Robust Simulation for Hybrid Systems: Chattering Path Avoidance

TL;DR

This paper introduces a robust computational framework for simulating hybrid systems with complex chattering behaviors, extending flow maps on multiple switching manifolds to improve solution uniqueness and simulation accuracy.

Contribution

It presents a novel formulation for extending flow maps on intersecting switching manifolds, enabling unique solutions and efficient simulation of complex hybrid system behaviors.

Findings

New formulation for flow map extension on multiple manifolds

Enhanced simulation accuracy for hybrid systems with chattering

Illustrative examples demonstrating the approach

Abstract

The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible scenario is that the solution trajectories may successively enter and exit as well as slide on switching mani-folds of different dimensions. Naturally, this arises in dynamical systems and control applications whenever there are multiple discontinuous control variables. The main contribution of this paper is to provide a robust computational framework for the most general way to extend a flow map on the intersection of p intersected (n--1)-dimensional switching manifolds in at least p dimensions. We explore a new formulation to which we can define unique solutions for such particular behavior in hybrid systems and investigate its efficient computation/simulation. We illustrate the concepts with examples throughout the paper.