Hierarchical control of piecewise affine hybrid systems

This paper extends the hierarchical control structures in [4], [6], [17] to the important class of piecewise affine (PWA) hybrid systems. In particular, we extend the notions of dynamical consistency (DC), hybrid in-block controllable (HIBC) partitions and DC partition machines to PWA hybrid systems. Using these notions, we show that if an HIBC partition of the state space is constructed, then controllability of the PWA hybrid system can be easily checked from the associated DC partition machine. Then, we construct the lattice of HIBC partitions and use it to build a hierarchical control structure of the system in which a control objective at any level of abstraction can be realized by state dependent control sequences at the lower levels.