Hierarchical Control using Approximate Simulation Relations

In this paper we present a new approach for hierarchical control based on the recent notions of approximate simulation relations and simulation functions. Given a complex system that need to be controlled, approximate simulation relations allow to characterize a simple approximation of the system, that can be used for the control design. The controller of this approximate system can be lifted to the complex system using an interface which is completely characterized by a simulation function. Then, the distance between the external trajectories of the complex system and the external trajectories of the approximation is guaranteed to remain bounded by a precision that can be evaluated from the simulation function. This makes our approach suitable for safety critical systems. We show an application to robot motion control