A model of systems with modes and mode transitions

We propose a method of classifying the operation of a system into finitely many modes. Each mode has its own objectives for the system's behaviour and its own algorithms designed to accomplish its objectives. A central problem is deciding when to transition from one mode to some other mode, a decision that may be contested and involve partial or inconsistent information. We propose some general principles and model mathematically their conception of modes for a system. We derive a family of data types for analysing mode transitions; these are simplicial complexes, both abstract and concretely realised as geometric spaces in euclidean space . In the simplicial complex, a mode is represented by a simplex and each state of a system can be evaluated by mapping it into one or more simplices. This evaluation measures the extent to which different modes are appropriate for the state and can decide on a transition. To illustrate the general model in some detail, we work though a case study of an autonomous racing car