How to predict a partial state-space model by specifying an initial state-space model.

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健斗
健斗 2023-12-14
回答： Tianyu 2024-5-1
Using this link (https://jp.mathworks.com/help/ident/ref/ssest.html#btpb7ww-5) as a reference, I predicted a state-space model using tt data as gray-box modeling with system identification.
I constructed init_sys and tried to estimate only the "NaN" part of the matrix, leaving the other elements as fixed values.
However, the output matrices were all free coefficients.
How can I estimate only the "NaN" part?
I thought that specifying "NaN" was not a good idea, so I put the nominal values in init_sys, but the output results were exactly the same as the nominal values.
Is it still dependent on the initial value matrix?
Code is following (This is a linear approximation model of cart pole.)
%grayboxmodeling
% State Space
A = [0 1 0 0
0 0 NaN 0
0 0 0 1
0 0 NaN 0];
B = [0
NaN
0
NaN];
C = eye(4);
D = zeros(4,1);
K = zeros(4,4);
x0 = [0;
0;
-0.03;
0];
Ts = 0.02;
init_sys = idss(A,B,C,D,K,x0,Ts);
apar = init_sys.Structure.A;
apar.Free(1,:) = false;
apar.Free(2,1) = false;
apar.Free(2,2) = false;
apar.Free(2,3) = true;
apar.Free(2,4) = false;
apar.Free(3,:) = false;
apar.Free(4,1) = false;
apar.Free(4,2) = false;
apar.Free(4,4) = false;
init_sys.Structure.A = apar;
bpar = init_sys.Structure.B;
bpar.Free(1,1) = false;
bpar.Free(3,1) = false;
init_sys.Structure.B = bpar;
init_sys.Structure.C.Free = false;
sysgray = ssest(tt,init_sys)

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采纳的回答

Tianyu
Tianyu 2024-5-1
Hi 健斗,
NaN is not accepted since the estimation requires a valid initial value to start.
The following code works for me.
%grayboxmodeling
load sdata2 tt2
tt = tt2;
% State Space
A = [0 1 0 0
0 0 1 0
0 0 0 1
0 0 1 0];
B = [0
1
0
1];
C = eye(1,4);
D = zeros(1,1);
K = zeros(4,1);
x0 = [0;
0;
-0.03;
0];
Ts = 0.1;
init_sys = idss(A,B,C,D,K,x0,Ts);
apar = init_sys.Structure.A;
apar.Free(1,:) = false;
apar.Free(2,1) = false;
apar.Free(2,2) = false;
apar.Free(2,3) = true;
apar.Free(2,4) = false;
apar.Free(3,:) = false;
apar.Free(4,1) = false;
apar.Free(4,2) = false;
apar.Free(4,4) = false;
init_sys.Structure.A = apar;
bpar = init_sys.Structure.B;
bpar.Free(1,1) = false;
bpar.Free(3,1) = false;
init_sys.Structure.B = bpar;
init_sys.Structure.C.Free = false;
sysgray = ssest(tt,init_sys)
>> sysgray.A
ans =
0 1.0000 0 0
0 0 2.2653 0
0 0 0 1.0000
0 0 0.2710 0

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