Citation
Walid Taha. "Enclosing Hybrid Behavior". Talk or presentation, 17, October, 2012.

Abstract
Rigorous simulation of hybrid systems relies critically on having a semantics that constructs enclosures. Edalat and Pattinson's work on the domain-theoretic semantics of hybrid systems almost provides what is needed, with two exceptions. First, domain-theoretic methods leave many operational concerns implicit. As a result, the feasibility of practical implementations is not obvious. For example, their semantics appears to rely on repeated interval splitting for state space variables. This can lead to exponential blow up in the cost of the computation. Second, common and even simple hybrid systems exhibit Zeno behaviors. Such behaviors are a practical impediment because they make simulators loop indefinitely. This is in part due to the fact that existing semantics for hybrid systems generally assume that the system is non-Zeno. The feasibility of reasonable implementations is addressed by specifying the semantics algorithmically. We observe that the amount of interval splitting can be influenced by the representation of function enclosures. Parameterizing the semantics with respect to enclosure representation provides a precise specification of the functionality needed from them, and facilitates studying their performance characteristics. For example, we find that non-constant enclosure representations can alleviate the need for interval splitting on dependent variables. We address the feasibility of dealing with Zeno systems by taking a fresh look at event detection and localization. The key insight is that computing enclosures for hybrid behaviors over intervals containing multiple events does not necessarily require separating these events in time, even when the number of events is unbounded. In contrast to current methods for dealing with Zeno behaviors, this semantics does not require reformulating the hybrid system model specifically to enable a transition to a post-Zeno state. The new semantics does not sacrifice the key qualities of the original work, namely, convergence on separable systems.

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• HTML

  Walid Taha. <a
  href="http://chess.eecs.berkeley.edu/pubs/943.html"
  ><i>Enclosing Hybrid Behavior</i></a>,
  Talk or presentation,  17, October, 2012.

• Plain text

  Walid Taha. "Enclosing Hybrid Behavior". Talk or
  presentation,  17, October, 2012.

• BibTeX

  @presentation{Taha12_EnclosingHybridBehavior,
      author = {Walid Taha},
      title = {Enclosing Hybrid Behavior},
      day = {17},
      month = {October},
      year = {2012},
      abstract = {Rigorous simulation of hybrid systems relies
                critically on having a semantics that constructs
                enclosures. Edalat and Pattinson's work on the
                domain-theoretic semantics of hybrid systems
                almost provides what is needed, with two
                exceptions. First, domain-theoretic methods leave
                many operational concerns implicit. As a result,
                the feasibility of practical implementations is
                not obvious. For example, their semantics appears
                to rely on repeated interval splitting for state
                space variables. This can lead to exponential blow
                up in the cost of the computation. Second, common
                and even simple hybrid systems exhibit Zeno
                behaviors. Such behaviors are a practical
                impediment because they make simulators loop
                indefinitely. This is in part due to the fact that
                existing semantics for hybrid systems generally
                assume that the system is non-Zeno. The
                feasibility of reasonable implementations is
                addressed by specifying the semantics
                algorithmically. We observe that the amount of
                interval splitting can be influenced by the
                representation of function enclosures.
                Parameterizing the semantics with respect to
                enclosure representation provides a precise
                specification of the functionality needed from
                them, and facilitates studying their performance
                characteristics. For example, we find that
                non-constant enclosure representations can
                alleviate the need for interval splitting on
                dependent variables. We address the feasibility of
                dealing with Zeno systems by taking a fresh look
                at event detection and localization. The key
                insight is that computing enclosures for hybrid
                behaviors over intervals containing multiple
                events does not necessarily require separating
                these events in time, even when the number of
                events is unbounded. In contrast to current
                methods for dealing with Zeno behaviors, this
                semantics does not require reformulating the
                hybrid system model specifically to enable a
                transition to a post-Zeno state. The new semantics
                does not sacrifice the key qualities of the
                original work, namely, convergence on separable
                systems. },
      URL = {http://chess.eecs.berkeley.edu/pubs/943.html}
  }
  

Posted by David Broman on 17 Oct 2012.
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