The Hierarchical Lattices of a Finite

The concept of dynamical consistency is introduced to deene a high level transition function for an arbitrary partition of the state space of a nite input-state machine M. The existence of a dynamically consistent transition from a partition member X i to a member X j corresponds to the existence, for every state x in X i , of some (x dependent) control sequence which takes that state directly into X j. This paper analyses what are termed in-block controllable partition machines and between-block controllable partition machines, and establishes the existence of the associated in-block controllable hierarchical lattice IBCP(M). It is shown that any partition machine in IBCP(M) is between-block controllable if and only if the base machine M is controllable. This setting allows the speciication of state to state control trajectories of M to be decomposed into high level and low level components.