Output-feedback control of an underactuated network of interconnected hyperbolic PDE–ODE systems

Abstract

In this paper, the output feedback stabilization of an underactuated chain of scalar hyperbolic systems coupled at one end with a finite-dimensional system is addressed. As encountered in practical applications, only the first PDE subsystem is actuated. The measurements are collocated with the actuation. The proposed approach uses a recursive dynamics interconnection framework. More precisely, we first estimate (delayed) values of the states at each subsystem’s boundaries. Then, we design a state-predictor that gives access to the boundary states’ present and future values. It becomes finally possible to design a state-observer for the entire system. Combining this observer with a stabilizing state-feedback law, we can recursively design an output-feedback control law that stabilizes the whole chain. Some illustrative examples complete the presentation.