Observer design for a class of piecewise affine hybrid systems

Abstract

A methodology for the design of observers is proposed for a special class of hybrid dynamical systems, which are motivated by traffic and manufacturing applications. The class of hybrid systems is characterized as switched system models with constant drift and constant output, rendering all subsystems unobservable by themselves. However, an observer can still be derived due to the fixed switching pattern, even though the switching times may be unknown. A main step in the observer design methodology is the usage of a discrete-time linear observer based on the discretized hybrid dynamics at the event times that are visible. Using this step, a continuous-time observer is built that incorporates additional modes compared to the original hybrid system. This continuous-time observer is shown to asymptotically reconstruct the state of the original system under suitable assumptions. Manufacturing and traffic applications are used to illustrate the proposed observer design methodology.