Citation
Edward A. Lee, Haiyang Zheng. "HyVisual: A Hybrid System Modeling Framework Based on Ptolemy II". IFAC Conference on Analysis and Design of Hybrid Systems, 2006; the right ball transfers its momentum to the middle ball, and then, without any time elapsing, the middle ball transfers its momentum to the left ball. The two events (state transitions in the state machine at the middle left)are simultaneous but ordered. Other initial conditions can be chosen where two simultaneous events are unordered (e.g., starting with two balls appropriately displaced). HyVisual allows a model to permit nondeterministic choice of enabled transitions.

Abstract
HyVisual is a hybrid systems modeling framework providing a block diagram visual syntax for specifying continuous dynamics and a bubble-and-arc syntax for specifying modal behavior. It is based on Ptolemy II, is written in Java, and is distributed open-source at http://ptolemy.eecs.berkeley.edu/hyvisual/. HyVisual has a rigorous operational semantics described in [1]. A key property is that it internally uses superdense time, where signals are modeled as partial functions of the form f:R+ נN * V , where R+ is the non-negative real numbers and represents time, V is the value set (a data type, such as Rn), and N is the set of natural numbers. Continuous-time functions are total, whereas discrete-event functions are defined only on a discrete subset of R+. The N in the domain permits signals to have multiple values in a well-defined order at a particular time. Using this framework, HyVisual gives a rigorous semantics to discontinuous signals (which have multiple values at the point of discontinuity), to discrete-event signals with multiple events at the same time, and to transient states, where the time spent in the state is zero. An example of a HyVisual model that leverages this is shown in fig. 1, which shows many features of HyVisual. This models Newton?s cradle, an apparatus with three (or more) balls hanging from strings (inspired by a one dimensional version in [2]). If the model is initialized with one of the balls displaced as shown in the HyVisual graphical animation at the lower left, then when the ball collides with the middle ball, a transient state results. At that time, the right ball transfers its momentum to the middle ball, and then, without any time elapsing, the middle ball transfers its momentum to the left ball. The two events (state transitions in the state machine at the middle left)are simultaneous but ordered. Other initial conditions can be chosen where two simultaneous events are unordered (e.g., starting with two balls appropriately displaced). HyVisual allows a model to permit nondeterministic choice of enabled transitions.

Electronic downloads

• http://ptolemy.eecs.berkeley.edu/publications/papers/06/hyvisual/

• HTML

  Edward A. Lee, Haiyang Zheng. <a
  href="http://chess.eecs.berkeley.edu/pubs/54.html"
  >HyVisual:  A Hybrid System Modeling Framework Based on
  Ptolemy II</a>, IFAC Conference on Analysis and Design
  of Hybrid Systems, 2006; the right ball transfers its
  momentum to the middle ball, and then, without
  any time
  elapsing, the middle ball transfers its momentum to the left
  ball.
  The two events (state transitions in the state
  machine at the middle left)are simultaneous but ordered.
  Other initial conditions can be chosen where two
  simultaneous events are unordered (e.g., starting with two
  balls appropriately displaced). HyVisual allows a model to
  permit nondeterministic choice of enabled transitions.

• Plain text

  Edward A. Lee, Haiyang Zheng. "HyVisual:  A Hybrid
  System Modeling Framework Based on Ptolemy II". IFAC
  Conference on Analysis and Design of Hybrid Systems, 2006;
  the right ball transfers its momentum to the middle ball,
  and then, without
  any time elapsing, the middle ball
  transfers its momentum to the left ball.
  The two events
  (state transitions in the state machine at the middle
  left)are simultaneous but ordered. Other initial conditions
  can be chosen where two simultaneous events are unordered
  (e.g., starting with two balls appropriately displaced).
  HyVisual allows a model to permit nondeterministic choice of
  enabled transitions.

• BibTeX

  @inproceedings{LeeZheng06_HyVisualHybridSystemModelingFrameworkBasedOnPtolemy,
      author = {Edward A. Lee and Haiyang Zheng},
      title = {HyVisual:  A Hybrid System Modeling Framework
                Based on Ptolemy II},
      booktitle = {IFAC Conference on Analysis and Design of Hybrid
                Systems},
      year = {2006},
      note = {the right ball transfers its momentum to the
                middle ball, and then, without
  any time elapsing,
                the middle ball transfers its momentum to the left
                ball.
  The two events (state transitions in the
                state machine at the middle left)are simultaneous
                but ordered. Other initial conditions can be
                chosen where two simultaneous events are unordered
                (e.g., starting with two balls appropriately
                displaced). HyVisual allows a model to permit
                nondeterministic choice of enabled transitions.},
      abstract = {HyVisual is a hybrid systems modeling framework
                providing a block diagram visual syntax for
                specifying continuous dynamics and a
                bubble-and-arc syntax for specifying modal
                behavior. It is based on Ptolemy II, is written in
                Java, and is distributed open-source at
                http://ptolemy.eecs.berkeley.edu/hyvisual/.
                HyVisual has a rigorous operational semantics
                described in [1]. A key property is that it
                internally uses superdense time, where signals are
                modeled as partial functions of the form f:R+ × N
                * V , where R+ is the non-negative real numbers
                and represents time, V is the value set (a data
                type, such as Rn), and N is the set of natural
                numbers. Continuous-time functions are total,
                whereas discrete-event functions are defined only
                on a discrete subset of R+. The N in the domain
                permits signals to have multiple values in a
                well-defined order at a particular time. Using
                this framework, HyVisual gives a rigorous
                semantics to discontinuous signals (which have
                multiple values at the point of discontinuity), to
                discrete-event signals with multiple events at the
                same time, and to transient states, where the time
                spent in the state is zero. An example of a
                HyVisual model that leverages this is shown in
                fig. 1, which shows many features of HyVisual.
                This models Newton?s cradle, an apparatus with
                three (or more) balls hanging from strings
                (inspired by a one dimensional version in [2]). If
                the model is initialized with one of the balls
                displaced as shown in the HyVisual graphical
                animation at the lower left, then when the ball
                collides with the middle ball, a transient state
                results. At that time, the right ball transfers
                its momentum to the middle ball, and then, without
                any time elapsing, the middle ball transfers its
                momentum to the left ball. The two events (state
                transitions in the state machine at the middle
                left)are simultaneous but ordered. Other initial
                conditions can be chosen where two simultaneous
                events are unordered (e.g., starting with two
                balls appropriately displaced). HyVisual allows a
                model to permit nondeterministic choice of enabled
                transitions.},
      URL = {http://chess.eecs.berkeley.edu/pubs/54.html}
  }
  

Posted by Mary Stewart on 4 May 2006.
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