Pseudo State System Modelling and a
New Separation Principle for Frequency Domain Optimal Control
An introduction will first be provided to a way of modelling systems
using so called Pseudo state system descriptions. These have the
advantage that they can be specialised to state equations and at the
same time be directly related to the frequency domain discrete or
continuous models for the process. It also enables a very general
separation principle of stochastic optimal control to be developed
which is relevant to systems described by frequency domain (transfer
function or polynomial) models.
The combined optimal control law and observer bear some relationship
to the wellknown Kalman filter separation principle results. However,
the observer would typically use a much smaller number of Pseudo state
variables for feedback and both the control and observer gains will in
general be dynamic. Further more, there are in fact two separation
principle results depending upon the order in which either the control
or filtering problems are solved. The total controllers obtained by
both results are of course identical and the two theorems also
coincide in the special case when Pseudo states are equal to real
state variables.
Other situations where the Pseudo state system description may be
helpful will be considered briefly and an example of the type of
results obtained will be provided.