w3 opp1
Post on 20-Nov-2015
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u = -inv(alpha^k * R + B'*S_k1*B)*B'*S_k1*A*x;
alpha = .9;
k = randi(100);
R = diag(rand(2,1));
B = randn(4,2);
A = randn(4);
S_k1 = 100*diag(rand(4,1));
x = randn(4,1);
% your solution to u below
u = ;
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LQR with discounting | Optional Problem | 6.832x Courseware | edX https://courses.edx.org/courses/MITx/6.832x/3T2014/courseware/wee...
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M = A'*S_k1*B*inv(alpha^k*R + B'*S_k1*B)*B'*S_k1*A;
alpha = .9;
k = randi(100);
R = diag(rand(2,1));
B = randn(4,2);
A = randn(4);
S_k1 = 100*diag(rand(4,1));
% your solution to u below
M = ;
alpha = .9;
N = 10;
A = [2 1; -3 .8];
B = [0;1];
Q = diag([5;1]);
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LQR with discounting | Optional Problem | 6.832x Courseware | edX https://courses.edx.org/courses/MITx/6.832x/3T2014/courseware/wee...
2 of 3 10/01/2015 14:14
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S{N+1} = S_N;
for k=N-1:-1:0,
S_k1 = S{k+2};
M = A'*S_k1*B*inv(alpha^k*R+B'*S_k1*B)*B'*S_k1*A;
S{k+1} = alpha^k*Q - M + A'*S_k1*A;
end
S_0 = S{1}
R = 1;
S_N = 10*eye(2);
S_0 =
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LQR with discounting | Optional Problem | 6.832x Courseware | edX https://courses.edx.org/courses/MITx/6.832x/3T2014/courseware/wee...
3 of 3 10/01/2015 14:14
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