The hierarchical control of ST-finite state machines

Abstract

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 /spl pi/. This formulation results in a definition of high level dynamics on the finite (partition) machine M/sup /spl pi// 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.