mpt_mplp_ver7

MPT_MPLP Explicitly solves the given linear program (LP)

 [Pn,Fi,Gi,activeConstraints,Phard,details]=mpt_mplp(Matrices,Options)

 ---------------------------------------------------------------------------
 DESCRIPTION
 ---------------------------------------------------------------------------
 Multiparametric linear programming

 Solves the problem
   V(x) = min (H + Dx)' U
           U
   s.t.   G U <= W + E x
          bndA*x <= bndb

 As a solution we get 'nR' regions
   Pn(i)={x : H x <= K}
 
 with the optimal control law
   U = Fi{i} x + Gi{i}

 and the corresponding cost function expression
   V(x) = Bi{i} x + Ci{i}
  
 ---------------------------------------------------------------------------
 INPUT
 ---------------------------------------------------------------------------
 Matrices - a struct with all the parameters which are needed.
            See description above for explanation.
   Matrices.H=H;
   Matrices.G=G;   
   Matrices.W=W;
   Matrices.E=E;
   Matrices.D=D;    
   Matrices.bndA=bndA;     Limits on exploration space, i.e. bndA*x<=bndb
   Matrices.bndb
   Matrices.constraintInfo;    

 Options.verbose      - level of verbosity
 Options.lpsolver     - which LP solver to use (help mpt_solveLP)
 Options.max_iter     - maximum number of iterations of the algorithm
 Options.step_size    - length of step over a facet (default: 1e-?)
 Options.f_perturb    - Perturbation of the optimization direction

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

 ---------------------------------------------------------------------------
 OUTPUT                                                                                                    
 ---------------------------------------------------------------------------
 Pn,Fi,Gi           - for region Pn(i).H*x <= Pn(i).K computed input is
                      U=Fi{i}*x+Gi{i}   
 activeConstraints  - Cell Array which stores the active constraints 
                      of the optimizer in each region.
 Phard              - Defines the feasible state space partition (i.e. union of
                      all regions) as Phard.H*x<=Phard.K
 details            - a structure with the following fields:
     nRegions  number of regions
     Pn        polyhedral partition
     Fi,Gi     optimizer matrices: u(x) = Fi * x + Gi
     Bi,Ci     value function matrices: J(x) = Bi * x + Ci
     nHard     number of hard constraints
     Phard     polytope given by hard constraints
     nb        number of constraints for each region
     LISTa     list of active constraints
     adjacencyInfo adjacency information of the polytopic partition
     adjacencyInfo.adjacencyList Adjacency list for each region of the
                                 parition indexed by the border numbers 
     adjacencyInfo.tSetList      List of infeasible boundaries of each region.