Building hybrid automata of complex physical systems for real-time applications

Dynamic behavior of complex physical systems is often nonlinear and includes multiple temporal scales. Singular perturbation methods decouple the fast and slow behavior and by assuming that the fast behavior is at a quasi steady state, the slow behavior of the system can be analyzed. The decoupling reduces the complex system of ordinary differential equations (ODE) to simpler ODE that allow fixed time step integration methods, and, therefore, are suitable for real-time applications. This model reduction may cause discontinuous jumps in the initial values of model variables. This paper applies and extends singular perturbation methods to compute discontinuous state changes for piecewise continuous, hybrid, models when the model configuration changes. Computing the explicit state change allows the use of hybrid automata as modeling framework when augmented with execution semantics for state vector updates around discontinuities.