A dynamic Quantized State System execution framework for Hybrid Automata

Abstract

Cyber–physical Systems (CPS) involve a network of discrete controllers that control physical processes, e.g., pacemakers controlling the heart rhythm. The intuitive and formal Hybrid Automata (HA) based modelling approach for CPS is gaining momentum. HA combines the model of the plant along with its discrete controller resulting in a piece-wise continuous system with discontinuities. Accurate detection of these discontinuities, using appropriate level crossing detectors, is a key challenge to simulation of CPS modelled in HA. Existing techniques employ time discrete numerical integration with bracketing for level crossing detection. These techniques involve back-tracking and are highly non-deterministic and hence error prone. As level crossings happen based on the values of continuous variables, Quantized State System (QSS)-integration may be more suitable.We propose a dynamic quanta based execution framework for HA. A CPS modelled as a HA is first translated into the proposed formal intermediate format called the Quantized State Hybrid Automata (QSHA). The QSHA is then executed using a discrete event simulation algorithm based on quantized state semantics. The developed formal model and the associated simulation framework guarantees that: ① all level crossings are accurately detected and ② the time of the level crossing is also accurate within floating point error bounds. Interestingly, benchmark results reveal that the proposed simulation technique takes 720, 2.17, 1.33 and 4.41 times fewer simulation steps compared to QSS-1, QSS-3, Runge–Kutta (RK)-45, and Differential Algebraic System Solver (DASSL) integration based techniques, respectively.