Hybrid I/O automata

Hybrid systems are systems that exhibit a combination of discrete and continuous behavior. Typical hybrid systems include computer components, which operate in discrete program steps, and real-world components, whose behavior over time intervals evolves according to physical constraints. Important examples of hybrid systems include automated transportation systems, robotics systems, process control systems, systems of embedded devices, and mobile computing systems. Such systems can be very complex, and very difficult to describe and analyze. This paper presents the Hybrid Input/Output Automaton (HIOA) modeling framework, a basic mathematical framework to support description and analysis of hybrid systems. An important feature of this model is its support for decomposing hybrid system descriptions. In particular, the framework includes a notion of external behavior for a hybrid I/O automaton, which captures its discrete and continuous interactions with its environment. The framework also defines what it means for one HIOA to implement another, based on an inclusion relationship between their external behavior sets, and defines a notion of simulation, which provides a sufficient condition for demonstrating implementation relationships. The framework also includes a composition operation for HIOAs, which respects the implementation relation and a notion of receptiveness, which implies that an HIOA does not block the passage of time. The framework is intended to support analysis methods from both computer science and control theory. This work is a simplification of our earlier HIOA model. The main simplification in the new model is a clearer separation between the mechanisms used to model discrete and continuous interaction between components. In particular, the new model removes the dual use of external variables for discrete and continuous interactions.