Analogue-digital systems with modes of operation.
Edwin J Beggs, John Vivian Tucker · 2014
We consider the nature of the relationship between physical environments, processes and systems, and the algorithms and software that monitor or govern them. In the case of complex physical situtations, no one mathematical model can serve; rather their physical behaviour or operation may reveal several distinct regimes or modes. Thus, for the design of complex physical environments, processes and systems, a set of mathematical models – possibly of disparate kinds – may be needed, each model having its own domain of application and representing a single mode of behaviour or operation of the complex system. We propose a general definition of an analogue-digital system with modes based upon a portfolio of models, and we tackle the computational problem of transitioning from using one mode/model to another. We show that the modes/models can be bound together and transitions between modes/models can be visualised by a simplicial complex. We illustrate the ideas by reflecting on a simple example of driverless racing cars. No plan survives contact with the enemy. After Helmuth von Moltke the Elder (1800-1891) There are known knowns; there are things we know that we know. There are known unknowns; that is to say, there are things that we now know we don’t know. But there are also unknown unknowns – there are things we do not know we don’t know. Donald Rumsfeld (2002)