We take a real-time embedded system to be the control system of a plant in an open environment, where the control is realized by computation in digital or analog form. The key characteristic of a real-time embedded system is that computation is interleaved or in parallel with actions of the plant and events in the environment. Various models for real-time embedded systems have been proposed in recent years, most of which are extensions of existing concurrency models with delays or time bounds on transitions. In this paper, we present a different approach to modeling real-time systems. We take the overall system as a dynamic system, in which time or event structures are considered as an intrinsic dimension. Our model, called the Constraint Net model (CN), is capable of expressing dynamic behaviors in real-time embedded systems. It captures the most general structure of dynamic systems so that systems with discrete as well as dense time and asynchronous as well as synchronous event structures can be modeled in a unified framework. It models the dynamics of the environment as well as the dynamics of the plant and the dynamics of the computation and control. It provides multiple levels of abstraction so that a system can be modeled and developed hierarchically. By explicitly representing locality, CN can be used to explore true concurrency in distributed systems. With its rigorous formalization, CN provides a programming semantics for the design of real-time embedded systems. It also serves as a foundation for specification, verification, analysis and simulation of the complete dynamic system.
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