## Constitutive Hybrid Processes: A Process-Algebraic Semantics for Hybrid Bond Graphs

Pieter J. L. Cuijpers, Jan F. Broenink, and Pieter J. Mosterman

### Abstract

Models of physical systems have to be based on
physical principles such as conservation of energy and continuity of
power. These principles are inherently enforced by the *bond
graph* modeling formalism. Often, however, physical components may
be best modeled as piecewise continuous with discrete mode changes,
which leads to a violation of continuity principles. To support
such *hybrid* models, bond graphs can be extended by facilitating
a dynamic model structure, resulting in *hybrid bond graphs*.
Behavior generation then requires computing continuous-time evolution,
detecting the occurrence of events, executing the discrete state
changes, and re-initializing the continuous-time state. This paper
presents a comprehensive representation of these different aspects of
behavior using *hybrid process algebra*. The behavior of a hybrid
bond graph can then be studied using a uniform representation while a
direct correspondence with the elements of the bond graph is
maintained. Additionally, nondeterminism can be included in hybrid
bond graph semantics which may alleviate the modeling task without
being detrimental to the required analyses.
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