Dimensionality reduction for uncertain dynamic systems

Dimensionality reduction is a beneficial step to alleviate some of the computation burden as well as to improve the accuracy associated with complex system analyses. This paper investigates dimensionality reduction techniques for linear, time-invariant systems subject to general non-linear parameter dependencies. In the context of this paper, dimensionality reduction refers to simultaneous reductions in both model state order and parameter order, i.e. number of uncertain parameters. Two complementary approaches will be presented, one based on the worst-case H-infinity norm error associated with both model state and parameter-order reductions, and another, which is essentially the inverse problem, that considers the largest allowable parameter bounds for a given total H-infinity norm error for the dimensionally reduced problem. Although applicable to larger-order systems, a simple low-order spring–mass example is used to demonstrate the usefulness of the techniques developed herein. Published in 2009 by John Wiley & Sons, Ltd.