Model Semantics and Simulation for Hybrid Systems Operating in Sliding Regimes

Abstract

We describe a model semantics and a simulation algorithm for characterizing a class of dynamic physical systems operating in the so-called sliding regimes. Many continuous physical systems operate at multiple time scales. To simplify behavior generation, we often abstract away details at faster time scales or near discontinuous boundaries and describe the resulting system as a hybrid system with distinct modes. Mode transitions are induced by internal state changes or external control signals. It is common for such systems to exhibit chattering behaviors at the discontinuous transition boundaries which presents challenges to conventional numerical methods for analyzing system behaviors. We present an efficient, adaptive algorithm for simulating this class of systems, based on a careful analysis of the model semantics at the boundaries of discontinuity. Simulation results show that the algorithm is chatter free and more efficient than conventional integration methods for sliding-mode systems.