On 17.06.2012, at 23:17, Ido Halperin wrote:
> Hello Lukas
>
> I appreciate your quick reply and I a apologize for the delay in my
> response. It took me some time to compile octave. Usually I makes use of
> debian binaries.
>
> a. Relating the results you attached, they seems to me erroneous. I
> compared the stable eigenvalues of the Hamiltonian:
>
> S = Bum*(R\Bum');
> H = [Am -S; -Qm -Am'];
> lambda1 = eig(H)
>
> and the eigenvalues of the closed loop system, according to the 'Km' you
> attached:
> lambda2 = eig(Am - Bum*Km);
>
> and they differ.
>
>
>
> b. I downloaded octave 3.6.2 source and lapack 3.4.1 from netlib and
> compiled them. It didn't helped. It gives the following:
>
>
> octave:33> [Km riccPm] = lqr(Am,Bum,Qm,R);
> error: are: 4: after reordering, roundoff changed values of some complex
> eigenvalues so that leading eigenvalues in the (generalized) Schur form
> no longer satisfy the stability condition; this could also be caused due
> to scaling
> error: called from:
> error: /home/ido/octave/control-2.3.51/care.m at line 162, column 15
> error: /home/ido/octave/control-2.3.51/lqr.m at line 95, column 16
> octave:33> [Km riccPm] = lqr(Am,Bum,Qm,R*3);
> error: are: 5: the computed dimension of the solution does not equal N
> error: called from:
> error: /home/ido/octave/control-2.3.51/care.m at line 162, column 15
> error: /home/ido/octave/control-2.3.51/lqr.m at line 95, column 16
> octave:33>
>
>
> Ido
Hi Ido
Have you tried to scale your equations in order to enhance numerics? SLICOT has
+/- 3 solvers for AREs: SB02MD, SB02OD and SB02RD:
Riccati Equations
SB02MD
Solution of algebraic Riccati equations (Schur vectors method)
SB02MT
Conversion of problems with coupling terms to standard problems
SB02ND
Optimal state feedback matrix for an optimal control problem
SB02OD
Solution of algebraic Riccati equations (generalized Schur method)
SB02PD
Solution of continuous algebraic Riccati equations (matrix sign
function method) with condition and forward error bound estimates
SB02QD
Condition and forward error for continuous Riccati equation solution
SB02RD
Solution of algebraic Riccati equations (refined Schur vectors method)
with condition and forward error bound estimates
SB02SD
Condition and forward error for discrete Riccati equation solution
I chose SB02OD back in 2010 because it was the easiest one to implement.
Unfortunately, SB02OD has no automatic scaling (the other 2 have it) and one of
my profs told me that the algorithm is not the most reliable one. Maybe we
should try SB02RD in conjunction with SB02MT, and I could ask the SLICOT
authors for their advice.
Lukas
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