Deriving Discontinuous State Changes for Reduced Order Systems and the Effect on Compositionality

Abstract

Dynamic behavior of complex physical systems is often nonlinear and includes multiple temporal scales. For efficient model analysis, singular perturbation methods can be employed to decouple and analyze the fast and slow behavior in two steps: (i) by assuming the fast behavior quickly reaches a quasi steady state, and (ii) by analyzing the slow behavior of the system. The decoupling achieved by applying the quasi steady state solution reduces the complex system of ordinary differential equations (ODEs) to simpler ODEs. This process of abstracting fast continuous behavior into algebraic constraints may cause discontinuous jumps in variable values when configuration changes occur, requiring the system variables to be reinitialized correctly. The application of traditional singular perturbation approach correspond to discontinuous changes resulting from parameter abstraction. This paper extends this notion to analysis of discontinuous changes caused by time scale abstraction. Deriving the explicit discontinuous jumps caused requires analysis of the interactions between model components, therefore, they are configuration dependent. Therefore, reduced order model components (or fragments) may not be valid in other configurations, and, therefore, may not be directly usable in a compositional modeling framework.