Feedforward Control is Dual to Deconvolution
Bo Bernhardsson and
International Journal of Control,
vol 57, pp 393-405, February 1993.
Dualities between control and estimation problems are useful
concepts in optimal control theory. By demonstrating a duality,
the solution to one set of problems can be applied also to the
dual set of problems. The paper discusses such a duality, which
does not seem to have been noticed before.
A duality is demonstrated between optimal feedforward control
deconvolution, or input estimation. These two problems are
normally discussed separately in the literature, but have
close similarities. Duality between them can be demonstrated
if and only if one uses general problem formulations, with
frequency-shaped weighting in the criteria.
For one of the problems, the dual problem can then be obtained
immediately from the block diagram, by reversing the directions of
arrows, interchanging summation points and node points
and transposing all transfer function matrices.
The result applies in continuous and discrete time,
for the minimization of all transfer function norms which are
invariant under transposition of transfer function matrices.
A derivation of a polynomial solution to the frequency-weighted
discrete-time MIMO LQG feedforward control problems
illustrates the use of the duality.
- Related publications:
in IJC 1988, in which a relation, but not a duality,
could be demonstrated.
in IEEE Trans. AC 1995, where the duality is utilized in
averaged H-2 robust design.
Book chapter 1993,
incuding multivariable on LQ disturbance measurement
in IEEE Trans. ASSP 1991, which includes multivariable