The Hierarchical Control of ST-Finite State Machines

This paper follows 3] where a new notion of state aggregation for nite machines was introduced via the concept of the dynamical consistency (DC) relation between the blocks of states in any given state space partition. This formulation results in a deenition of high level dynamics on the nite (partition) machine M 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 ow from a set of source states (S) to a set of target states (T) which is to be achieved by (hierarchical) control. A generali-sation of the theory of 3] 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.