G. Gang, E. Lemch, P.E. Caines
In this work, we are
analysing and extending the following aspects of the hierarchical-hybrid
control theory initiated by Caines and Wei (see this report) by considering
the following:
(i) Generalizations
of the notion of the lattice of hierarchical control systems for any
given base system *S*; this is in the case where
the notion of controllability is generalized to that of controllability from
certain source states to certain target states of *S*, and where timing
constraints are put on the accessibility of states (work partially
in cooperation with V. Gupta of Xerox-PARC).
(ii) An analysis of the sensitivity
of the finite state partition machine obtained from the partition of the state
space of continuous system *S* (see the summary of work on hierarchical-hybrid systems
by Caines and Wei in this report). This is in terms of the sensitivity of the
dynamics of the partition machine for any given
continuous base system *S* with respect to changes in the boundaries of the
state space partition (work partly supported by NASA-Ames, Sunnyvale, CA.).
(iii) Studies of the nature of the suboptimality of hierarchical-hybrid
control; this
involves a general analysis of the optimality loss when trajectories are found
by,
first, optimal trajectory selection in the given higher level partition machine,
and then, second,
by optimal control selection in each of the cells of the lower level base
machine *S*.

Mon Apr 7 12:54:24 EDT 1997