Description of mpt_iterativePWA

DESCRIPTION

MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems

 ctrlStruct = mpt_iterativePWA(sysStruct,probStruct),
 ctrlStruct = mpt_iterativePWA(sysStruct,probStruct,Options),

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 DESCRIPTION
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 Computes the solution of a minimum-time problem for a given PWA system
       x(k+1) = A_i x(k) + B_i u(k) + f_i
       y(k)   = C_i x(k) + D_i u(k) + g_i
       for i such that guardX(i) x(k) + guardU(i) u(k) <= guardC(i)  
   s.t.
       (ymin, ymax, umin, umax, dumin, dumax)

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 INPUT
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 sysStruct           - System structure in the sysStruct format
 probStruct          - Problem structure in the probStruct format

 Options.iterative=0    
       Use reduced-switching policy (0=no, 1=yes)
 Options.maxiterations=100
       Maximum number of iterations
 Options.lyapunov_type
       a string which denotes which Lyapunov function should be computed to
       testify stability of one-step controllers:
         'any'  - first a PWQ function is computed, if it fails, a PWA
                  Lyapunov function will be computed as well
         'pwq'  - only PWQ Lyapunov function
         'pwa'  - only PWA Lyapunov function
         'none' - do not compute any Lyapunov function; no closed-loop
                  stability is guaranteed
 Options.verbose
       Level of verbosity (see help mpt_init for more details)
 Options.PWA_savemode=0
       Saving intermediate results in fesibility iterations.
 Options.PWA_warmend=0
       Loads an intermediate result and finishes the controller calculations.
           (without trying to extend the feasible region).
 Options.PWA_loadn=0
       Loads intermediate result from iteration n. (0=Uses last iteration.)
 Options.PWA_savefile='PWA_save'
       Specifies filename prefix for result files.
           Filename is appended with iteration number.
 Options.PWA_savefilelast='PWA_lastsave'
       Specifies filename for info about last sucessful iteration.
 Options.PWA_warmstart=0 (Not implemented yet)
       Loads intermediate result (latest or n), and continues feasibility iteration. 
 Options.PWA_maxTsetTime=Inf
       Interrupts the feasibility iterations after specified time, and continues with 
           current feasible set.
 Options.details
       If set to 1, provides some details about the solution in
       truct.details. (default value controlled by mptOptions.details)

 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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 ctrlStruct    - Controller structure with following fields:
   Pn,Fi,Gi    - for region Pn(i).H*x <= Pn.K(i) computed input is U=Fi{i}*x+Gi{i}   
   Ai,Bi,Ci    - cost associated to each region (x'Aix + Bi*x + Ci)
                 Note that Ai and Bi are zero matrices, Ci contains the
                 step distance to the origin
   Pfinal      - The maximum control invariant set as a polytope or a polyarray
   dynamics    - Dynamics active in region Pn(i)
   details     - Details about the solution

 see also MPT_CONTROL, MPT_ITERATIVE

CROSS-REFERENCE INFORMATION

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

dimension DIMENSION Returns dimension of the given polytope

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

end END Returns the last element in a given polytope array

fliplr FLIPLR Flips array of polytopes

isfulldim ISFULLDIM Checks if a polytope is full dimensional

isminrep ISMINREP Checks if a given polytope is in minimal representation

le LE Checks if polytope P is a subset of polytope Q

length LENGTH Returns number of elements in a polytope array

merge MERGE merges polytopes together

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

reduceunion REDUCEUNION Removes redundant elements from a polytope array

regiondiff REGIONDIFF Region difference

regiondiffXU REGIONDIFFXU Computes region difference in lifted XU space

size SIZE Returns size of the given polytope object

union UNION convex union computation

unique UNIQUE Removes redundant entries from a polytope array

mpt_computePWATset MPT_COMPUTEPWATSET Computes a stabilizing control invariant set (+ controllers) around the origin

mpt_getPWALyapFct MPT_GETPWALYAPFCT Calculates PWA Lyapunov function

mpt_getPWQLyapFct MPT_GETPWQLYAPFCT Calculates PWQ Lyapunov function

mpt_getQuadLyapFct MPT_GETQUADLYAPFCT Computes common Lyapunov function for PWA system

mpt_removeOverlaps MPT_REMOVEOVERLAPS Removes overlaps from (a set of) polyhedral partitions with associated linear cost

mpt_addTset MPT_ADDTSET Adds terminal set constraint to Matrices

mpt_error MPT_ERROR Function called if MPT toolbox is not initialized

mpt_isnoise MPT_ISNOISE Checks if noise object is not empty

mpt_lti2pwa MPT_LTI2PWA Converts an LTI system to a PWA system

mpt_statusbar Status bar function

mpt_sysStructInfo MPT_SYSSTRUCTINFO Returns information about system structure

mpt_verifySysProb MPT_VERIFYSYSPROB Verifies system and problem structures

mpt_constructMatrices MPT_CONSTRUCTMATRICES Constructs matrices for the finite time constrained optimal control problem

mpt_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems

mpt_mplp MPT_MPLP Explicitly solves the given linear program (LP)

mpt_mpqp MPT_MPQP Explicitly solves the given quadratic program (QP)

mpt_maxCtrlSet MPT_MAXCTRLSET Computes the maximal robust control invariant set C_inf

mpt_control MPT_CONTROL Main control routine. Computes explicit controller for a given problem

mpt_iterativePWA

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION