Home > mpt > extras > analysis > mpt_infset.m

# mpt_infset

## PURPOSE

MPT_INFSET Calculates the maximal positively invariant set for an LTI system

## SYNOPSIS

function [Oinf,tstar,fd,isemptypoly] = mpt_infset(A,X,tmax,Pnoise,Options)

## DESCRIPTION

MPT_INFSET Calculates the maximal positively invariant set for an LTI system

[Oinf,tstar,fd,isemptypoly] = mpt_infset(A,X,tmax,Pnoise,Options)

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DESCRIPTION
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Calculates the maximal positively invariant set for an autonomous discrete-time
LTI system
Takes into account polytopic and additive system uncertainty, if defined
in "sysStruct" / "Pnoise", respectively.

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INPUT
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A                - The A matrix of the discrete-time LTI system x{k+1} = Ax{k}.
X                - State constraints given as a polytope (x \in X)_
tmax             - Maximum number of iterations allowed.
Options.lpsolver - Solver for LPs (see help mpt_solveLP for details)
Options.verbose  - level of verbosity (see help mpt_init for details)
Options.abs_tol  - absolute tolerance

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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Oinf         - Maximal positively invariant set contained in X, i.e.
Oinf = {x_k \in X: x_{k+1} = Ax_k \in X}.
tstar        - Determinedness index.
fd           - 1 if Oinf is finitely determined (tstar <= tmax).
0 if Oinf tstar > tmax.
isemptypoly  - 1 if resulting polyhedron is empty; 0 otherwise

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Literature:
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"Theory and Computation of Disturbance Invariant Sets for Discrete-Time Linear Systems"
I. Kolmanovsky and E. G. Gilbert, Mathematical Problems in Egineering, vol (4), 1998,
pages 317-367

AND

"Linear systems with state and control constraints: the theory and
applications of maximal output admissible sets", E. G. Gilbert and K. Tin Tan,
IEEE Transcations on Automatic Control, 1991, vol 36, number 9, pages 1008--1020

see also MPT_INFSETPWA

## 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
• length LENGTH Returns number of elements in a polytope array
• polytope POLYTOPE Default constructor for the POLYTOPE object
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• mpt_isnoise MPT_ISNOISE Checks if noise object is not empty
• mpt_solveLPi MPT_SOLVELPi Interface to various LP solvers (version without errorchecks)
This function is called by: