Towards Procedures for Systematically Deriving Hybrid Models of Complex Systems

In many cases, complex system behaviors are naturally modeled as nonlinear differential equations. However, these equations are often hard to analyze because of “stiffness” in their numerical behavior and the difficulty in generating and interpreting higher order phenomena. Engineers often reduce model complexity by transforming the nonlinear systems to piecewise linear models about operating points. Each operating point corresponds to a mode of operation, and a discrete event switching structure is added to implement the mode transitions during behavior generation. This paper presents a methodology for systematically deriving mixed continuous and discrete, i.e., hybrid models from a nonlinear ODE system model. A complete switching specification and state vector update function is derived by combining piecewise linearization with singular perturbation approaches and transient analysis. The model derivation procedure is then cast into the phase space transition ontology that we developed in earlier work. This provides a systematic mechanism for characterizing discrete transition models that result from model simplification techniques. Overall, this is a first step towards automated model reduction and simplification of complex high order nonlinear systems.