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* Draft * Analysis * Synthesis -> LMI? * Synthesis?* -> Lyapunov?* -> LQR?* -> LMI? * Advanced Usage? * Theory Theory * -> Analysis * -> Synthesis -> LMI? * Synthesis* -> Lyapunov?* -> LQR* -> LMI? * Methods

Draft

Common user-toolbox interaction

PreUsage

Add /ract directory in Matlab path

Directory tree and files

-- @UBASE

 definition and few auxilary routines for a new type of variable:
 uncertain parameter
 -- PRIVATE
   routines for random matrix generation (NO EDIT NEED)
 -- display.M
   nice way to display uncertain param. variable in Matlab (EDIT ONLY
   IN CASE of new random distributions)
 -- distrtype.M
   auxilary (NO EDIT NEED)
 -- ubase.M
   create a new uncertain variable, for more details type 'help ubase'
   (EDITABLE)
 -- ubasesample.M
   return some number of samples of an uncertain variable (EDITABLE)

-- ADDONS

 generators of random in some case matrices
 (obsolete, saved for historical  reasons and in reserve)
 most of the code used in @UBASE/PRIVATE (NO EDIT NEED)

-- PRIVATE

 two main subroutines of the toolbox
 -- plusproj.M
   projection of symmetric matrix to the cone of positive matrices
   (EDITABLE)
 -- usample.M
   sampling of uncertain variables, but can accept cell arrays of
   uncertain variables! (for the first glance, NO EDIT NEED)

-- RACTDEMOS

  -- hurwitz_demo.M
     a demonstration of the toolbox. The only one yet. :-)
     Usage: make RACT\RACTDEMOS as current dir, and run it
     (ABSOLUTELY EDITABLE)

-- RACTTEMPLATES

  templates for users and developers
  -- tmpl_function.M
    template for user-defined function, that
    1 -- should define a set of uncertain variables
    2 -- should return an object by given samples of uncertain
    variables (EDITABLE)
  -- tmpl_help1.M
    inline help lines structure

ex_lqr.M

  script of an example to test.
  Unfortunately, I've failed to make use of it, so (SKIP & EDITABLE)

ex1_a.M

  same as previous (SKIP & EDITABLE)

ex_robhurwitz.M

  example of user-defined polynomial, the task is to check probability
  of stability of the uncertain polynomial. Used by HURWITZ_DEMO.M
  (ABSOLUTELY EDITABLE)

lqr_grad.M

  a try to implement construction of LQR-controller. Failed (seems to
  be error somewhere) (SKIP & EDITABLE)

 !!ok, now the issue files!!

uevaluate.M

  return array of uncertain object samples,
  by evaluating user-defined uncertain function on a number of samples
  allows vectorization
  (seems GOOD, by still EDITABLE)

uprobperf.M

  check if a property of an uncertain object performs with accuracy Eps and

confidence 1-Delta

  both the property and uncertain object given by links to
  user-defined functions. Chernoff bound used for the number of
  samples needed. (EDITABLE)
  It is the most thing possible in the toolbox.

utest.M

  return a portion of samples of uncertain object, for which a
  property satisfied (property and object are defined by user)
  Used to estimate of probabilty if perfomance.
  Few properties, namely 'unit', 'is_hurwitz', 'is_schur',
  'is_positive_definite' are already implemented as subfunctions
  (ABSOLUTELY EDITABLE)

The mechanism/usage.

Keep in mind that only the perfomance probability estimation works.

Step 1.

  User defines an uncertain object by creating and naming
  a function using the template TMPL_FUNCTION.M,
  this function must return an object itself or the value of
  a property (0 -- if not satisfied, 1 -- if satisfied)

Step 2.

  User calls
  prob_est = UPROBPERF(user_function_name, 'hurwitz', Eps, Delta)
  where 'schur' or 'posdef' as second argument are possible
  to check corresponding property, or 'unit' if user function  already returns the property of an uncertain object;
  Eps is accuracy and 1-Delta is confidence level.

Background

Vectorization and parameter calling conventions. To discuss.

Errata

Found an incompatability with Matlab 6. Latest version at .

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Page last modified on February 27, 2007, at 10:15 PM