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Reduced-order discrete-time LQG design for systems with white parameters

Reduced-order discrete-time LQG design for systems with white parameters

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22 May 2008 (Updated )

Optimal compensation of time-varying discrete-time linear systems with white stochastic parameters

[pm,gm,cm,pms,gms,cms,pgms,pcms,pva,gva,cva,pgva,pcva,...
% SPRTVVEX : Function specifying a reduced-order infinite horizon
%            discrete-time LQG problem with white paramaters.
%
%            [pm,gm,cm,pms,gms,cms,pva,gva,cva,v,w,q,r,nc,H,x0c,...
%            N,x0m]=sprotvex(i);
%
%            L.G. Van Willigenburg, W.L. De Koning, 28-11-95.
%
% Remark:    The problem data were originally obtained from Matlab's
%            function drmodel. They are now typed since the output
%            of drmodel has changed in recent Matlab versions.
%            This is probably due to a change in output of the build-in
%            Matlab function orth used by drmodel.
%
%
  function [pm,gm,cm,pms,gms,cms,pgms,pcms,pva,gva,cva,pgva,pcva,...
            v,w,q,r,mc,me,nc,H,x0c,N,x0m]=sprtvvex(i);

%
% Uncertainty measure lambda
%
  global lambda;
%
% Mean model
%
  nx=2; nu=1; ny=1; srp=1.25; seed=10;
  pm=[-0.9653 0.7942; -0.7942 -0.9653];
  gm=[0.4492; 0.1784]; cm=[0.6171 0.3187];
  v=diag([0.7327 0.8612]); me=[-0.06770117183575; -0.05359504337124];
  q=diag([0.0437 0.1108]); mc=[-0.08594697024019; -0.01072882684447];
  w=0.9334; r=0.3311;

% Time-varying pm  
  pm=(1+0.2*sin(i-1))*pm;

%
% Model uncertainty computation.
%
  pms=kron(pm,pm) ; pva=lambda*pms  ; pms=pms+pva;
  gms=kron(gm,gm) ; gva=lambda*gms  ; gms=gms+gva;
  cms=kron(cm,cm) ; cva=lambda*cms  ; cms=cms+cva;
  pgms=kron(pm,gm); pgva=lambda*pgms; pgms=pgms+pgva;
  pcms=kron(pm,cm); pcva=lambda*pcms; pcms=pcms+pcva;

  H = 0.1*eye(nx);
%
% initial state statistics
% 
  x0c=H; x0m=ones(nx,1);
%
% Number of time steps
%
  N = 9;
%
% Prescribed compensator order
%
  nc=[1 1 1 1 2 2 1 1 1 1];

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