Continuous automata: bridging the gap between discrete and continuous time system models

The principled use of models in design and maintenance of a system is fundamental to the engineering methodology. As the complexity and sophistication of systems increase so do the demands on the system models required to design them. In particular the design of agent systems situated in the real world, such as robots, will require design models capable of expressing discrete and continuous changes of system parameters. Such systems are referred to as mode-switching or hybrid systems.This thesis investigates ways in which time is represented in automata system models with discretely and continuously changing parameters. Existing automaton approaches to hybrid modelling rely on describing continuous change at a sequence of points in time. In such approaches the time that elapses between each point is chosen non- deterministically in order to ensure that the model does not over-step a discrete change. In contrast, the new approach this thesis proposes describes continuous change by a continuum of points which can naturally and deterministically capture such change. As well as defining the semantics of individual models the nature of the temporal representation is particularly important in defining the composition of modular com­ponents. This new approach leads to a clear compositional semantics based on the synchronization of input and output values.The main contribution of this work is the derivation of a limiting process which provides a theoretical foundation for this new approach. It not only provides a link between dis­crete and continuous time representations, but also provides a basis for deciding which continuous time representations are theoretically sound. The resulting formalism, the Continuous I/O machine, is demonstrated to be comparable to Hybrid Automata in expressibility, but its representation of time gives it a much stronger compositional semantics based on the discrete synchronous machines from which it is derived.TThe conclusion of this work is that it is possible to define an automaton model that describes a continuum of events and that this can be effectively used to model complete mode-switching physical systems in a modular fashion