ndBasis
Basis functions for tunable gain surface
Description
You use basis function expansions to parameterize gain
surfaces for tuning gain-scheduled controllers, with the tunableSurface
command.
The complexity of such expansions grows quickly when you have multiple
scheduling variables. Use ndBasis
to build N-dimensional
expansions from low-dimensional expansions. ndBasis
is
analogous to ndgrid
in the
way it spatially replicates the expansions along each dimension.
forms
the outer (tensor) product of two basis function expansions. Each
basis function expansion is a function that returns a vector of expansion
terms, such as returned by shapefcn
= ndBasis(F
1,F
2)polyBasis
.
If and ,
then shapefcn
is a vector of terms of the form:
The terms are listed in a column-oriented fashion, with i varying first, then j.
forms
the outer product of three or more basis function expansions. The
terms in the vector returned by shapefcn
= ndBasis(F
1,F
2,...,F
N)shapefcn
are
of the form:
These terms are listed in sort order that of an N-dimensional
array, with i1 varying first,
then i2, and so on. Each Fj
can
itself be a multi-dimensional basis function expansion.
Examples
Input Arguments
Output Arguments
Tips
The
ndBasis
operation is associative:ndBasis(F1,ndBasis(F2,F3)) = ndBasis(ndBasis(F1,F2),F3) = ndBasis(F1,F2,F3)
Version History
Introduced in R2015b