A compositional semantics of Simulink/Stateflow based on quantized state hybrid automata

Abstract

Simulink/Stateflow® is the de-facto tool for design of Cyber-physical Systems (CPS). CPS include hybrid systems, where a discrete controller guides a continuous plant. Hybrid systems are characterised by their continuous time dynamics with sudden discontinuities, caused by level/zero crossings. Stateflow can graphically capture hybrid phenomenon, making it popular with control engineers. However, Stateflow is unable to correctly and efficiently simulate complex hybrid systems, especially those characterised by even number of level crossings. In this paper we first propose a new formal model for hybrid systems called Quantized State Hybrid Input Output Automaton (QSHIOA). QSHIOA is used to give a deterministic semantics to Stateflow in addition to efficiently handling even number of level crossing detections. In the proposed compositional semantics, a network of Stateflow charts can be compiled into a network of QSHIOAs. Benchmark results show that in the median case, the proposed stateflow execution technique, via QSHIOA, is 84% faster than using the best variable-step size solvers in Simulink/Stateflow®.