================================================

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

merge MERGE merges polytopes together

mpt_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law

mpt_optMerge

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION