domain

DOMAIN Computes polytope that is mapped to an another polytope using affine map

 [R,keptrows,feasible]=domain(P,A,f,Q,horizon)

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 DESCRIPTION
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   Compute polytope contained in "Q" that is mapped to "P" in "horizon" steps.
   R=domain(P,A,f,Q,horizon) computes polytope R that is under an
   affine mapping m: 
   R={x(0) \in Q | x(horizon) \in P, x(k+1)=Ax(k)+f}

   NOTE: Q is R^n as default

 This function is almost identical to "mpt_getReachSubset". However, here we
 assume the feedback to be time invariant while "mpt_getReachSubset" assumes
 the feedback to be time-variant.

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 INPUT
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 P       - Polytope (or union thereof); 
 A, f    - Dynamics matrices; x(k+1)=Ax(k)+f
 Q       - Polytope (or union thereof); 
 horizon - length of the mapping
 Options.noReduce - if set to 1, resulting polytope will not be in minimal
                    representation and 'keptrows' will be an empty matrix
                    (off by default)

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 OUTPUT
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 R         - Polytope (or union thereof); See definition in DESCRIPTION;
 keptrows   - is a vector containing the origin of each facet of R
                1 means that the facet originated from active constraints in Q
                0 means that the facet originated from reachability restrictions P
              If P and Q are polygons "keptrows" returns the indices
               of the original polytope P for which transition R(i) was computed.         
 feasible  - 1 if a feasible transition was found (i.e., R is full dimensional);
             0 otherwise;

 see also MPT_GETREACHSUBSET, RANGE