Physical systems are by nature continuous, but often display nonlinear
behaviors that make them hard to analyze. Typically, these nonlineari
ties occur at a time scale that is much smaller than the time scale at
which gross system behavior needs to be described. In other situation
s, nonlinear effects are small and of a parasitic nature. To achieve e
fficiency and clarity in building complex system models, and to reduce
computational complexity in the analysis of system behavior, modelers
often abstract away any parasitic component parameter effects, and an
alyze the system at more abstract time scales. However, these abstract
ions often introduce abrupt, instantaneous changes in system behavior.
To accommodate mixed continuous and discrete behavior, this paper dev
elops a hybrid modeling formalism that dynamically constructs bond gra
ph model fragments that govern system behavior during continuous opera
tion. When threshold values are crossed, a meta-level control model in
vokes discontinuous state and model configuration changes. Discontinui
ties violate physical principles of conservation of energy and continu
ity of power, but the principle of invariance of state governs model b
ehavior when the control module is active. Conservation of energy and
continuity of power again govern behavior generation as soon as a new
model configuration is established This allows for maximally constrain
ed continuous model fragments. The two primary contributions of this p
aper ave an algorithm for inferring the correct new mode and state var
iable values in the hybrid modeling framework, and a verification sche
me that ensures hybrid models conform to physical system principles ba
sed on the principles of divergence of time and temporal evolution in
behavior transitions. These principles are employed in energy phase sp
ace analysis to verify physical consistency of models. (C) 1997 The Fr
anklin Institute. Published by Elsevier Science Ltd.