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.