In this paper a hybrid (base) system is modelled as quintuple consisting of a state space (which is the direct product of a set of discrete states and an n-dimensional manifold), sets of admissible continuous and discrete controls, a family of controlled autonomous vector fields assigned to each discrete state, and a (partially defined) map of discrete transitions. Next, generalizing the theory presented in (Caines 8. Wei 1998), the notion a finite analytic partition II of a state space of a hybrid system is defined. Then the notion of dynamical consistency is generalized to that of hybrid dynamical consistency. Based on these notions, the partition machine H rl of a hybrid system H is defined in such a way that, in the class of in-block controllable partitions, the controllability of the high level system (described by the partition machine, which is a discrete finite state machine) is equivalent (under some technical conditions) to the controllability of the low level system (described by differential equations). Within the hybrid partition machine framework, a discrete controller supervises its continuous subsystems via hierarchical feedback relations; furthermore, each continuous subsystem is itself (internally) subject to feedback control.
Jan-11-2006, 10:48:37 GMT