Towards the Modular Specification and Validation of Cyber-Physical Systems

Abstract

Cyber-Physical Systems (CPS) are systems controlled by one or more computer-based components tightly integrated with a set of physical components, typically described as sensors and actuators, that can either be directly attached to the computer components, or at a remote location, and accessible through a network connection. The modeling and verification of such systems is a hard task and error prone that require rigorous techniques. Hybrid automata is a formalism that extends finite-state automata with continuous behavior, described by ordinary differential equations. This paper uses a rewriting logic-based technique to model and validate CPS, thus exploring the use of a formal technique to develop such systems that combines expressive specification with efficient state-based analysis. Moreover, we aim at the modular specification of such systems such that each CPS component is independently specified and the final system emerges as the synchronous product of its constituent components. We model CPSs using Linear Hybrid Automaton and implement them in Real-Time Maude, a rewriting logic tool for real-time systems. With this method, we develop a specification for the n-reservoir problem, a CPS that controls a hose to fill a number of reservoirs according to the physical properties of the hose and the reservoirs.Most CPS have to cope with design requirements that are imposed onto them by their multiple applications in the real world. Typically a CPS has to be specified and tested against environments that require the system to:operate in real-time, realize reactive computations, leverage concurrent and distributed processing, deal with synchronization issues.In [2], one of the major books on CPS in a vast (e.g. [3,4,10,15,17,24,26,27]) literature on the subject, Alur describes how Linear Hybrid Automata (LHA) can be used for modeling CPS. In this context, the 2-reservoirs problem [17], a text-book problem on dynamic systems where a control system needs to decide to which of two tanks a hose needs to be moved given the reservoirs and hose's physical characteristics, is a CPS and therefore can be modeled as a LHA. In this paper we generalize this problem to an arbitrary number of reservoirs, each with their individual physical characteristics, and by adding latency to hose dislocation. We model and analyze both the standard problem description and the generalized version using Rewriting Logic [19], an expressive formalism for the specification and verification of concurrent and distributed systems [22]. Moreover, we specify the n-reservoir system modularly as the synchronous product [5] of its constituent components. This paper contribution is manifold : (i) a precise definition of the synchronous product of real-time rewrite systems, extending [18], (ii) a model of the n-reservoir problem as an LHA, (iii) how to describe a CPS as a LHA in Rewriting Logic by representing its components, sensors, actuators and controllers, as mathematical tuples denoting objects that communicate asynchronously, (iv) a modular specifi...

A Strategy-Based Formal Approach for Fog Systems Analysis

“…The Maude language has been cited in many scientific articles and books. It has been used to formally specify and execute context-aware systems [29], cloud systems [30], supply chain management [31], and cyber-physical systems [32].…”

Hybrid Rebeca: Modeling and Analyzing of Cyber-Physical Systems

“…This approach relies on simulation to analyze a system, and no formal analysis is supported. In [17] a modular approach for specifying and validating CPSs using rewriting logic-based technique is purposed. In this work a CPS is described as a linear hybrid automata in rewriting logic where the components of the system communicate asynchronously.…”