Computer Aided Control System Design
Hybrid Dynamic Systems
Chair: Pieter J. Mosterman      
Control Systems Society

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Hybrid Systems Glossary

This page contains terms as used in hybrid systems literature and their definition. If you have any additions or changes please send me e-mail.

   hybrid automata Automata that may contain differential equations in the discrete states.
  I/O automata Automata where connections between sub-systems define input/output relations.
  linear hybrid automata Automata where the continuous components can change only linearly, and all terms used must be linear.
  rectangular automata An automata with each continuous variable, x, being part of a differential inclusion, i.e., satisfying a differential equation of the form a < dx/dt < b, where a and b are rational constants.
  timed automata Automata that may contain clocks in the discrete states. The value of a clock may be reset as part of a state transition action.
bond graphs
  hybrid bond graphs Bond graphs that contain junctions that act as ideal switches and that are controlled by local finite state machines.
  switched bond graphs Bond graphs extended with an ideal switch element.
chattering Repeated switching between two modes of continuous operation.
clock A continuous variable that changes with a constant rate.
complementarity models Models with a differential equation part and switching conditions of the form x>=0, y>=0, x*y=0. For example, used in multi-body dynamics to model contact constraints (either normal force, N>=0 and separation, d=0, or N=0 and d>=0).
  state event An event that is detected.
  step event An event that occurs at a completed numerical integration step.
  time event An event that has a time of occurrence that can be predicted.
event iteration The processing of a sequence of consecutive discrete events.
  modeling The modeling of a physical system by means of a hybrid formalism.
  simulation Behavior generation of a hybrid system.
  system A model specified by a hybrid formalism.
ideal switch Element with two constituent equations (in complementarity form), x>=0,y>=0, x*y=0, and variable causality.
impulse space Space in which discontinuous changes in continuous state variables occur.
instantaneous equation Equation that determines the posteriori value of a continuous variable at a discontinuity.
jump space See impulse space.
limit cycle Behavior that cycles through a sequence of modes in continuous time.
mode A system configuration of continuous operation.
  mythical mode A mode that is entered with variable values that cause an immediate further mode transition.
Petri nets
  batch nets Extend hybrid Petri nets with a new kind of batch places and batch transitions.
  DAE-Petri nets Focuses on the interaction between a Petri net model and a continuous model which is a set of Differential Algebraic Equations (DAE). It can be seen as an extension of hybrid automata.
  differential Petri nets Introduces the differential place (whose marking may also be negative) and the differential transition and can integrate all kinds of discrete Petri nets.
  first-order hybrid Petri nets Consist of continuous places holding fluid, discrete places containing a non-negative integer number of tokens, and either discrete or continuous transitions. The continuous flows have constant rates and the fluid content of each continuous place varies linearly with time.
  fluid stochastic Petri nets Extend stochastic Petri nets by introducing places with continuous tokens and arcs with fluid flow so as to handle stochastic fluid flow systems. No continuous transitions are present in this model.
  high-level hybrid nets Nets characterized by the use of structured individual tokens.
  hybrid flow nets Consist of a continuous flow net interacting with a Petri net according to a control interaction, i.e., the Petri net controls the continuous flow net and vice versa.
  hybrid Petri nets Consist of a "continuous part" (continuous places and transitions) and a "discrete part" (discrete places and transitions).
pinnacle A point in behavior evolution that is achieved in a mode that is only active at a point in time.
variable causality Variables that dynamically change their character. For example, the variables of an ideal switch may change from input to output and vice versa.
Zenoness Characterizes system behavior that can reach and exceed any point in time. Non-Zeno behavior may converge to a limit point, e.g., by advancing time over an interval of half the size of the previous interval. In Zeno's Paradox Achilles fails to catch a turtoise because every time he reaches its position, the turtoise has moved some as well.


This page was last updated Mai 27, 2002.