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Non-Deterministic Reactive Systems, from Hybrid Systems and Behavioural Systems Perspectives

Abstract A reactive system is an entity which takes as inputs signals from a certain set, and transforms them to produce as outputs signals in some further set, where a signal is modeled as a function from a time domain to a value space, and time domains are linearly ordered sets. Building on our previous work which generalizes Aubin's Evolutionary Systems model, we develop a general formulation of non-deterministic input-output reactive systems that is uniform for discrete, continuous and hybrid time, and which extends Willems’ Behavioural Systems input-output model by allowing hybrid time, and by allowing different time domains for input and output signals. However, our approach differs from these existing frameworks in that instead of taking as primitive signals over infinite-length time domains, we work with finite-length paths and utilize their algebraic and partial-order structure. We illustrate our framework with a generic model of event-driven A/D conversion, transforming a continuous-time input signal into a discrete-time output signal via an intermediate hybrid-time signal.