mpt_maxCtrlSet

MPT_MAXCTRLSET     Computes the maximal  robust control invariant set C_inf
                   or the maximal robust attractive set K_inf

  [invSet,iterations] = mpt_maxCtrlSet(sysStruct,Options)

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 DESCRIPTION
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 Computes the maximal control invariant set C_inf or the maximal attractive set K_inf
 Assume a system x(k+1)=f(x(k),u(k),w(k)) subject to constraints x(k) \in X and u(k) \in U; 
 Then
       C_inf = {x \in R^n | \exists u(k) \in U, s.t. x(k) \in X, \forall k >=0}
       
 The N-step attractive set K_inf is defined as with respect to the target set Phi: 
       K_inf = {x \in R^n | \exists u(k) \in U, s.t. x(k) \in X, x(N) \in Phi, \forall k >=0}

 Here, by default, Phi is an invariant set around the origin. By default N->Infty.
 The function is able to deal with additive and polytopic uncertainty in the system 
 matrices. 

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 INPUT
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 sysStruct        - System structure in the sysStruct format

    See the MPT Manual for additional details on the structure format or   
   consult one of the example systems (e.g. Double_Integator) which were  
    provided with this package.                                            

 Options.y0bounds - add constraints on y0? (1 - yes, 0 - no)
 Options.Kinf     - If set to 1, then K_inf will be computed. If set to 0,
                    C_inf will be computed. (default is 0)
 Options.maxCtr   - Maximum number of iterations (default is 1000)
                    (corresponds to N-step attractive set)
 Options.verbose  - Optional: level of verbosity
 Options.scaling  - Scaling the set at each iteration with a parameter 
                    0 < lambda < 1 guarantees finite time convergence to a
                    robust invariant subset of the maximal control invariant
                    set. (Default: Options.scaling = 1) 
 Options.Vconverge - A non-zero value will force the algorithm to break if
                     relative increase of volume of atractive set at the next
                     iteration compared to volume of the set at the previous
                     iteration decreases below this value. E.g.
                     Options.Vconverge=1 will terminate the procedure if
                     (Vnew-Vold)/Vold*100 < 1.
                     NOTE! Currently works only for LTI systems!
                     NOTE! Value of this option has percents as units!
                     NOTE! Should only be used if you are computing Kinf set!!! 
 Options.set_limit - If the invariant set has a chebychev redius which is
                     smaller than this value the iteration is aborted. 
                     (Default is 1e-3) 
 Options.useprojection - if true, uses projections to obtain feasible set. if
                         false, feasible sets are obtained by solving a
                         multi-parametric program.
                         (Default is true)
 Options
   .Q, .R, .Tset  - additional problem-depended options
   .probStruct    - the whole problem structure can be passed as well

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

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 OUTPUT
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  invSet          - maximal control invariant (or attractive set)
  iterations      - number of iterations that were required to compute set
  Piter           - sets obtained at each iteration

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 LITERATURE
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 "Robust Low Complexity Feedback Control of Constrained Systems", P. Grieder and M. Morari;
  submitted

 see also MPT_ONESTEPCTRL