The hierarchical control of ST-finite state machines

This paper follows Caines and Wei (1995) where a new notion of state aggregation for finite machines was introduced via the concept of the dynamical consistency (DC) relation between the blocks of states in any given state space partition π. This formulation results in a definition of high level dynamics on the finite (partition) machine M ^π whose states correspond to the given partition elements. This paper treats the more general case of ST-systems where there is a preferred sense of how from a set of source states (S) to a set of target states (T) which is to be achieved by hierarchical control. A generalisation of the theory in the above article to ST-systems is given which includes the generalisation of the notions of dynamical consistency, in block controllability and hierarchical feedback control on the associated hierarchical lattices