Home > mpt > extras > analysis > mpt_getReachSubset.m

# mpt_getReachSubset

## PURPOSE

MPT_GETREACHSUBSET Computes a subset of P which enters Pfin

## SYNOPSIS

function [Pret,keptrows,feasible] = mpt_getReachSubset(P,Pfin,A,B,F,G,horizon,Options)

## DESCRIPTION

```MPT_GETREACHSUBSET Computes a subset of P which enters Pfin

[Pret,keptrows,feasible] = mpt_getReachSubset(P,Pfin,A,B,F,G,horizon,Options)

---------------------------------------------------------------------------
DESCRIPTION
---------------------------------------------------------------------------
this function returns a subset Pret={x | H x <= K} of a polyhedron defined by P
from which all points enter a final polytope Pfin in N steps. This function is
almost identical to "domain". However, here we assume the feedback
to be time-varying while "domain" assumes the feedback to be time-invariant.

---------------------------------------------------------------------------
INPUT
---------------------------------------------------------------------------
P                 - polyhedral partition given by the polytopic array
Pfin              - target polytope which should be reached in "horizon" steps
Fi,Gi             - optimal feedback law given by u=Fi{i}*x+Gi{i}
A, B              - system dynamics are given by x(k+1)=Ax(k)+Bu(k)
horizon           - number of steps in which the target poly should be reached
Options.abs_tol   - if abs(x)<tolerance x is considered to be zero
Options.lpsolver  - LP solver to be used (see help mpt_solveLP for details)

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

---------------------------------------------------------------------------
OUTPUT:
---------------------------------------------------------------------------
Pret       - subset Pret.H*x<=Pret.K of the input poly P.H*x<=P.K whose
points enter (P) in "horizon" steps
keptrows   - is a vector containing the origin of each facet of Pret.H*x<=Pret.K
1 means that the facet originated from active constraints in P
0 means that the facet originated from reachability restrictions Pfin
feasible   - is 1 if the resulting region is not empty

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• double DOUBLE Function used to access internal properties of the given polytope
• end END Returns the last element in a given polytope array
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• isinside ISINSIDE Checks if a given point lies in the interior of a given polytope
• isnormal ISNORMAL Checks if a given polytope is in normalized description
• length LENGTH Returns number of elements in a polytope array
• normalize NORMALIZE Normalizes a given polytope
• polytope POLYTOPE Default constructor for the POLYTOPE object
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
This function is called by:
• mpt_optInfControl MPT_OPTINFCONTROL Solves the infinite-time constrained optimal control problem for LTI systems

Generated on Thu 30-Mar-2006 10:26:47 by m2html © 2003