A Network Model of Analogue Computation over Metric Algebras

We define a general concept of a network of analogue modules connected by channels, processing data from a metric space A, and operating with respect to a global continuous clock T. The inputs and outputs of the network are continuous streams u : T → A, and the input-output behaviour of the network with system parameters from A is modelled by a function Φ : C[T, A]×Ar → C[T, A] (p, q > 0, r ≥ 0), where C[T, A] is the set of all continuous streams equipped with the compact-open topology. We give an equational specification of the network, and a semantics which involves solving a fixed point equation over C[T, A] using a contraction principle. We analyse a case study involving a mechanical system. Finally, we introduce a custom-made concrete computation theory over C[T, A] and show that if the modules are concretely computable then so is the function Φ.