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

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)

Answer 1

[Tianyu]

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