Description of mptctrl

DESCRIPTION

MPTCTRL Constructor for the MPT controller object

 ctrl = mptctrl(ctrlStruct)
 ctrl = mptctrl(sysStruct, probStruct)

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 DESCRIPTION
 ---------------------------------------------------------------------------

 Creates an MPT controller object. The controller can represent both an
 explicit control law (i.e. a Piecewise-Affine feedback law defined over a
 polyhedral partition of a state-space), or an implicit controller (i.e. an MPC
 controller where the optimization problem is being solved at every time step
 for current measurements of the states).

 USAGE:

   ctrl = mptctrl(ctrlStruct)

     If called with one input parameter, the input is assumed to be a
     controller structure, as defined in the MPT manual. The output will then
     be an explicit controller.

   ctrl = mptctrl(sysStruct, probStruct)

     If called with two input parameters, creates an on-line controller.

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 REPRESENTATION OF CONTROLLERS
 ---------------------------------------------------------------------------

 Each MPTCTRL object is internally represented as a structure with following
 fields:

   .type        - type of the controller {'explicit' | 'online'}
   .sysStruct   - system structure
   .probStruct  - problem structure
   .Pn          - polyhedral partition over which the explicit controller is
                  defined (POLYTOPE object)
   .Pfinal      - feasible set of the controller, i.e. set of states for which
                  there exists a control law (POLYTOPE object) 

   .Fi          - if the given state "x" is in region Pn(i), the associated
   .Gi          /    control law is given by U = Fi{i}*x + Gi{i}

   .Ai          \
   .Bi          - value of the objective function at point 'x' is given by
   .Ci          /    J = x'*Ai{i}*x + Bi{i}*x + Ci{i}

   .dynamics    - a vector which associates dynamics of a PWA system to a given
                     region of controller parition. 
   .details     - additional details about the solution
   .overlaps    - binary flag, takes a "true" value if regions of the
                     controller partition overlap, "false" otherwise
   .simplified  - binary flag, takes a "true" value if regions of the
                     controller partition have been simplified using greedy or
                     optimal merging, "false" otherwise 


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 ACCESING INTERNAL DATA OF A CONTROLLER OBJECT
 ---------------------------------------------------------------------------

 Even though the MPT controller is represented as an object, it's fields can
 still be accessed as it were a structure. That means that you can do, for
 instance, the following:

   ctrl.Pn
   ctrl.details

 and so on. There are also couple of short-cut functions defined to quickly
 access important fields:

 nR = length(ctrl)    - returns number of regions of the controller partition
 time = runtime(ctrl) - returns runtime
 isexplicit(ctrl)     - returns 1 if the controller is an explicit one, 0 if it
                          is an on-line controller

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 INPUT
 ---------------------------------------------------------------------------
 either: 
   ctrlStruct  - valid controller structure (see manual for more details)

 or:
   sysStruct   - valid system structure
   probStruct  - valid problem structure

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 OUTPUT                                                                                                    
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 ctrl          - an MPTCTRL object


 see also MPTCTRL/ANALYZE, MPTCTRL/ISEXPLICIT, MPTCTRL/LENGTH, MPTCTRL/PLOT

CROSS-REFERENCE INFORMATION

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

copyvalidfields COPYVALIDFIELDS copies only fields listed in 'allowedfields' from ctrlStruct to ctrl

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

ne NE Checks if two polytopes are not equal

polytope POLYTOPE Default constructor for the POLYTOPE object

size SIZE Returns size of the given polytope object

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_error MPT_ERROR Function called if MPT toolbox is not initialized

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_lti2pwa MPT_LTI2PWA Converts an LTI system to a PWA system

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_sysStructInfo MPT_SYSSTRUCTINFO Returns information about system structure

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_pwa2mld MPT_PWA2MLD Converts a PWA system into the MLD representation

mpc_mip ===============================================================================

mpt_blockingMatrices MPT_BLOCKINGMATRICES Constructs matrices for the CFTOC problem for move blocking strategies

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

mpt_yalmipcftoc MPT_YALMIPCFTOC CFTOC of PWA systems

modify MODIFY Modifies an MPTCTRL object

mpt_infsetPWA MPT_INFSETPWA Computes (robust) positive invariant subset for PWA systems

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_optQuadCtrl MPT_OPTQUADCTRL CFTOC of PWA systems with quadratic cost

mpt_simplexContr MPT_SIMPLEXCONTR Computes a piecewise affine feedback law defined over simplices

mpt_yalmipcftoc MPT_YALMIPCFTOC CFTOC of PWA systems

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

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_simplify MPT_SIMPLIFY simplifies a given explicit controller by merging regions with identical control law

mptctrl

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION