A priori detection of Zeno behavior in communication networks modeled as hybrid systems

A. Abate, A.D. Ames, S. Sastry
2006 2006 American Control Conference  
In this paper, we show that the sufficient conditions for the existence of Zeno behavior in hybrid systems derived in [3] correctly predict such executions in a modeling instance of the fluid-flow approximation of the TCP-like protocol for wireless communication networks. I. INTRODUCTION Hybrid systems are systems that display both continuous and discrete behavior, and so are endowed with powerful modeling capabilities. Unfortunately, the yin to this yang is that hybrid models may exhibit non
more » ... bust and pathological behaviors due to their structural interconnections. Zeno behavior provides a notorious, and peculiar, example of this; its existence can be disruptive to both analysis and simulation. This motivates the need to understand Zeno behavior and, specifically, detect it a priori. The literature on Zeno behavior can be categorized within three general areas: analysis, elimination (or regularization) and detection (either sufficient or necessary conditions for the existence of Zeno behavior). The first area studies the dynamical properties associated with this phenomenon, its relation to real world systems, and the computational problems it arises. The second area attempts to understand how to modify a hybrid model in order to guarantee the absence of such a behavior (see, for instance, [4], [7], [11]). The final area, providing necessary and/or sufficient conditions for the existence of Zeno behavior, has drawn some interest in recent years; while the Literature has results on necessary conditions, which are based on the interconnections between the domains of the system, we focus here on sufficient conditions, which focus on the structure of the vector fields. In [3] , the first-as far as the authors are aware-sufficient conditions for the existence of Zeno behavior in hybrid systems with non-trivial (or non-constant) dynamics were provided; there, a simple class of hybrid systems with simple dynamics, termed diagonal first quadrant (DFQ) hybrid systems was studied. These results were generalized in [6] to include arbitrary nonlinear dynamics through the use of Lyapunov-type techniques. This work utilizes the framework of hybrid systems to model Communication Networks that employ the Transmission Control Protocol (TCP). These complex models of
doi:10.1109/acc.2006.1657234 fatcat:evvhpg3a2ngvnn2hkohtncdzni