end

PURPOSE

SYNOPSIS

DESCRIPTION

END Returns the last element in a given polytope array

 ---------------------------------------------------------------------------
 DESCRIPTION
 ---------------------------------------------------------------------------
 If P is a polytope array (i.e. P=(U Pi)), returns the last element in the array

 USAGE:
   P(end)

 ---------------------------------------------------------------------------
 INPUT
 ---------------------------------------------------------------------------
 none

 ---------------------------------------------------------------------------
 OUTPUT                                                                                                    
 ---------------------------------------------------------------------------
 last element in the polyarray

 see also LENGTH, SUBSREF

CROSS-REFERENCE INFORMATION

• length LENGTH Returns number of regions over which the explicit control law is defined
• length LENGTH Returns number of elements in a polytope array

• analyze ANALYZE Analyzes a given explicit controller and suggests further actions
• cancompile CANCOMPILE Returns true if a given controller can be compiled
• char CHAR Provides textual description of a given controller
• display DISPLAY Displays details about a given MPT controller
• get GET Get MPTCTRL properties
• info INFO Displays more detailed information a given MPT controller
• isinvariant ISINVARIANT Decides if a given explicit controller is invariant
• isstabilizable STABILIZES Decides if a given controller is stabilizable
• length LENGTH Returns number of regions over which the explicit control law is defined
• modify MODIFY Modifies an MPTCTRL object
• mptctrl MPTCTRL Constructor for the MPT controller object
• plot PLOT Plots regions of the explicit controller
• plotj PLOTJ Plots value function associated to a given controller
• plotu PLOT Plots value of the control action
• addMLDconstraints ADDMLDCONSTRAINTS Adds state and output constraints to MLD matrices
• copyvalidfields COPYVALIDFIELDS copies only fields listed in 'allowedfields' from ctrlStruct to ctrl
• runtime RUNTIME returns runtime needed to compute a given explicit controller
• set SET Set a field of MPTCTRL objects
• sim SIM Simulates a given controller
• simplot SIMPLOT Plots a simulated trajectory
• subsref SUBSREF Indexed referencing for MPTCTRL object
• analyticCenter ANALYTICCENTER Computes an analytic center of a polytope
• and AND Intersection of n polytopes
• bounding_box BOUNDING_BOX Compute a bounding box for a given polytope
• chebyball CHEBYBALL Computes center and radius of the largest ball inscribed in a polytope
• dimension DIMENSION Returns dimension of the given polytope
• display DISPLAY Displays details about the given polytope
• distance DISTANCE Distance between two sets
• distribpoints DISTRIBPOINTS Distribute n points such that distances between them are maximized
• dointersect DOINTERSECT Checks if two polytopes / polyarrays intersect
• domain DOMAIN Computes polytope that is mapped to an another polytope using affine map
• double DOUBLE Function used to access internal properties of the given polytope
• envelope ENVELOPE Computes envelope of n polytopes
• eq EQ Checks if two polytopes are equal
• extreme EXTREME Calculates extreme points of a given polytope
• facetcircle FACETCIRCLE Returns largest circle inside facet 'ind' of polytope P
• facetvoronoi FACETVORONOI Computes an equivalent of voronoi diagrams for facets
• fliplr FLIPLR Flips array of polytopes
• ge GE Checks if polytope P is a superset of polytope Q
• get GET Get polytope properties
• getInnerEllipsoid GETINNERELLIPSOID Computes the largest ellipsoid inscribed in a polytope
• getOutterEllipsoid GETOUTTERELLIPSOID Computes the smallest ellipsoid which covers the polytope P
• gt GT Checks if polytope P is a strict superset of polytope Q
• horzcat HORZCAT Concatenates polytopes into a polytope array
• hull HULL Convex hull of n polytopes
• intersect INTERSECT Intersection of 2 polytopes or polytope arrays
• isbounded ISBOUNDED Checks if a polytope is bounded
• isconvex ISCONVEX Checks if a polytope array forms a convex union
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• isinside ISINSIDE Checks if a given point lies in the interior of a given polytope
• isminrep ISMINREP Checks if a given polytope is in minimal representation
• isnormal ISNORMAL Checks if a given polytope is in normalized description
• isredundant ISREDUNDANT Check if a constraint is redundant
• le LE Checks if polytope P is a subset of polytope Q
• length LENGTH Returns number of elements in a polytope array
• loadobj LOADOBJ load filter for POLYTOPE objects.
• lt LT Checks if polytope P is a strict subset of polytope Q
• merge MERGE merges polytopes together
• minus MINUS Pontryagin difference
• mldivide MLDIVIDE Set difference
• mtimes MTIMES Polytope multiplication
• nconstr NCONSTR Returns number of constraints that form an H-representation of a polytope
• ne NE Checks if two polytopes are not equal
• normalize NORMALIZE Normalizes a given polytope
• or OR Convex union of n polytopes
• pelemfun PELEMFUN Execute the specified function on each element of a polytope array
• plot PLOT Plots polytopes in 2D or 3D
• plus PLUS Minkowski sum of two polytopes
• polytope POLYTOPE Default constructor for the POLYTOPE object
• bboxvertices BBOXVERTICES Computes all vertices of a bounding box
• chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• lrs_adj adjacency information
• lrsextreme
• uniquerows2 UNIQUEROWS1 Fast method to obtain indices of unique rows of a given matrix
• projection PROJECTION Projection of a polytope or a polytope array
• range RANGE Affine transformation of a polytope
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• reduceunion REDUCEUNION Removes redundant elements from a polytope array
• regiondiff REGIONDIFF Region difference
• regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space
• set SET Used to modify internal properties of a given polytope object
• size SIZE Returns size of the given polytope object
• slice SLICE cuts a polytope (polytope array) at prespecified values
• subsasgn SUBSASGN Indexed assignments for polytope objects
• subsref SUBSREF Indexed referencing for polytope objects
• triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes
• uminus UMINUS Unary minus for a polytope
• union UNION convex union computation
• unique UNIQUE Removes redundant entries from a polytope array
• uplus UPLUS Unary plus for a polytope
• vertcat VERTCAT Concatenates polytopes into a polytope array
• volume VOLUME Calculates volume of a polytope
• ballandplatedemo "Ball and Plate" demo
• mpt_demo1 MPT_DEMO1 Explains basic manipulation with polytopes
• mpt_demo2 MPT_DEMO2 Tour through visualization capabilities of the toolbox
• mpt_demo3 MPT_DEMO3 Explains control routines for LTI systems
• mpt_demo4 MPT_DEMO4 Control of PWA systems
• mpt_makedemos MPT_MAKEDEMOS creates MAT files with data needed to run demos
• two_tanks TWO_TANKS 2nd order PWA example
• two_tanks_sim TWO_TANKS_SIM S-function of the two tank system
• duffing_oscillator Duffing Oscillator example (nonlinear system)
• pw_nonlin Example of an piecewise nonlinear model:
• ownmpc10
• ownmpc4
• ownmpc7
• ownmpc8
• reachdemo2 reachability computation demo
• verifdemo1 verification demo
• verifdemo2 verification demo
• mpt_buildAdjacency MPT_BUILDADJACENCY Builds adjacency information
• mpt_checkLyapFct MPT_CHECKLYAPFCT Checks if a function is a Lyapunov function for a given ctrlStruct
• mpt_computePWATset MPT_COMPUTEPWATSET Computes a stabilizing control invariant set (+ controllers) around the origin
• 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_getQuadLyapFct MPT_GETQUADLYAPFCT Computes common Lyapunov function for PWA system
• 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_isPWAbigger MPT_ISPWABIGGER Test if one PWA function is bigger than a second PWA function
• 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
• 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_transmap MPT_TRANSMAP Computes transition map
• mpt_verify MPT_VERIFY Verifies if states enter a given set in a given number of steps
• display DISPLAY Display information about a HASHTABLE object
• hashtable HASHTABLE Constructor for the HASHTABLE object
• subsasgn SUBSREF Subreferencing operator for HASHTABLE objects
• subsref SUBSREF Subreferencing operator for HASHTABLE objects
• identifyRegion IDENTIFYREGION plots the number of the polytopes into the current figure
• mousepoly MOUSEPOLY Allows to specify polytope by mouse-clicks
• mpt_addTset MPT_ADDTSET Adds terminal set constraint to Matrices
• mpt_allcombs MPT_ALLCOMBS All combinations of discrete-valued inputs
• mpt_defaultField MPT_DEFAULTFIEL Sets default value of field of a structure
• mpt_defaultOptions MPT_DEFAULTOPTIONS Sets default values of undefined fields of Options structure
• mpt_dlqr MPT_DLQR Linear-quadratic regulator design for discrete-time systems.
• mpt_dummyCS MPT_DUMMYCS Returns a dummy controller structure
• mpt_evalPWA MPT_EVALPWA Evaluates a PWA function at a given location
• mpt_evalSystem MPT_EVALSYSTEM Extracts data from sysStruct and probStruct structures
• mpt_feasibleStates MPT_FEASIBLESTATES returns equidistantly spaced data points in feasible set
• mpt_getCommonLyapFct MPT_GETCOMMONLYAPFCT Computes common Lyapunov function for PWA system
• mpt_getFullRankSubset MPT_GETFULLRANKSUBSET Removes rows from matrix Gt until it has full row rank
• mpt_getOptimizer MPT_GETOPTIMIZER For a given state, extracts the optimizer obtained by a multi-parametric solver
• mpt_greedyMerging MPT_GREEDYMERGING Greedy merging of polyhedra
• mpt_ineq2eq MPT_INEQ2EQ Detects inequality constraints whihc form equalities
• mpt_isValidCS MPT_ISVALIDCS Checks if input argument is a valid controller structure
• mpt_isnoise MPT_ISNOISE Checks if noise object is not empty
• mpt_issysstruct MPT_ISSYSSTRUCT Returns true if input argument is a sysStruct structure
• mpt_lrs MPT_LRS Matlab implementation of the LRS algorithm
• mpt_lti2pwa MPT_LTI2PWA Converts an LTI system to a PWA system
• mpt_mergeCS MPT_GLUECS Merges a cell array of ctrlStruct structures
• mpt_mldsim MPT_MLDSIM Simulates an MLD system for one time step
• 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_mpsol2ctrl MPT_MPSOL2CTRL Convert solution of multi-parametric program into a controller structure
• mpt_norm2pwa MPT_NORM2PWA transformes a linear norm into an equivalent PWA fcn representation
• mpt_optControlPWAold MPT_OPTCONTROLPWA Solves the CFTOC problem for a given PWA system
• mpt_options MPT_OPTIONS Read / modify solver settings for MPT
• mpt_performance MPT_PERFORMANCE Computes performance (i.e. sum of closed-loop costs) associated to a given controller
• 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_pwa2hys MPT_PWA2HYS Converts a PWA system described in sysStruct into a HYSDEL model
• mpt_randLTISys MPT_RANDLTISYS Generates random LTI systems
• mpt_randPWASys MPT_RANDPWASYS generates random PWA systems
• mpt_solveLPi MPT_SOLVELPi Interface to various LP solvers (version without errorchecks)
• mpt_solveLPs MPT_SOLVELPS Interface to various LP solvers ("safe" version)
• mpt_solverInfo MPT_SOLVERINFO returns information about a given solver
• mpt_statusbar Status bar function
• mpt_sysStructInfo MPT_SYSSTRUCTINFO Returns information about system structure
• mpt_update MPT_UPDATE Checks for updates of the Multi-Parametric Toolbox
• mpt_verifyProbStruct MPT_VERIFYPROBSTRUCT Verifies the probStruct structure
• mpt_verifySysProb MPT_VERIFYSYSPROB Verifies system and problem structures
• mpt_verifySysStruct MPT_VERIFYSYSSTRUCT Verifies the sysStruct structure
• mpt_yalmip2mpt mpt_yalmip2mpt - expand YALMIP model and convert it to MPT format
• mpt_yalmipDU MPT_YALMIPDU Augmentes the system to cope with deltaU constraints
• mpt_yalmipTracking MPT_YALMIPTRACKING Extends system and problem matrices to deal with tracking
• sbprogress [nph,nfh] = function SBPROGRESS(ph,x,msg,fh,title,modal)
• sub_computeTrajectory sub_COMPUTETRAJECTORY Calculates time evolution of state trajectories subject to control
• sub_getyalmipdata SUB_GETYALMIPDATA Internal function
• sub_setyalmipdata Copyright is with the following author(s)
• unitbox UNITBOX Creates a unit box centered at origin
• within
• PWAwelldefined 1.) check if the polyhedral partition covers the whole xr-ur space defined
• findFAS ===============================================================================
• hys2pwa HYS2PWA Transformation of HYSDEL model into PWA model
• mpt_hyparr ===============================================================================
• mpt_pwa2mld MPT_PWA2MLD Converts a PWA system into the MLD representation
• mpt_pwa2sys MPT_PWA2SYS Converts structure generated by hys2pwa.m to a sysStruct structure
• remAL ===============================================================================
• syminfo info = syminfo(S, vname, vtype, vkind, vindex)
• gen_log ===============================================================================
• mpc_buildmatFAST ===============================================================================
• mpc_checkSysWeight ===============================================================================
• mpc_mip ===============================================================================
• 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_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems
• 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_nonlinfcn MPT_NONLINFCN Template function for (piecewise) nonlinear systems
• mpt_oneStepCtrl MPT_ONESTEPCTRL Computes low complexity controller for LTI systems
• mpt_optBoolCtrl MPT_OPTBOOLCTRL Computes optimal controller for systems with discrete inputs
• mpt_optControl MPT_OPTCONTROL Solves the CFTOC problem for a given LTI system
• 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_optInfControlPWA MPT_OPTINFCONTROLPWA Solves the infinite-time constrained optimal control problem for PWA systems
• mpt_optMixedCtrl MPT_OPTMIXEDCTRL Computes optimal controller for systems discrete and continuous inputs
• mpt_optQuadCtrl MPT_OPTQUADCTRL CFTOC of PWA systems with quadratic cost
• 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_yalmipcftoc MPT_YALMIPCFTOC CFTOC of PWA systems
• intersectHP1 Tobias Geyer, 2003-2004
• mpt_exHyperAdv ===============================================================================
• mpt_hyparr2 ===============================================================================
• mpt_intersectHP1 Tobias Geyer, 2003-2004
• mpt_merge5 ===============================================================================
• mpt_optMerge ===============================================================================
• mpt_optMergeDivCon ===============================================================================
• polyinnerball CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• readEspressoOne ===============================================================================
• tg_polyreduce
• writeEspressoOnOff ===============================================================================
• hull HULL Converts vertices/polytope array into an H-representation polytope
• 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_plotJ MPT_PLOTJ Plots value function associated to a given controller
• mpt_plotLyapunov MPT_PLOTLYAPUNOV Plots lyapunov function stored in a controlle
• mpt_plotPWA MPT_PLOTPWA Plots a PWA function defined over a given polyhedral partition
• mpt_plotPWQ MPT_PLOTPWQ Plots a PWQ function defined over polyhedral partition
• mpt_plotPartition MPT_PLOTPARTITION Plots a polyhedral partition obtained by mpt_control
• mpt_plotSysStruct MPT_PLOTSYSSTRUCT Plots the system partitions of a PWA system
• mpt_plotTimeTrajectory MPT_PLOTTIMETRAJECTORY Plots trajectories of states, inputs, outputs and disturbances
• mpt_plotTrajectory MPT_PLOTTRAJECTORY Graphical interface for piloting trajectories for LTI and PWA systems subject to control
• mpt_plotU MPT_PLOTU For a given explicit controller, plots value of the control action
• mpt_plotellip mpt_PLOTELLIP function to plot polytopes
• 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_init MPT_INIT Initializes the MPT toolbox
• mpt_invariantSet MPT_INVARIANTSET Computes (robust) positive invariant subset of an explicit controller
• mpt_lyapunov MPT_LYAPUNOV Computes a Lapunov-type function for a given explicit controller
• mpt_ownmpc MPT_OWNMPC The "Design your own MPC" function
• mpt_setup MPT_SETUP Main setup function
• mpt_simSys MPT_SIMSYS Simulates evolution of a given system
• mpt_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law
• mpt_studio MPT_STUDIO MPT Graphical user interface
• mpt_sys MPT_SYS Converts an object to sysStruct structure
• runExample RUNEXAMPLE Demonstrates MPT control routines
• mpt_mplp MPT_MPLP Explicitly solves the given linear program (LP)
• mpt_mpmilp MPT_MPMILP Multi-Parametric Mixed-Integer LP solver
• mpt_mpmiqp MPT_MPMIQP Multi-Parametric Mixed-Integer QP solver
• mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)
• mpt_solveLP MPT_SOLVELP Interface to various LP solvers
• 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