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double

PURPOSE

DOUBLE Function used to access internal properties of the given polytope

SYNOPSIS

function [H,K] = double(P)

DESCRIPTION

```DOUBLE Function used to access internal properties of the given polytope

[H,K] = double(P)

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DESCRIPTION
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Function used to access internal properties of the POLYTOPE object

USAGE:
HK = DOUBLE(P) returns matrix [H K] of a polyhedron P={x|H x<=K}
[H,K] = DOUBLE(P)

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INPUT
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P   - Polytope

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OUTPUT
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H,K          - Matrices describing the H-representation of the polytope P
(i.e. P={x|H x<=K})

CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• 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
This function is called by:
• info INFO Displays more detailed information a given MPT controller
• analyticCenter ANALYTICCENTER Computes an analytic center of a polytope
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• dointersect DOINTERSECT Checks if two polytopes / polyarrays intersect
• getInnerEllipsoid GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
• getOutterEllipsoid GETOUTTERELLIPSOID Computes the smallest ellipsoid which covers the polytope P
• projection PROJECTION Projection of a polytope or a polytope array
• regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• union UNION convex union computation
• mpt_checkLyapFct MPT_CHECKLYAPFCT Checks if a function is a Lyapunov function for a given ctrlStruct
• mpt_dlyap_infnorm Lyapunov equation with inf-norm for discrete-time LTI systems
• 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_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_removeOverlaps MPT_REMOVEOVERLAPS Removes overlaps from (a set of) polyhedral partitions with associated linear cost
• mpt_searchTree MPT_SEARCHTREE Computes a search-tree for a given explicit solution
• mpt_verify MPT_VERIFY Verifies if states enter a given set in a given number of steps
• mpt_evalSystem MPT_EVALSYSTEM Extracts data from sysStruct and probStruct structures
• mpt_getCommonLyapFct MPT_GETCOMMONLYAPFCT Computes common Lyapunov function for PWA system
• mpt_greedyMerging MPT_GREEDYMERGING Greedy merging of polyhedra
• mpt_lrs MPT_LRS Matlab implementation of the LRS algorithm
• 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_norm2pwa MPT_NORM2PWA transformes a linear norm into an equivalent PWA fcn representation
• mpt_prepareDU MPT_PREPAREDU Extends system and problem matrices to deal with deltaU constraints
• mpt_prepareTracking MPT_PREPARETRACKING Extends system and problem matrices to deal with tracking
• mpt_randPWASys MPT_RANDPWASYS generates random PWA systems
• mpt_solveLPi MPT_SOLVELPi Interface to various LP solvers (version without errorchecks)
• mpt_update MPT_UPDATE Checks for updates of the Multi-Parametric Toolbox
• hys2pwa HYS2PWA Transformation of HYSDEL model into PWA model
• mpc_buildmatFAST ===============================================================================
• mpt_blockingMatrices MPT_BLOCKINGMATRICES Constructs matrices for the CFTOC problem for move blocking strategies
• mpt_boolMinTime MPT_BOOLMINTIME Computes minimum time controller for systems with discrete inputs
• mpt_constructMatrices MPT_CONSTRUCTMATRICES Constructs matrices for the finite time constrained optimal control problem
• mpt_getInputXU MPT_GETINPUTXU For a given state, extracts the an output from an XUset
• mpt_getStabFeedback MPT_GETSTABFEEDBACK Computes a stabilizing feedback law for a PWA system
• 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_optBoolCtrl MPT_OPTBOOLCTRL Computes optimal controller for systems with discrete inputs
• mpt_optControlPWA MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
• mpt_optInfControl MPT_OPTINFCONTROL Solves the infinite-time constrained optimal control problem for LTI systems
• mpt_optMixedCtrl MPT_OPTMIXEDCTRL Computes optimal controller for systems discrete and continuous inputs
• mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices
• mpt_solveMPC MPT_SOLVEMPC Solves the on line optimization MPC problem
• mpt_optMerge ===============================================================================
• mpt_optMergeDivCon ===============================================================================
• tg_polyreduce
• mpt_delaunay MPT_DELAUNAY Computes the delaunay triangulation of a polytope
• mpt_voronoi MPT_VORONOI Computes the voronoi diagram via mpLP
• mpt_getInnerEllipsoid MPT_GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
• mpt_getOutterEllipsoid MPT_GETOUTTERELLIPSOID Computes the smallest ellipsoid which covers the polytope P
• mpt_plotArrangement MPT_PLOTARRANGEMENT Plots hyperplane arrangement of a polytope in H-representation
• mpt_computeTrajectory MPT_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
• mpt_control MPT_CONTROL Main control routine. Computes explicit controller for a given problem
• mpt_getInput MPT_GETINPUT For a given state, extracts the (optimal) output from a controller structure
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)
• mpt_solveMILP MPT_SOLVEMILP Interface to various MILP solvers
• mpt_solveMIQP MPT_SOLVEMIQP Interface to various MIQP solvers
• mpt_solveQP MPT_SOLVEQP Interface to various QP solvers

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