Model Reduction for Control of Uncertain Systems

Carolyn Beck, Control and Dynamical Systems, California Institute of Technology

The emphasis of this thesis is on the development of systematic methods for reducing the size and complexity of uncertain system models. Given a model for a large complex system, the objective of these methods is to find a simplified model which accurately describes the physical system, thus facilitating subsequent control design and analysis.

In this thesis we present model reduction methods and realization theory for uncertain systems represented by a Linear Fractional Transformation (LFT) on a block diagonal uncertainty structure. Following a brief discussion of the construction of LFT models for uncertain systems, a necessary and sufficient condition for exact reducibility of uncertain systems, the converse of minimality, is presented. This condition generalizes the role of controllability and observability gramians, and is expressed in terms of singular solutions to a pair of Linear Matrix Inequalities (LMIs). A related generalization of balanced truncation model reduction with guaranteed error bounds is then given, which is based on solutions to the same LMIs. This reduction method provides for both uncertainty simplification and state order reduction in the case of uncertain systems, but also may be interpreted as state order reduction for multi-dimensional systems.

A simple procedure for computing balanced reduced models of uncertain systems is presented, followed by a discussion of the application of this procedure to a pressurized water reactor for a nuclear power plant.