| Abstract
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This paper describes a comprehensive model … This paper describes a comprehensive model building framework for mixed continuous/discrete, i.e., hybrid physical system models. Hybrid models arise naturally when modeling embedded systems (physical systems with digital controllers) and complex physical systems whose behavior may be simplified by introducing discrete transitions to replace fast nonlinear dynamics. We study time scale and parameter abstraction methods, and derive transition semantics that are consistent with physical system principles. These are translated into a systematic modeling methodology with formal execution semantics for deriving hybrid behaviors in three distinct modes of operation: (i) continuous, (ii) pinnacles, and (iii) mythical. Behavior in the continuous modes is governed by a system of differential algebraic equations (DAEs). Pinnacles, an artifact of time scale abstraction, compress behaviors over small intervals to a point in real time, and define a discrete switching model based on a priori state values. Mythical modes, an artifact of parameter abstractions, involve transitions through modes that have no real existence on the time line. Discrete switching transitions for mythical modes are defined in terms of a posteriori state values. In conjunction with the formal mathematical specification language for hybrid models, we also derive a set of model verification procedures, the principles of invariance of state, divergence of time, and temporal evolution of state, that provide the framework for designing hybrid simulators. We adopt hybrid automata as the computational model for our hybrid specification language. We have applied this model building framework in a number of different domains. Recent work has focused on developing a compositional modeling framework to facilitate the model construction task. to facilitate the model construction task.
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