Structure-preserving model reduction of interconnected dynamical systems

Abstract

This paper presents model reduction techniques for two classes of interconnected dynamical systems: firstly, feedback interconnections between large-scale linear systems and static nonlinearities and, secondly, interconnections between (many) linear dynamical systems. For the first class we provide both balancing-based and moment matching approaches that are applicable to large-scale systems, by reducing the linear part only and leaving the nonlinearity intact. Hence, the original feedback interconnection structure is preserved as well. Moreover, we provide a reduction error bound that expresses reduction accuracy depending on the level of reduction of the linear part and the properties of the nonlinearities. In addition, these methods preserve (global and incremental) stability properties. For the second class of systems, we present an approach to link reduction accuracy specifications on the level of the sub-systems to related specifications on the level of the interconnected system. This allows for a modular approach that preserves the structure of the high-order, interconnected system. In turn, this promotes the interpretability of the reduced-order system. In addition, we introduce the concept of abstracted reduction for interconnected linear systems, which enables the modular reduction of the sub-systems, while taking into account the dynamics of the rest of the interconnected system in a computationally tractable way. Finally, these methods also provide an error bound and preserve stability and (optionally) passivity.