Create a piecewiselinear nonlinearity estimator object
NL = pwlinear
NL = pwlinear(Name,Value)
creates
a default piecewiselinear nonlinearity estimator object with 10 break
points for estimating HammersteinWiener models. The value of the
nonlinearity at the break points are set to NL
= pwlinear[]
.
The initial value of the nonlinearity is determined from the estimation
data range during estimation using nlhw
.
Use dot notation to customize the object properties, if needed.
creates
a piecewiselinear nonlinearity estimator object with properties specified
by one or more NL
= pwlinear(Name,Value
)Name,Value
pair arguments. The
properties that you do not specify retain their default value.
pwlinear
is an object that stores the piecewiselinear
nonlinearity estimator for estimating HammersteinWiener models.
Use pwlinear
to define a nonlinear function $$y=F(x,\theta )$$,
where y and x are scalars, and θ represents
the parameters specifying the number of break points and the value
of nonlinearity at the break points.
The nonlinearity function, F, is a piecewiselinear
(affine) function of x. There are n
breakpoints
(x_{k},y_{k}), k =
1,...,n, such that y_{k} =
F(x_{k}). F is
linearly interpolated between the breakpoints.
F is also linear to the left and right
of the extreme breakpoints. The slope of these extensions is a function
of x_{i} and y_{i} breakpoints.
The breakpoints are ordered by ascending x
values,
which is important when you set a specific breakpoint to a different
value.
There are minor difference between the breakpoint values you set and the values stored in the object because the toolbox has a different internal representation of breakpoints.
For example, in the following plot, the breakpoints are x_{k} = [2,1,4] and the corresponding nonlinearity values are y_{k} = [4,3,5].
The value F(x)
is computed by evaluate(NL,x)
,
where NL
is the pwlinear
object.
When using evaluate
, the break points have to
be initialized manually.
For pwlinear
object properties, see Properties.
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside single quotes (' '
). You can
specify several name and value pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
Use Name,Value
arguments to specify additional properties of pwlinear
nonlinearity.
For example, NL= pwlinear('NumberofUnits',5)
creates
a piecewiselinear nonlinearity estimator object with 5 breakpoints.
pwlinear
object properties include:

Number of breakpoints, specified as an integer. Default: 

Break points, x_{k}, and the corresponding nonlinearity values at the breakpoints, y_{k}, specified as one of the following:
When the nonlinearity object is created, the breakpoints are
ordered by ascending Default: 