Balancing Approach to Minimal Realization and Model Reduction of Stable Nonlinear Systems

This paper presents a computational approach to determine a reduced order model of a nonlinear system. The procedure is closely related to balanced model reduction and introduces the concept of covariance matrices for local controllability and observability analysis of a nonlinear system. These covariance matrices are an extension of gramians of a linear system and are used to determine unobservable and uncontrollable parts of the system for a given operating region. Additionally, an algorithm is introduced that eliminates these non-minimal parts of the model and can further reduce the model, i.e. the number of state variables. This minimal realization/model reduction procedure is simple to implement and can be applied locally to any stable system without making any assumptions about observability and controllability. Examples are presented to demonstrate the procedure. When the algorithm is applied to linear systems, it reduces to well-known techniques for minimal realization and balanced model reduction.