Class representing binary-tree nonlinearity estimator for nonlinear ARX models
treepartition is an object that stores the
binary-tree nonlinear estimator for estimating nonlinear ARX models.
The object defines a nonlinear function , where F is
a piecewise-linear (affine) function of x, y is
scalar, and x is a 1-by-
Compute the value of F using
where t is the
a binary tree nonlinearity estimator object specified by properties
in treepartition Properties. The
tree has the number of leaves equal to
J is the number of nodes in the tree and
set by the property
NumberOfUnits. The default
NumberOfUnits is computed automatically
and sets an upper limit on the actual number of tree nodes used by
a binary tree nonlinearity estimator object with
in the binary tree expansion (the number of nodes in the tree). When
you estimate a model containing
t, the value of
t is automatically changed to show the actual
number of leaves used—which is the largest integer of the form
less than or equal to
You can include property-value pairs in the constructor to specify the object.
After creating the object, you can use
dot notation to access the object property values. For example:
% List all property values get(t) % Get value of NumberOfUnits property t.NumberOfUnits
You can also use the
set function to set
the value of particular properties. For example:
set(t, 'NumberOfUnits', 5)
setmust be the name of a MATLAB® variable.
Integer specifies the number of nodes in the tree.
you estimate a model containing a
Structure containing the following fields:
Structure containing the following fields that affect the initial model:
treepartition to specify the nonlinear
estimator in nonlinear ARX models. For example:
The following commands provide an example of using advanced
% Define the treepartition object. t=treepartition('num',100); % Set the Threshold, which is a field % in the Options structure. t.Options.Threshold=2; % Estimate the nonlinear ARX model. m=nlarx(Data,Orders,t);
The mapping F is defined by a dyadic partition P of the x-space, such that on each partition element Pk, F is a linear mapping. When x belongs to Pk, F(x) is given by:
where L is 1-by-m vector and d is a scalar common for all elements of partition. Ck is a 1-by-(m+1) vector.
The mapping F and associated partition P of the x-space are computed as follows:
Given the value of J, a dyadic tree with J levels and N = 2J–1 nodes is initialized.
Each node at level 1 < j < J has two descendants at level j + 1 and one parent at level j – 1.
The root node at level 1 has two descendants.
Nodes at level J are terminating leaves of the tree and have one parent.
One partition element is associated to each node k of the tree.
The vector of coefficients Ck is computed using the observations on the corresponding partition element Pk by the penalized least-squares algorithm.
When the node k is not a terminating leaf, the partition element Pk is cut into two to obtain the partition elements of descendant nodes. The cut is defined by the half-spaces (1,x)Bk > 0 or <=0 (move to left or right descendant), where Bk is chosen to improve the stability of least-square computation on the partitions at the descendant nodes.
When the value of the mapping F,
defined by the
treepartition object, is computed
at x, an adaptive algorithm selects the active
node k of the tree on the branch of
partitions which contain x.
Focus option in
a noniterative technique for estimating parameters. Iterative refinements
are not possible for models containing this nonlinearity estimator.
You cannot use
this nonlinearity estimators is not differentiable. Minimization of
simulation error requires differentiable nonlinear functions.