Computing Flowpipe of Nonlinear Hybrid Systems with Numerical Methods

摘要

Modern control-command systems often include controllers that performnonlinear computations to control a physical system, which can typically bedescribed by an hybrid automaton containing high-dimensional systems ofnonlinear differential equations. To prove safety of such systems, one mustcompute all the reachable sets from a given initial position, which might beuncertain (its value is not precisely known). On linear hybrid systems,efficient and precise techniques exist, but they fail to handle nonlinear flowsor jump conditions. In this article, we present a new tool name HySon whichcomputes the flowpipes of both linear and nonlinear hybrid systems usingguaranteed generalization of classical efficient numerical simulation methods,including with variable integration step-size. In particular, we present analgorithm for detecting discrete events based on guaranteed interpolationpolynomials that turns out to be both precise and efficient. Illustrations ofthe techniques developed in this article are given on representative examples.