minus

MINUS Pontryagin difference

 MINUS  Minkowski (Pontryagin) difference

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 DESCRIPTION
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  The algorithm for efficiently computing the Minkowski difference between a
  union of polytopes and a polytope is based on a talk by 
  S. Rakovic and D. Mayne entitled "Constrained Control Computations"
  It was the keynote address at the GBT Meeting, London, November, 2002.

 NOTE: If Q ia a polyarray, Q=[Q1 Q2 ... Qn], then Q is considered
 as the space covered with polytopes Qi, and the minus.m computes P-Q according
 to the definition 
   P-Q=\{x\in P| x+w\in P \forall w\in Q\}=(P-Q1)&(P-Q2)&...&(P-Qn) 

 USAGE:
   R=P-Q
   R=minus(P,Q,Options)

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 INPUT
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 P,Q                     - Polytopes or arrays of polytopes
 Options.extreme_solver  - Which method to use for extreme points computation
                           (see help extreme)
 Options.lpsolver        - Which LP solver to use (see help mpt_solveLP)
 Options.merge           - If set to true (default), simplifies the final
                           polytope description using merge.m
 Options.merge_method    - Valid only if .merge is set to 1, if 'greedy'
                           (default) greedy merging will be used,
                           otherwise optimal merging is used

 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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 R     - polytope (or polytope array) describing the Pontryagin difference

 see also PLUS, MLDIVIDE