A subspace approach to balanced truncation for model reduction of nonlinear control systems

TLDR

The paper introduces a new model‑reduction method for nonlinear control systems. The method constructs an approximately balanced realization using only standard matrix computations, applies to linear systems as conventional balanced truncation, and for nonlinear systems uses simulation or experimental data to identify input–output dynamics, demonstrated on a nonlinear mechanical system. The resulting reduced‑order model remains nonlinear and retains input–output structure suitable for control. © 2002 John Wiley & Sons, Ltd.

Abstract

Abstract In this paper, we introduce a new method of model reduction for nonlinear control systems. Our approach is to construct an approximately balanced realization. The method requires only standard matrix computations, and we show that when it is applied to linear systems it results in the usual balanced truncation. For nonlinear systems, the method makes use of data from either simulation or experiment to identify the dynamics relevant to the input–output map of the system. An important feature of this approach is that the resulting reduced‐order model is nonlinear, and has inputs and outputs suitable for control. We perform an example reduction for a nonlinear mechanical system. Copyright © 2002 John Wiley & Sons, Ltd.