The fundamental notion here is that of dynamical consistency between an ordered pair of blocks of a hierarchical aggregation (partition) of the states of a system. This property is said to hold when all the states of the first block may be driven directly (by some initial state dependent control sequence) into the second block. The concept of dynamical consistency permits the definition of a hierarchical lattice of increasingly aggregated sub-systems of a given system, and hence of the set of hierarichal control systems of a given system. Such configurations are naturally expressed in terms of hierachies of COCOLOG control languages. Furthermore, these constructions naturally extend to the case where the finest (base) system is a continuous (ODE) system and this gives rise to a theory of dynamically consistent hybrid system.
Y-J. Wei, P.E. Caines