A Subspace Approach to Balanced Truncation for Model Reduction of Nonlinear Control Systems

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.