This paper focuses on the challenges of modeling cyber-physical systems (CPSs) that arise from the intrinsic heterogeneity, concurrency, and sensitivity to timing of such systems. It uses a portion of an aircraft vehicle management system (VMS), specifically the fuel management subsystem, to illustrate the challenges, and then discusses technologies that at least partially address the challenges. Specific technologies described include hybrid system modeling and simulation, concurrent and heterogeneous models of computation, the use of domain-specific ontologies to enhance modularity, and the joint modeling of functionality and implementation architectures.

Modeling Cyber–Physical Systems

This paper is about better engineering of cyber-physical systems (CPSs) through better models. Deterministic models have historically proven extremely useful and arguably form the kingpin of the industrial revolution and the digital and information technology revolutions. Key deterministic models that have proven successful include differential equations, synchronous digital logic and single-threaded imperative programs. Cyber-physical systems, however, combine these models in such a way that determinism is not preserved. Two projects show that deterministic CPS models with faithful physical realizations are possible and practical. The first project is PRET, which shows that the timing precision of synchronous digital logic can be practically made available at the software level of abstraction. The second project is Ptides (programming temporally-integrated distributed embedded systems), which shows that deterministic models for distributed cyber-physical systems have practical faithful realizations. These projects are existence proofs that deterministic CPS models are possible and practical.

The past, present and future of cyber-physical systems: a focus on models.

This paper argues that cyber-physical systems present a sub-stantial intellectual challenge that requires changes in both theories of computation and dynamical systems theory. The CPS problem is not the union of cyber and physical problems, but rather their intersection, and as such it demands models that embrace both. Two complementary approaches are identified: cyberizing the physical (CtP) means to endow physical subsystems with cyber-like abstractions and interfaces; and physicalizing the cyber (PtC) means to endow software and network components with abstractions and interfaces that represent their dynamics in time.

CPS foundations

Model-based design is a powerful design technique for cyber-physical systems, but too often literature assumes knowledge of a methodology without reference to an explicit design process, instead focusing on isolated steps such as simulation, software synthesis, or verification. We combine these steps into an explicit and holistic methodology for model-based design of cyber-physical systems from abstraction to architecture, and from concept to realization. We decompose model-based design into ten fundamental steps, describe and evaluate an iterative design methodology, and evaluate this methodology in the development of a cyber-physical system.

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A model-based design methodology for cyber-physical systems

Twenty years of rewriting logic

We define a family of execution policies for a programming model called PTIDES (Programming Temporally Integrated Distributed Embedded Systems). A PTIDES application (factory automation, for example) is given as a discrete-event (DE) model of a distributed real-time system that includes sensors and actuators. The time stamps of DE events are bound to physical time at the sensors and actuators, turning the DE model into an executable specification of the system with explicit real-time constraints. This paper first defines a general execution strategy that conforms to the DE semantics, and then specializes this strategy to give practical, implementable and distributed policies. Our policies leverage network time synchronization to eliminate the need for null messages, allow independent events to be processed out of time stamp order, thus increasing concurrency and making more models feasible (w.r.t. real-time constraints), and improve fault isolation in distributed systems. The policies are given in terms of a safe to process predicate on events that depends on the time stamp of the events and the local notion of physical time. In a simple case we show how to statically check whether program execution satisfies timing constraints.

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Execution Strategies for PTIDES, a Programming Model for Distributed Embedded Systems

: We study the simultaneous use of multiple modeling techniques in the design of embedded systems. We begin with a pre-existing Statecharts model of a simple case study, a traffic light for a pedestrian crossing. This model combines two distinct models of computation (MoCs), finite state machines (FSMs) and synchronous/reactive (SR). We add an additional MoC to the mix, a discrete-event (DE) model of the environment in which the traffic light operates, including a simple fault model. We construct a second model of a hardware deployment. This exercise reveals hidden assumptions in the original model about implementation that require refactoring to get a distributed deployment model. We show that the portions of the models defining the control logic of the lights can be shared between the functional and deployment models using actor-oriented classes. This eases maintenance of the models. Finally, we show that models used for verification are abstractions of the functional models that can be synthesized from the other models, suggesting practical design-for-verification techniques. The result is that this simple example uses three distinct models of the system (functional, deployment, verification), two of which hierarchically combine distinct modeling techniques (DE, SR, FSM).

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Model Engineering using Multimodeling

: We describe a programming model called PTIDES (Programming Temporally Integrated Distributed Embedded Systems), that extends the discrete-event model of computation with a carefully chosen relationship between real time and model time. PTIDES provides a framework for exploring a family of execution strategies for distributed embedded systems. Our objective in this paper is to present an execution strategy that 1) allows independent events to be processed out of time stamp order, 2) uses clock synchronization as a replacement for null message communication across distributed platforms, 3) defines a notion of when events are safe to process and 4) presents an implementation of a PTIDES model. This work puts forward an execution strategy that is aggressive in concurrent execution of events.

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PTIDES: A Programming Model for Distributed Real-Time Embedded Systems

Verifying hierarchical Ptolemy II discrete-event models using Real-Time Maude

This paper shows how Ptolemy II discrete-event (DE) models can be formally analyzed using Real-Time Maude. We formalize in Real-Time Maude the semantics of a subset of hierarchical Ptolemy II DE models, and explain how the code generation infrastructure of Ptolemy II has been used to automatically synthesize a Real-Time Maude verification model from a Ptolemy II design model. This enables a model-engineering process that combines the convenience of Ptolemy II DE modeling and simulation with formal verification in Real-Time Maude.

Thomas Huining Feng

Papers

Execution Strategies for PTIDES, a Programming Model for Distributed Embedded Systems

Model Engineering using Multimodeling

PTIDES: A Programming Model for Distributed Real-Time Embedded Systems

Verifying hierarchical Ptolemy II discrete-event models using Real-Time Maude

Verifying Ptolemy II Discrete-Event Models Using Real-Time Maude