User`s guide

Estimating Nonlinear G rey-Box Models
One category of method s co nsists of the min imization sch em es that are
based on line-search metho ds , including Gauss-Newton type methods,
steepest-descent methods, and Levenberg-Marquardt methods.
The Trust-Region Reflective Newton method of nonlinear least-squares
(
lsqnonlin), where the cost is the sum of squares of e rrors between the
measured and simulated outputs, requires Optimization Toolbox™ software.
When the p aramete r bounds differ from the default +/- Inf, this se arch
method handles the bounds better than the schemes based on a line search.
However, unlike the line-search-based methods,
lsqnonlin only works with
Criterion='Trace'.
By default,
SearchMethod is set to Auto, which automatically selects a
method from the available minimizers. If the Optimization Toolbox product is
installed,
SearchMethod is set to 'lsqnonlin'.Otherwise,SearchMethod is a
combina tion of line-search based schemes.
Gradient Options
You can specify the method for calculating gradients using the
GradientOptions field of the Algorithm property. Gradients are the
derivatives of errors with respect to unknown parameters and initial states.
Gradients are calculated by numerically perturbing unknown quantities and
measuring their effects on the simulation error.
Option for gradient computation include the choice of the differencing scheme
(forward, backward or central), the size of minimum perturbation of the
unknown quantities, and whether the gradients are calculated simultaneously
or individually.
Example – Specifying Algorithm Properties
You can specify the A lgorithm fields directly in the estimation syntax, as
property-value pairs.
For example, you can specify the following properties as part o f the
pem syntax:
m = pem(data,init_model,'Search','gn',...
'MaxIter',5,...
'Display','On')
5-21