MPT_INFSETPWA Computes (robust) positive invariant subset for PWA systems
[Pn,dynamics] = mpt_infsetPWA(ctrl)
[Pn,dynamics] = mpt_infsetPWA(ctrl,Options)
[Pn,dynamics] = mpt_infsetPWA(Pn,A,f,Wnoise,Options)
[Pn,dynamics,invCtrlStruct] = mpt_infsetPWA(ctrlStruct,Options)
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DESCRIPTION
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Computes the maximal (robust) positive invariant set of a PWA System
x(k+1)=A{i}x(k)+f{i}+w for x(k) \in Pn(i), w \in Wnoise
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INPUT
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Pn - Polytope array defining the area where the PWA system is defined
A - Cell array containing dynamic matrices A_i
f - Cell array containing dynamic matrices f_i
Wnoise - Polytope which bounds additive uncertainty w \in Wnoise (can be empty)
ctrl - Explicit controller (MPTCTRL object)
Options.verbose - Level of verbosity 0,1 or 2
Options.nohull - If set to 1, do not compute convex unions
Options.maxIter - maximum number of iterations. Set is not invariant if
iteration is aborted prior to convergence (default is 200)
Options.useTmap - If set to true (default is false), transition map will be
computed to rule out certain transitions
Options.sphratio - Gives factor which governs maximum number of separating
hyperplanes computed in transition maps. Number of
separating hyperplnaes computed at each step is given by
length(Pn)*length(targetPn) / Options.ratio
Default value is 20.
Set this option to 0 if you don't want to impose any limit
on number of separating hyperplanes.
Options.mergefinal - If set to true (default), tries to simplify
final result by merging regions
Options.simplify_target - If set to true, tries to merge regions between
iteration steps, after Minkowski calculations,
and after detecting a non-convex union of more than
two polytopes in iterations. Default value is set to
TRUE if system is subject to noise, and to FALSE
otherwise.
Options.simplify_method - valid only if .simplify_target set; 'greedy'
(default) - uses greedy merging, other string -
uses optimal merging
NOTE: Length of Pn, A, f must be identical
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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Pn - Polytope array defining the (robust) positive invariant set
dynamics - Integer array defining the active dynamics A_i,f_i for each
polytope Pn(i)
invCtrl - optional; returns a controller which contains control
laws associated to the positive invariant set
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LITERATURE
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"Computation of Invariant Sets for Piecewise Affine Discrete Time Systems
subject to Bounded Disturbances"
S. Rakovic, P. Grieder, M. Kvasnica, D. Q. Mayne and M. Morari, 2003, submitted
check http://control.ee.ethz.ch for latest info
see also MPT_INFSET