Constitutive hybrid processes: A process-algebraic semantics for hybrid bond graphs

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, non-determinism can be included in hybrid bond graph semantics which may alleviate the modeling task without being detrimental to the required analyses.