A Modeling and Simulation Methodology for Hybrid Dynamic Physical Systems

Pieter J. Mosterman
Institute for Robotics and System Dynamics
DLR Oberpfaffenhofen

Gautam Biswas
Department of Computer Science
Vanderbilt University


This paper develops a mathematical framework for specification of hybrid physical system models to develop a robust simulation methodology for hybrid system analyses. Our framework for modeling hybrid dynamic physical systems encompasses time scale and parameter abstractions, and results in behavior patterns that undergo discrete transitions between modes of continuous behavior evolution. Using this framework we develop formal execution semantics for characterizing hybrid behaviors in terms of three distinct modes of system operation: (i) continuous, (ii) pinnacles, and (iii) mythical. Continuous modes represent normal physical system behavior, where the system variables evolve continuously in time. Pinnacles, an artifact of time scale abstraction, define behaviors at a point in real time. Mythical modes, an artifact of parameter abstractions, are defined by sequences of instantaneous local switching transitions in the hybrid model, and have no real existence on the time line. A key aspect of the work is the link established between the switching transitions and the a priori and a posteriori state vector values, which leads to the definition of recursive mode switching functions that govern the interactions between the continuous and discrete components of the system models. The mathematical specifications are developed into an implementation model that allows for a direct mapping of system components onto model fragments, and facilitates simulation of system behavior. Discrete switching in the simulation model is implemented as instantaneous transition functions, and continuous behavior generation is based on differential equation models. We demonstrate the effectiveness of this approach on a number of physical system models.

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