Hierarchical control system design using approximate simulation

In this paper, we present a new approach for hierarchical control based on the recent notions of approximate simulation and simulation functions, a quantitative version of the simulation relations. Given a complex system that needs to be controlled and a simpler abstraction, we show how the knowledge of a simulation function allows us to synthesize hierarchical control laws by first controlling the abstraction and then lifting the abstract control law to the complex system using an interface. For the class of linear control systems, we give an effective characterization of the simulation functions and of the associated interfaces. This characterization allows us to use algorithmic procedures for their computation. We show how to choose an abstraction for a linear control system such that our hierarchical control approach can be used. Finally, we show the effectiveness of our approach on an example.