50 lines
1.6 KiB
Mathematica
50 lines
1.6 KiB
Mathematica
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%%***********************************************************
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%% lmiexamp3: generate SDP data for the following LMI problem
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%%
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%% max eta
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%% s.t. [A*P+P*A' P*B'] + eta*[0 0] <= [-G 0]
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%% [B*P 0 ] [0 I] [ 0 0]
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%% P >= 0
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%% P and eta are variables, P symmetric.
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%%
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%% Ref: Body et al, Linear matrix inequalities in system and
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%% control theory, p. 10.
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%%***********************************************************
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%% Here is an example on how to use this function to
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%% find an optimal P.
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%%
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%% A = [-1 0 0; 0 -2 0; 1 1 -1];
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%% B = [1 3 5; 2 4 6];
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%% G = ones(3,3);
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%%
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%% [blk,Avec,C,b] = lmiexamp3(A,B,G);
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%% [obj,X,y,Z] = sqlp(blk,Avec,C,b);
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%% n = size(A,2); N = n*(n+1)/2;
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%% blktmp{1,1} = 's'; blktmp{1,2} = n;
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%% P = smat(blktmp,y(1:N));
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [blk,Avec,C,b] = lmiexamp3(A,B,G);
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%%
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[m,n] = size(A);
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[m2,n2] = size(B);
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if (n ~= n2); error('lmiexamp3: A, B not compatible'); end;
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%%
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blk{1,1} = 's'; blk{1,2} = m + m2;
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I = speye(n);
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Avec(1,1) = lmifun2(A,I,I,B);
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tmp = [sparse(m,n+m2); sparse(m2,n) speye(m2,m2)];
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Avec{1} = [Avec{1} svec(blk,tmp,1)];
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%%
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C{1,1} = [-G sparse(m,m2); sparse(m2,n+m2)];
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%%
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N = n*(n+1)/2;
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b = [zeros(N,1); 1];
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%%**********************************************************
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