High Fidelity Simulation of Hybrid Systems using Higher Order Hybrid Automata

Hybrid systems are a subset of Cyber-Physical System (CPS), where a physical process (the plant) is controlled by a discrete controller. The controller induces mode switches, which are modelled as guard conditions leading to sudden discontinuities. Correctly capturing sudden discontinuities during simulation is the primary challenge to maintain fidelity. De-facto industry standard tools, such as Simulink and Modelica, have been known to produce incorrect outputs when simulating systems involving complicated guards. For example, transcendental guards leading to the well-known even number of level crossing detection problem or guards leading the system state into the complex plane have been shown to produce invalid results. To tackle this problem we propose Higher Order Hybrid Automata and its compositional execution semantics. Using this semantics a novel numerical simulation approach for hybrid systems is developed. The key idea is to approximate the guard and Ordinary Differential Equations with Taylor polynomials so as to accurately detect zero-crossings induced by the guards. Simulation results show that systems with transcendental guards can be simulated using our approach efficiently, while maintaining high simulation fidelity.