Analysis of Zeno behaviors in a class of hybrid systems

Heymann, Michaël; Lin, Feng; Meyer, George E.; Resmerita, Stefan

doi:10.1109/tac.2005.843874

Cited by 89 publications

(43 citation statements)

References 13 publications

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“…The rates of the variables in different modes is shown in Figure 1. Two tank system model, a popular [16,12] example of hybrid systems, can be modeled as MMS as shown below.…”

Section: Examplesmentioning

confidence: 99%

“…Using similar restrictions as [18] the ideas presented in this paper can be generalized to handle linear dynamics with some effort. Heymann et al [12] study checking whether a given hybrid system, under several restrictions, is strongly Zeno and characterize LP feasibility test for this problem. Like Nghiem et al [17], Heymann et al only consider hyperrectangular safety states and starting states in the interior of the safety region.…”

Section: Introductionmentioning

confidence: 99%

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Optimal scheduling for constant-rate multi-mode systems

Alur

Trivedi

Wojtczak

2012

Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control

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Constant-rate multi-mode systems are hybrid systems that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. The schedulability problem for such systems is to design a mode-switching policy that maintains the state within a specified safety set. The main result of the paper is that schedulability can be decided in polynomial time. We also generalize our result to optimal schedulability problems with average cost and reachability cost objectives. Polynomial-time scheduling algorithms make this class an appealing formal model for design of energy-optimal policies. The key to tractability is that the only constraints on when a scheduler can switch the mode are specified by global objectives. Adding local constraints by associating either invariants with modes, or guards with mode switches, lead to undecidability, and requiring the scheduler to make decisions only at multiples of a given sampling rate, leads to a PSPACE-complete schedulability problem.

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“…The rates of the variables in different modes is shown in Figure 1. Two tank system model, a popular [16,12] example of hybrid systems, can be modeled as MMS as shown below.…”

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal scheduling for constant-rate multi-mode systems

Alur

Trivedi

Wojtczak

2012

Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control

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“…This result represents, to the authors' knowledge, the only known necessary and sufficient result for Zeno behavior in uncontrolled hybrid systems. Necessary and sufficent conditions for Zeno behavior in a significantly different class of controlled hybrid systems were found in [4].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov-Like Conditions for the Existence of Zeno Behavior in Hybrid and Lagrangian Hybrid Systems

Lamperski

Ames

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-Lyapunov-like conditions that utilize generalizations of energy and barrier functions certifying Zeno behavior near Zeno equilibria are presented. To better illustrate these conditions, we will study them in the context of Lagrangian hybrid systems. Through the observation that Lagrangian hybrid systems with isolated Zeno equilibria must have a onedimensional configuration space, we utilize our Lyapunov-like conditions to obtain easily verifiable necessary and sufficient conditions for the existence of Zeno behavior in systems of this form.

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“…[3], [14]) or sufficient conditions (cf. [2], [9]) for the existence of this behavior. Unfortunately, the necessary conditions obtained to date tend to be extremely conservative and the sufficient conditions tend to be applicable only to very limited classes of hybrid systems, e.g., [9] provides sufficient conditions for Zeno behavior in a class hybrid systems that are, in important ways, different than the systems considered in this paper (this results in conditions that are in a much different spirit than the conditions presented here).…”

Section: Introductionmentioning

confidence: 78%

Sufficient conditions for the existence of zeno behavior in a class of nonlinear hybrid systems via constant approximations

Ames

Abate²,

Sastry³

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-The existence of Zeno behavior in hybrid systems is related to a certain type of equilibria, termed Zeno equilibria, that are invariant under the discrete, but not the continuous, dynamics of a hybrid system. In analogy to the standard procedure of linearizing a vector field at an equilibrium point to determine its stability, in this paper we study the local behavior of a hybrid system near a Zeno equilibrium point by considering the value of the vector field on each domain at this point, i.e., we consider constant approximations of nonlinear hybrid systems. By means of these constant approximations, we are able to derive conditions that simultaneously imply both the existence of Zeno behavior and the local exponential stability of a Zeno equilibrium point. Moreover, since these conditions are in terms of the value of the vector field on each domain at a point, they are remarkably easy to verify.

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Analysis of Zeno behaviors in a class of hybrid systems

Cited by 89 publications

References 13 publications

Optimal scheduling for constant-rate multi-mode systems

Optimal scheduling for constant-rate multi-mode systems

Lyapunov-Like Conditions for the Existence of Zeno Behavior in Hybrid and Lagrangian Hybrid Systems

Sufficient conditions for the existence of zeno behavior in a class of nonlinear hybrid systems via constant approximations

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