Description of mpt_simplexContr

DESCRIPTION

MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices

 function [ctrlStruct,vol]=mpt_simplexContr(sysStruct,probStruct,Options)

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 DESCRIPTION
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 Partitions the feasible set into simplical cells and subsequently computes 
 the input sequence for each vertex of each simplex. By linear interpolation, 
 we obtain a piecewise affine feedback law defined for each simplex.

               This function is not based on multi-parametric programming !

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 INPUT
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 sysStruct       - System structure in the sysStruct format (see Manual)
 probStruct      - Problem structure in the probStruct format (see Manual)
 Options.verbose - Level of verbosity
 Options.maxCtr  - Maximum number of iterations (default is 1000)

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 OUTPUT
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 ctrlStruct    - controller structure with the 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    - open-loop cost associated to each region (x'Aix + x'Bi + Ci)
   Pfinal      - Defines the feasible state space partition (i.e. union of
                 all regions) as Phard.H*x<=Phard.K
   dynamics    - dynamics active in region Pn(i)
   details     - contains additional information:
                 +Volume: volume of polySet

  vol          - the volume of the controller partition

CROSS-REFERENCE INFORMATION

length LENGTH Returns number of regions over which the explicit control law is defined

mptctrl MPTCTRL Constructor for the MPT controller object

plot PLOT Plots regions of the explicit controller

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

hull HULL Convex hull of n polytopes

isfulldim ISFULLDIM Checks if a polytope is full dimensional

length LENGTH Returns number of elements in a polytope array

plot PLOT Plots polytopes in 2D or 3D

polytope POLYTOPE Default constructor for the POLYTOPE object

projection PROJECTION Projection of a polytope or a polytope array

size SIZE Returns size of the given polytope object

triangulate TRIANGULATE Calculates triangulation of arbitrary polytopes

mpt_error MPT_ERROR Function called if MPT toolbox is not initialized

mpt_verifyProbStruct MPT_VERIFYPROBSTRUCT Verifies the probStruct structure

mpt_verifySysStruct MPT_VERIFYSYSSTRUCT Verifies the sysStruct structure

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

hull HULL Converts vertices/polytope array into an H-representation polytope

mpt_solveLP MPT_SOLVELP Interface to various LP solvers

mpt_solveQP MPT_SOLVEQP Interface to various QP solvers

runExample RUNEXAMPLE Demonstrates MPT control routines

mpt_simplexContr

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION