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Timing, Sensitivity and Optimality Properties of Hierarchical-Hybrid Systems

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.

Thierry Baron
Mon Apr 7 12:54:24 EDT 1997