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make feedback differentiable by avoiding try-catch #596

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make feedback differentiable by avoiding try-catch #596

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31 changes: 14 additions & 17 deletions src/connections.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -286,28 +286,23 @@ See Zhou, Doyle, Glover (1996) for similar (somewhat less symmetric) formulas.
D = [s1_D11 + α*s1_D12*s2_D22*s1_D21 α*s1_D12*s2_D21;
s2_D12*s1_D21 s2_D11 + α*s2_D12*s1_D22*s2_D21]
else
# inv seems to be better than lu
R1 = try
inv(α*I - s2_D22*s1_D22) # slightly faster than α*inv(I - α*s2_D22*s1_D22)
catch
R1 = lu(α*I - s2_D22*s1_D22, check=false) # slightly faster than α*inv(I - α*s2_D22*s1_D22)
issuccess(R1) || # Avoid try-catch for differtiability
error("Ill-posed feedback interconnection, I - α*s2_D22*s1_D22 or I - α*s2_D22*s1_D22 not invertible")
end

R2 = try
inv(I - α*s1_D22*s2_D22)
catch
R2 = lu(I - α*s1_D22*s2_D22, check=false)
issuccess(R2) || # Avoid try-catch for differtiability
error("Ill-posed feedback interconnection, I - α*s2_D22*s1_D22 or I - α*s2_D22*s1_D22 not invertible")
end

A = [sys1.A + s1_B2*R1*s2_D22*s1_C2 s1_B2*R1*s2_C2;
s2_B2*R2*s1_C2 sys2.A + α*s2_B2*R2*s1_D22*s2_C2]
A = [sys1.A + s1_B2*(R1\s2_D22)*s1_C2 s1_B2*(R1\s2_C2);
s2_B2*(R2\s1_C2) sys2.A + α*s2_B2*(R2\s1_D22)*s2_C2]

B = [s1_B1 + s1_B2*R1*s2_D22*s1_D21 s1_B2*R1*s2_D21;
s2_B2*R2*s1_D21 s2_B1 + α*s2_B2*R2*s1_D22*s2_D21]
C = [s1_C1 + s1_D12*R1*s2_D22*s1_C2 s1_D12*R1*s2_C2;
s2_D12*R2*s1_C2 s2_C1 + α*s2_D12*R2*s1_D22*s2_C2]
D = [s1_D11 + s1_D12*R1*s2_D22*s1_D21 s1_D12*R1*s2_D21;
s2_D12*R2*s1_D21 s2_D11 + α*s2_D12*R2*s1_D22*s2_D21]
B = [s1_B1 + s1_B2*(R1\s2_D22)*s1_D21 s1_B2*(R1\s2_D21);
s2_B2*(R2\s1_D21) s2_B1 + α*s2_B2*(R2\s1_D22)*s2_D21]
C = [s1_C1 + s1_D12*(R1\s2_D22)*s1_C2 s1_D12*(R1\s2_C2);
s2_D12*(R2\s1_C2) s2_C1 + α*s2_D12*(R2\s1_D22)*s2_C2]
D = [s1_D11 + s1_D12*(R1\s2_D22)*s1_D21 s1_D12*(R1\s2_D21);
s2_D12*(R2\s1_D21) s2_D11 + α*s2_D12*(R2\s1_D22)*s2_D21]
end

return StateSpace(A, B[:, Wperm], C[Zperm,:], D[Zperm, Wperm], timeevol)
Expand Down Expand Up @@ -390,10 +385,12 @@ end

"""
starprod(sys1, sys2, dimu, dimy)
starprod(sys1, sys2)

Compute the Redheffer star product.

`length(U1) = length(Y2) = dimu` and `length(Y1) = length(U2) = dimy`
If `dimu, dimy` are not provided, the maximum interconnection is formed, where all inputs and outputs of `sys2` are connected.

For details, see Chapter 9.3 in
**Zhou, K. and JC Doyle**. Essentials of robust control, Prentice hall (NJ), 1998
Expand Down