Hierarchical strategies for hybrid process control problems

Hybrid control methods offer an alternative to "traditional" nonlinear controller synthesis techniques when specifications are "coarse" and may hence be represented through quantized variables. A standard approach is to first construct a conservative discrete abstraction for the nonlinear continuous model-discrete abstraction and discrete specification form a purely discrete synthesis problem, which can subsequently be solved using standard methods from DES (discrete event systems) theory. Unfortunately, this approach suffers from the "curse of dimensionality": even for very moderately sized continuous models and simple specifications, the state set of the resulting discrete problem tends to "explode". To alleviate this problem, additional hierarchical structure is introduced. We discuss an approach that provides sufficient conditions for the "correct" functioning of the hierarchical hybrid control system.