A THEORY OF DISCONTINUITIES IN PHYSICAL SYSTEM MODELS

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.