mpt_getReachSubset

MPT_GETREACHSUBSET Computes a subset of P which enters Pfin

 [Pret,keptrows,feasible] = mpt_getReachSubset(P,Pfin,A,B,F,G,horizon,Options)

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 DESCRIPTION
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 this function returns a subset Pret={x | H x <= K} of a polyhedron defined by P
 from which all points enter a final polytope Pfin in N steps. This function is 
 almost identical to "domain". However, here we assume the feedback 
 to be time-varying while "domain" assumes the feedback to be time-invariant.

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 INPUT
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 P                 - polyhedral partition given by the polytopic array
 Pfin              - target polytope which should be reached in "horizon" steps
 Fi,Gi             - optimal feedback law given by u=Fi{i}*x+Gi{i}
 A, B              - system dynamics are given by x(k+1)=Ax(k)+Bu(k)
 horizon           - number of steps in which the target poly should be reached
 Options.abs_tol   - if abs(x)<tolerance x is considered to be zero
 Options.lpsolver  - LP solver to be used (see help mpt_solveLP for details)

 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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 Pret       - subset Pret.H*x<=Pret.K of the input poly P.H*x<=P.K whose
              points enter (P) in "horizon" steps
 keptrows   - is a vector containing the origin of each facet of Pret.H*x<=Pret.K
               1 means that the facet originated from active constraints in P
               0 means that the facet originated from reachability restrictions Pfin
 feasible   - is 1 if the resulting region is not empty

 see also DOMAIN, RANGE