Comparison of theoretical and computational characteristics of dimensionality reduction methods for large-scale uncertain systems

Synthesizing optimal controllers for large scale uncertain systems is a cha llenging computational problem. This has motivated the recent interest in d eveloping polynomial-time algorithms for computing reduced dimension models for uncertain systems. Here we present algorithms that compute lower dimen sional realizations of an uncertain system, and compare their theoretical a nd computational characteristics. Three polynomial-time dimensionality redu ction algorithms are applied to the Shell Standard Control Problem, a conti nuous stirred-tank reactor (CSTR) control problem, and a large scale benchm ark problem, where it is shown that the algorithms can reduce the computati onal effort of optimal controller synthesis by orders of magnitude. These a lgorithms allow robust controller synthesis and robust control structure se lection to be applied to uncertain systems of increased dimensionality. (C) 2001 Elsevier Science Ltd. All rights reserved.