Modelling of Complex Systems: Systems as dataflow machinesDaniel KrobEcole Polytechnique & CNRS |
We present a unified functional formalism for modelling complex systems, that is to say systems that are composed of a number of heterogeneous components, including typically software and physical devices. Our approach relies on non-standard analysis that allows us to model continuous time in a discrete way.
Systems are defined as generalized Turing machines with temporized
input, internal and output mechanisms. Behaviors of systems are
represented by transfer functions. A transfer function is said to
be implementable if it is associated with a system. This
notion leads us to define a new class – which is natural in our
framework – of computable functions on (usual) real
numbers.
We show that our definitions are robust: on one hand, the class of
implementable transfer functions is closed under composition; on
the other hand, the class of computable functions in our meaning
includes analytical functions whose coefficients are computable in
the usual way, and is closed under addition, multiplication,
differentiation and integration. Our class of computable functions
also includes solutions of dynamical and Hamiltonian systems
defined by computable functions. Hence, our notion of system
appears to take suitably into account physical systems.
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