  Cyber-physical systems involve a network of discrete controllers that control
physical processes. Examples range from autonomous cars to implantable medical
devices, which are highly safety critical. Hybrid Automata (HA) based formal
approach is gaining momentum for the specification and validation of CPS. 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 based on 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.
Existing QSS integrators, based on fixed quanta, are also unsuitable for
simulating HAs. This is since the quantum selected is not dependent on the HA
guard conditions, which are the main cause of discontinuities. Considering
this, we propose a new dynamic quanta based formal model called Quantized State
Hybrid Automata (QSHA). 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, benchmarking results reveal that
the proposed simulation technique takes 720, 1.33 and 4.41 times fewer
simulation steps compared to standard Quantized State System (QSS)-1,
Runge-Kutta (RK)-45, and Differential Algebraic System Solver (DASSL)
integration based techniques respectively.

Systems and Control