Formal Modeling and Performance Evaluation for Hybrid Systems: A Probabilistic Hybrid Process Algebra-Based Approach

Abstract

Probabilistic behavior is omnipresent in computer-controlled systems, in particular, so-called safety-critical hybrid systems, due to various reasons, like uncertain environments or fundamental properties of nature. In this paper, we extend the existing hybrid process algebra ACP[Formula: see text] with probability without sacrificing the nondeterministic choice operator. The existing approximate probabilistic bisimulation relation is fragile and not robust in the sense of being dependent on the deviation range of the transition probability. To overcome this defect, a novel approximate probabilistic bisimulation is proposed which is inspired by the idea of Probably Approximately Correct (PAC) by relaxing the constraints of transition probability deviation range. Traditional temporal logics, even probabilistic temporal logics, are expressive enough, but they are limited to producing only true or false responses, as they are still logics and not suitable for performance evaluation. To settle this problem, we present a new performance evaluation language that expands quantitative analysis from the value range of [Formula: see text] to real number to reason over probabilistic systems. After that, the corresponding algorithms for performance evaluation are given. Finally, an industrial example is given to demonstrate the effectiveness of our method.