Chattering-Free Simulation for Hybrid Dynamical Systems Semantics and Prototype Implementation

Chattering is a fundamental phenomenon that is unique to hybrid systems, due to the complex interaction between discrete dynamics (in the form of discrete transitions) and continuous dynamics (in the form of time). In practice, simulating chattering hybrid systems is challenging in that simulation eectively halts near the chattering time point, as an innite number of discrete transitions would need to be simulated. In this paper, formal conditions are provided for when the simulated models of hybrid systems display chattering behavior, and methods are proposed for avoiding chattering "on the fly" in runtime. We utilize dynamical behavior analysis to derive conditions for detecting chattering without enumeration of modes. We also present a new iterative algorithm to allow for solutions to be carried past the chattering point, and we show by a prototypical implementation how to generate the equivalent chattering-free dynamics internally by the simulator in the main simulation loop. The concepts are illustrated with examples throughout the paper.