Modelling of Cyber-Physical Systems

Abstract

Cyber-Physical systems are heterogenous with both physical and cyber components. This chapter will briefly explain CPS, its generic architecture, modeling requirements, modeling languages and levels of CPS integration. The different modeling techniques of CPS are briefly discussed as a primer for subsequent chapters.

KEYWORDS

Cyber-physical systems, UML, SySML, Model-based systems engineering, modeling , Simulation

Introduction

Systems that integrate computational and physical components closely are called Cyber-Physical Systems (CPS). With the breakthroughs in emerging domains such as Machine learning, IoT, Blockchain, AR/VR, and Cloud computing technologies that will enable CPS, there is a need for significant improvement in the modelling and simulation of core CPS. Today's CPS is still in its primitive state regarding its adaptability, autonomy, efficiency, functionality, reliability, safety, and usability[1]. Therefore, before adding new enabling technologies to the CPS, the system requirements must be modelled, simulated and validated with efficient modeling and simulation tools and techniques.

From systems that respond more quickly, such as autonomous collision avoidance, to more precise systems, such as robotic surgery and nano-tolerance manufacturing, the cyber and physical components must be strongly intertwined. Hence, the CPS models built and simulated using the computing facilities before actual development and implementation cannot afford to be an approximate representation of the real world.

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Generic Architecture of CPS

CPS are generally very complex with intertwined networks between the physical and the cyber components. However, we can simplify and generalize the CPS structure as consisting of Cyber System, Physical System and Interface systems (A/D and D/A) as shown in Figure 1.1.

CPS Modeling requirements

To model any CPS, it is necessary to understand the functional and nonfunctional features and the requirements imposed by these features. The Functional features comprise the intended use of what that CPS is designed for, while the nonfunctional requirements constitute the external ambient constraints and noise factors that can affect the intended operations of the functional features. Both the functional and the nonfunctional requirements need to be considered while modeling and designing the CPS.

Functional requirements

The system's behaviour and response to particular inputs are described in the functional specifications. The publish-subscribe (event-driven) and request-reply execution models are the two sorts of models that the functional behaviour of CPS defines (conversational). Messages or physical actions can be used to communicate amongst the various parts of the system. These components offer functionalities, which may be physical or software-based[3].

Nonfunctional requirements

The nonfunctional specifications are the external constraints imposed by the super system surrounding the CPS that characterize the behaviour offered by the system. They have been classified as time-related properties, physical properties and behavioural properties. Time-related properties are temporal properties associated with time-based or event-based actions of the physical system. Time-based properties are required to be accurate, which, if missed, can render the functionality of the entire CPS zero. Physical properties refer to the spatial properties that are static or dynamic depending on their dependency on the temporal domain. Behavioral properties refer to the human-centric properties that, when violated, can affect the safety and liveness of the CPS and the human[4].?

CPS Modelling and Simulation Languages

Cyber-physical systems constitute discrete and continuous systems but are deeply intertwined. This makes it very challenging to model and simulate even simple CPS applications. Hence, many software programming languages have been explored for modeling and simulation. While most of them are successful, more discrete-continuous systems need further integration to improve accuracy and realistic representation of the actual CPS deployed in the field.

Modelica

The principal object-oriented modelling language used for multi-domain programming and simulation has been Modelica. Modelica features casual as well as a casual connection of multi-domain subsystems ( such as mechanical, electrical, electronic, and thermal), which usually is controlled and governed by mathematical equations. Since it is free and open source, many software packages such as Open Modelica(open source), solidThinking Activate by Altair, Simplorer by ANSYS, Dymola by Dassault Systemes, Simulation X by ESI ITI GmbH, Maplesim by Maplesoft and Wolfram SystemModeler by Wolfram are developed using Modelica framework. It also features free editors such as Atom, Modelica Development tooling, and OneModelica. ?

Modelica is extensively used for modelling CPS. One example is demonstrated in a robot where accurate timing simulations based on the TrueTime simulator were integrated into the Modelica Embedded Systems framework [5]. Here, both network simulations and simulations of task scheduling in real-time kernels were included in the timing simulations using the robot as an example. Modelica supports equation-based connections between the CPS components, not Message passing communication (MPC). However, a method to include MPC in Modelica is discussed in [6]. Modelica is also used with other CPS modelling languages, such as AADL[7] and FORM-L[8].

BPMN

Business Process Model and Notation (BPMN) is a business process modelling language comprising graphical notations to model business processes. It is a standard developed to ease the collaboration between business systems and integrate the deep interconnections between business systems and physical device frameworks such as IoT[9].

?UML

Traditionally, Unified Modeling Language (UML) is used to model the behaviour of software systems using UML state machines and activity notations before they are coded. Systems Modeling Language (SysML), an extension of UML for Model-based Systems Engineering, can be used to model the behavioural properties of CPSs[10]. Another extension of UML designed explicitly for real-time embedded systems is MARTE, which stands for Modeling and Analysis of Real-Time Embedded Systems(RTES) can be used to model CPS to some extent[11].

AADL

Developed initially for RTES, Abstract Architecture Description Language (AADL) can be used to model the systems architecture comprising the deeply intertwined hardware and software subsystems. However, AADL does not support the modelling of physical properties. However, this drawback can be nullified by designing extensions or combining them with other simulation tools such as Simulink[12].

CPS LEVELS OF INTEGRATION

A CPS can be considered a system of heterogeneous systems. So CPS can be designed at the component or subsystem or sub-assembly level, at a systems level and super systems level. Subsystem CPSs comprise individual CPSs that integrate to form the system level CPS. The super-system CPS is generally the environment in the system level CPS functions.

For example, suppose an autonomous car is considered a system-level CPS. In that case, the intelligent vehicular transport infrastructure is the Super system level CPS and the battery management system can be subsystem level CPS. Therefore, for modeling and design of any CPS, it has to consider the tight integration of its subsystems and super systems. This required coordination and codesign of the CPS OEM with its suppliers and clients. For the above, A car company such as Tesla may need to codesign with a transportation infrastructure service provider and its battery management system supplier. ?

CPS Modelling techniques

There are significant challenges in the modelling and simulation of CPSs due to their heterogeneous component systems, concurrency of spatial and temporal properties, and levels of abstraction, to name a few. For more accuracy and functionality, the CPS modelling techniques must incorporate both the functional and the nonfunctional requirements. Some of the modeling techniques were surveyed in [13]. Other sources are adaptive discrete event model, model-based design methodologies, Cyber-Physical complementary approach, multi-modal dynamics approach, and meta-architectural design methodologies.

Adaptive Discrete Event Model

For CPSs, An adaptive discrete event model based on Discrete-Event Calculus(DEC) was proposed by [14]. Utilizing DEC permits processing ambient events while preventing discrepancies in the formulation of domain rules. The CPS's cyber part can be more adaptive by adding additional anomalous reasoning set to enhance the discretional capabilities of the CPS for adverse and ad-hoc environmental circumstances.

Model-Based Design Methodologies

In the Model-Based Systems Engineering (MBSE) approach, the requirements analysis, design, prototyping, testing, analysis and validation systems are model-centric. MBS is prevalent in designing complex hybrid systems using SysML and other prominent system modelling languages, thus making it favourable for CPS design of CPSs. In [15], a ten-step MBSE approach is suggested for the design of CPSs, starting from the problem statement, problem statement, physical modelling process, problem characterization, control algorithm development, selection of computational models, hardware specification, simulation, construct, synthesize and lastly validate using tests. The coupling of discrete event-based and continuous time-based models using the MBSE approach in the CPSs was discussed in [16].

?Cyber-Physical Complimentary Approach

This approach encapsulates the software abstractions around the physical entities and the physical abstractions in the software and networking subsystems [17]. As the CPS modelling becomes more realistic, more abstractions increase thus reducing the error in integrating cyber and physical entities when they eventually merge as a single CPS.

Multi-modal dynamics approach

As per this approach, a CPS system is characterized as operating at different modes where the modal dynamics of each mode are well known. To ensure the safety of the CPS, it is essential to switch accurately between two consecutive modes. The switching logic between two consecutive modes must be synthesized using intramode dynamics[18].?

Meta-Architectural Design Methodologies

Meta-architectural specification languages can be used to specify the intended properties of the model without the requirement of achieving them. It helps synthesize CPS systems with Realtime constraints[19]. Meta-Architecture design using AADL.

Other methods or approaches can be explored in the literature apart from those discussed above. Some methods include codesigning, the use of semantics, and specializing middleware. However, the approaches do not entirely model?but can at least help with partial modeling requirements of CPS.

References

[1]???????National Science Foundation, “Cyber-Physical Systems (CPS),” nsf21551, 2021. https://www.nsf.gov/pubs/2021/nsf21551/nsf21551.pdf.

[2]???????P. Radanliev, D. De Roure, M. Van Kleek, O. Santos, and U. Ani, "Artificial intelligence in cyber-physical systems," AI Soc., vol. 36, no. 3, pp. 783–796, 2021.

[3]???????I. Graja, S. Kallel, N. Guermouche, S. Cheikhrouhou, and A. Hadj Kacem, "A comprehensive survey on modelling of cyber‐physical systems," Concurr. Comput. Pract. Exp., vol. 32, no. 15, p. e4850, 2020.

[4]???????A. Rajhans et al., “An architectural approach to the design and analysis of cyber-physical systems,” Electron. Commun. EASST, vol. 21, 2009.

[5]???????D. Henriksson and H. Elmqvist, "Cyber-physical systems are modelling and simulation with Modelica," in Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical University; Dresden; Germany, 2011, no. 063, pp. 502–509.

[6]???????V. Sanz and A. Urquia, "Cyber-physical system modelling with Modelica using message passing communication," Simul. Model. Pract. Theory, vol. 117, p. 102501, 2022, DOI: https://doi.org/10.1016/j.simpat.2022.102501.

[7]???????T. Huang, Z. Cao, and Q. Li, “Verification and Fault Analysis based on Combination of AADL and Modelica,” in Journal of Physics: Conference Series, 2022, vol. 2261, no. 1, p. 12014.

[8]???????D. Bouskela et al., "Formal requirements modelling for cyber-physical systems engineering: An integrated solution based on FORM-L and Modelica," Required. Eng., vol. 27, no. 1, pp. 1–30, 2022.

[9]???????I. About, Y. K. Bekali, and R. Saidi, "Modelling IoT Behaviour in Supply Chain Business Processes with BPMN: A Systematic Literature Review," J. ICT Stand., pp. 439–468, 2022.

[10]?????A. Hayward, M. Rappl, and A. Fay, “A SysML-based Function-Centered Approach for the Modeling of System Groups for Collaborative Cyber-Physical Systems,” in 2022 IEEE International Systems Conference (SysCon), 2022, pp. 1–8.

[11]?????V. Sood, M. K. Nema, R. Kumar, and M. J. Nene, "A framework for prototyping Distributed Cyber-Physical Systems with reference nets," Simul. Model. Pract. Theory, vol. 117, p. 102488, 2022.

[12]?????X. Xu, S. Wang, B. Zhan, X. Jin, J.-P. Talpin, and N. Zhan, "Unified graphical co-modelling, analysis and verification of cyber-physical systems by combining AADL and Simulink/Stateflow," Theor. Comput. Sci., vol. 903, pp. 1–25, 2022.

[13]?????S. K. Khaitan and J. D. McCalley, "Design techniques and applications of cyber-physical systems: A survey," IEEE Syst. J., vol. 9, no. 2, pp. 350–365, 2014.

[14]?????K. Yue, L. Wang, S. Ren, X. Mao, and X. Li, "An adaptive discrete event model for the cyber-physical system," in Analytic Virtual Integration of Cyber-Physical Systems Workshop, 2010, pp. 9–15.

[15]?????J. C. Jensen, D. H. Chang, and E. A. Lee, “A model-based design methodology for cyber-physical systems,” in 2011 7th international wireless communications and mobile computing conference, 2011, pp. 1666–1671.

[16]?????J. Fitzgerald, C. Gamble, R. Payne, P. G. Larsen, S. Basagiannis, and A. E.-D. Mady, “Collaborative Model-based Systems Engineering for Cyber-Physical Systems, with a Building Automation Case Study,” INCOSE Int. Symp., vol. 26, no. 1, pp. 817–832, Jul. 2016, doi: https://doi.org/10.1002/j.2334-5837.2016.00195.x.

[17]?????E. A. Lee, “CPS foundations,” in Design automation conference, 2010, pp. 737–742.

[18]?????S. Jha, S. Gulwani, S. A. Seshia, and A. Tiwari, “Synthesizing switching logic for safety and dwell-time requirements,” in Proceedings of the 1st ACM/IEEE International Conference on Cyber-Physical Systems, 2010, pp. 22–31.

[19]?????C. Hang, P. Manolios, and V. Papavasileiou, “Synthesizing cyber-physical architectural models with real-time constraints,” in International Conference on Computer Aided Verification, 2011, pp. 441–456.