On-line co-ordination under uncertainty of weakly interacting dynamical systems

The problem of on-line co-ordination of a hierarchically controlled dynamical system under uncertainty by using the interaction balance principle is discussed. For the sake of simplicity, a two-level system consisting of two subsystems interconnected by means of buffer storages is considered. In order to avoid measure theoretic difficulties, only a finite set of typical disturbance realizations are taken to represent the uncertainty in the system. The uncertainty leads to a co-ordination method based on a 'balance in the mean' condition. It turns out that the weakness of the mutual interaction between the subsystems is an important concept. In the case considered the buffer storages contribute to the weakness of the interaction to a noticeable degree.