Randomized Algorithms Control Toolbox Code

function PerfLevel = perfwc(hFuncObj, hFuncPerf, ProbEst, Delta, varargin)
%PERFWC returns worst-case performance level estimation
%
%   PerfLevel = PERFWC(HANDLEOBJ, HANDLEPERF, PROBEST, DELTA)
%   PerfLevel = PERFWC(HANDLEOBJ, HANDLEPERF, PROBEST, DELTA, VECOBJ)
%   PerfLevel = PERFWC(HANDLEOBJ, HANDLEPERF, PROBEST, DELTA, VECOBJ, VECPERF)
%
%   returns a performance level PerfLevel such that
%   with probability at least 1-DELTA 
%   Prob{ J(.} <= PerfLevel } >= PROBEST
%   where
%   HANDLEOBJ - user-defined function with uncertain object definition,
%   HANDLEPERF - performance function ('J' in formulae above), built-in
%     function names like 'ident' etc allowed,
%   PROBEST - (high) probability to achieve,
%   VECOBJ = {-1, 0, 1} - flag to show if user-defined uncertain object allow
%     vectorization, (default = -1)
%   VECPERF = {-1, 0, 1} - flag to show if performance function allow
%    vectorization, (default = -1)
%
%   EXAMPLE
%     tic; PerfLevel = perfwc(@probworstcase_demo_ex, @probworstcase_demo_aux, 0.95, 0.01, 0); t_elapsed = toc;
%
% See also UTEST3.
%
% Calafiore, Dabbene, Tempo, "Randomized Algorithms in Robust Control", CDC42, 2003

% $Id$

% parameter check
if any([Delta >= 1, Delta <= 0])
  error(['RACT:perfwc:InputType', 'Delta should be in (0, 1) interval.']);
end
if any([ProbEst >= 1, ProbEst <= 0])
  error(['RACT:perfwc:InputType', 'ProbEst should be in (0, 1) interval.']);
end

switch nargin
  case 4
    VecObj = -1;
    VecPerf = -1;
  case 5
    VecObj = varargin{1};
    VecPerf = -1;
  case 6
    VecObj = varargin{1};
    VecPerf = varargin{2};
  otherwise
    error(['RACT:perfwc:InputSize', ['Incorrect number of parameters: ' num2str(nargin)]]);
end

% estimate number of samples by log-over-log bound
nSamples = ceil(log(1/Delta)/log(1/ProbEst));
disp(['Number of samples by ''log-over-log'' bound is: ' num2str(nSamples)]);


% calculate maximum of performance level
PerfLevel = utest3(hFuncObj, hFuncPerf, 'maxval', nSamples, VecObj, VecPerf); 
% no vectorization by object sampling, but vectorization on second crit.

disp(['With probability ' num2str(1-Delta) ',  Prob{Performance <= ' num2str(PerfLevel) '} >= ' num2str(ProbEst)]);