Design of the interfaces based on approximate hierarchies

Hierarchical control method imposing a (at least) two-layer hierarchical structure on the control system architecture is a recently developed efficient method for the investigation of system properties and the design of control laws. This method is worth studying because of the powerful forces it shows in complex dynamics, especially large-scale systems. In this paper, a new approach for hierarchical control for nonlinear systems is discussed based on the notion of approximate simulation relation recently introduced. An approximate simulation could allow us to synthesize hierarchical control law and guarantee that an approximate bound is easily obtained. Then, we present a new technique for the design of interface functions which lift the controller of abstract or approximate system to the concrete or complex system. Finally, an example illustrates the correctness and the effectiveness of our design technique.