fixpar (System Identification Toolbox)

Fix parameters in structures defined by ms2th and arx2th.

thn = fixpar(tho,matrix)
thn = fixpar(tho,matrix,elements,parval)

Description

The fixpar function produces a new model structure thn in the theta format from an old one tho, by fixing certain parameters to certain values. The matrix tho must be originally defined by arx, arx2th, canstart, iv4, or ms2th but may have been modified later on by fixpar, pem, thinit, or unfixpar.

To modify a state-space structure

the argument matrix is set equal to one of 'A', 'B', 'C', 'D','K', or 'x0'. The argument elements is a matrix with two columns, in which each row specifies the indices of the element in the chosen system matrix that need to be fixed. For example, to fix the 1,2-element and the 3,5-element of the A matrix use

thn = fixpar(tho,'A',[1,2;3,5]);

If the argument elements is omitted (or entered as the empty matrix) all elements of the indicated matrix will be fixed. In this case parval can be given a scalar number, and all the indicated elements will be fixed to that number.

The default is that the elements are fixed to their nominal (initial or currently estimated) value. To fix them to something else use the fourth input argument parval. The r-th entry of this vector contains the value corresponding to the element defined by the r-th row of elements.

To modify an ARX model

the argument matrix is set equal to one of 'A1', 'A2', ..., 'B0', 'B1', .... The argument elements is then a matrix with two columns, where each row gives the indices of the element in the chosen ARX matrix that need to be fixed. The role of parval is the same as for the state-space case above.

The routine does not apply to special model structures that you have originally defined using mf2th, or to black-box input-output models other than ARX models. Fixing certain parameters can, in those cases, be achieved by using the third argument in pem during the estimation phase.

Examples

Converting a state-space structure with all elements in the Kalman gain matrix K free to an output error structure in which K is fixed to zero.

thn = fixpar(thn,'K',[],0)

Fixing the

parameter to 1 in a scalar ARX model, and then estimating the remaining parameters:

th = arx(z,[2 3 0]);
th = fixpar(th,'B2',[1,1],1);
th = pem(z,th);