mpt_removeOverlaps

MPT_REMOVEOVERLAPS Removes overlaps from (a set of) polyhedral partitions with associated linear cost

 [newCtrlStruct]=mpt_removeOverlaps(ctrl,Options)

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 DESCRIPTION
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 Given 'n' (possibly overlapping) polyhedral partitions with associated linear cost,
 this function detect such overlaps and removes them by picking up regions which
 have the least cost associated to them. If intersection of the overlapping regions
 is non-empty, slicing is introduced to create one non-overlapping polyhedral
 partition.
 
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 INPUT
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 ctrl        - Explicit controller a cell aray thereof; with fields:
      Pfinal - maximum feasible set (i.e. the outer hull of U Pn)
      Pn     - polytopic regions
      Fi,Gi  - cells containing control law (u = Fi{j} x + Gi{j})
      Bi,Ci  - cells containing the linear cost (i.e. J = Bi{j} x + Ci{j})
 Options.verbose   - level of verbosity
 Options.lpsolver  - default solver for LP's
 Options.abs_tol   - absolute tolerance
 Options.rel_tol   - relative tolerance
 Options.Vpruning  - whether or not to prune non-valid intersections by
                     examining extreme points (0 is default)
 Options.lowmem    - defines memory saving mode
                       0 - no memory saving - fast computation (default)
                       1 - heavy memory saving (slow computation)

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

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 OUTPUT                                                                                                    
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 newCtrl    - controller which consists of purely non-overlapping regions

 see also POLYTOPE/REDUCEUNION, POLYTOPE/UNIQUE