mpt_reachSets

MPT_REACHSETS Computes sets of reachable states for a given system / controller

 [Rsets, Vsets] = mpt_reachSets(structure, X0, U0, N, Options)

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 DESCRIPTION
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 Calculates set of states which are reachable from a given polytope X0 in N
 steps. The system under consideration can be either linear (LTI), or PWA.
 Input argument can be either a system in sysStruct format, or an explicit
 controller computed by mpt_control. In that case, the autonomous system is
 defined as:
   x(k+1) = (A+Fi)*x + (Gi+f)

 If the system is not autonomuos, it is converted to such by setting
   x(k+1) = A*x + fcl
 where
   fcl = f + B*Options.U

 Options.U is set to zero by default.

 WARNING: By default, this function computes only fully dimensional reachable
 sets! Use "Options.lowdim=1" to tell the function to compute lower dimensional
 sets as well.

 USAGE:
   Psets = mpt_reachSets(sysStruct, X0, N, Options)     - assumes u = 0
   Psets = mpt_reachSets(sysStruct, X0, U0, N, Options) - assumes u \in U0
   Psets = mpt_reachSets(ctrl, X0, N, Options)
   [Psets, Vsets] = mpt_reachSets(sysStruct, X0, N, Options)
   [Psets, Vsets] = mpt_reachSets(sysStruct, X0, U0, N, Options)
   [Psets, Vsets] = mpt_reachSets(ctrl, X0, N, Options)

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 INPUT
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 structure       - either a sysStruct structure, or an explicit controller
 X0              - set of initial states (polytope or a polyarray)
 U0              - set of admissible inputs (polytope object)
 N               - number of steps over which to compute reachable sets
 Options.lowdim  - if set to 1, evolution of lower-dimensional sets will be
                  computed. in such case, these lower-dimensional sets will be
                  returned as V-represented polytopes (with vertices stored
                  column-wise!). Default: 0
 Options.reduceV - if set to 1, V-represented lower-dimensional polytopes will
                   be reduced to a minimal representation. Default: 0
 Options.verbose - level of verbosity (0/1/2)

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 OUTPUT                                                                                                    
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 Psets       - Sets of fully dimensional reachable states (polyarray)
 Vsets       - Lower-dimensional reachable sets (returned as a cell array, each
               element represents one polytope in V-representation with
               vertices stored row-wise).

 see also POLYTOPE/RANGE, MPT_REACHXU, MPT_VERIFY