Home > mpt > @polytope > chebyball.m

# chebyball

## PURPOSE

CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope

## SYNOPSIS

function [xc,R,lambda] = chebyball(P,Options,force)

## DESCRIPTION

```CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope

[xc,R,lambda] = chebyball(P,Options,force)

---------------------------------------------------------------------------
DESCRIPTION
---------------------------------------------------------------------------
Returns center and radius of a largest ball that can be inscribed in a polytope P

USAGE:
[xc, Rc] = chebyball(P)
[xc, Rc] = chebyball(P, Options)
[xc, Rc, lambda] = chebyball(P)

NOTE: usually the 'POLYTOPE' constructor computes these values automatically.
If they are already stored in the internal structure, no computation will
be performed unless force=1

For nice plots, call:
mpt_plotArrangement(P);
hold on
[xc,R] = chebyball(P);
plotellip(eye(2)/R^2,xc);

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INPUT
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P                 - Polytope
Options.lpsolver  - LP solver to use (see help mpt_solveLP)
force             - force recomputing of the Chebyshev's ball

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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xc                - Center of Chebyshev's ball
R                 - Radius of Chebyshev's ball
lambda            - Set of lagrangian multipliers

## 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
• end END Returns the last element in a given polytope array
• length LENGTH Returns number of elements in a polytope array
• normalize NORMALIZE Normalizes a given polytope
• size SIZE Returns size of the given polytope object
• mpt_solveLPs MPT_SOLVELPS Interface to various LP solvers ("safe" version)
This function is called by:
• modify MODIFY Modifies an MPTCTRL object
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• extreme EXTREME Calculates extreme points of a given polytope
• isbounded ISBOUNDED Checks if a polytope is bounded
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• isredundant ISREDUNDANT Check if a constraint is redundant
• minus MINUS Pontryagin difference
• polytope POLYTOPE Default constructor for the POLYTOPE object
• projection PROJECTION Projection of a polytope or a polytope array
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• regiondiff REGIONDIFF Region difference
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• mpt_getCommonSOSLyapFct MPT_GETCOMMONSOSLYAPFCT Calculates Common SOS Lyapunov function for system with additive disturbance
• mpt_getPWALyapFct MPT_GETPWALYAPFCT Calculates PWA Lyapunov function
• mpt_getPWPLyapFct MPT_GETPWPLYAPFCT Calculates Piecewise Polynomial (sum of squares) Lyapunov function
• mpt_getPWQLyapFct MPT_GETPWQLYAPFCT Calculates PWQ Lyapunov function
• mpt_getReachSubset MPT_GETREACHSUBSET Computes a subset of P which enters Pfin
• mpt_infset MPT_INFSET Calculates the maximal positively invariant set for an LTI system
• mpt_infsetPWA MPT_INFSETPWA Computes (robust) positive invariant subset for PWA systems
• mpt_maxCtrlSet MPT_MAXCTRLSET Computes the maximal robust control invariant set C_inf
• mpt_reachSets MPT_REACHSETS Computes sets of reachable states for a given system / controller
• mpt_reachXU MPT_REACHXU One-step reachability computation for an affine system
• identifyRegion IDENTIFYREGION plots the number of the polytopes into the current figure
• mpt_mplp_ver1 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver2 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver3 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver4 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver5 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver6 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mplp_ver7 MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_iterativePWA MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems
• mpt_mixedMinTime MPT_MIXEDMINTIME Computes minimum time controller for systems with discrete and continuous inputs
• mpt_optInfControl MPT_OPTINFCONTROL Solves the infinite-time constrained optimal control problem for LTI systems
• mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices
• mpt_plotPWA MPT_PLOTPWA Plots a PWA function defined over a given polyhedral partition
• mpt_plotU MPT_PLOTU For a given explicit controller, plots value of the control action
• mpt_invariantSet MPT_INVARIANTSET Computes (robust) positive invariant subset of an explicit controller
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)

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