PDE based observer design for nonlinear systems with large output delay

Abstract

In this paper, we develop a new observer design method for nonlinear systems with large transport delays. The new observer design is a generalization of the PDE-based backstepping-like observer design approach. First developed for delayed linear systems, this approach relies on a modelling of the output time-delay by a 1st order hyperbolic equation, leading to an ODE–PDE representation of the system, and on coordinate transformations of the innovative system. The major technical challenge, that is faced in the generalization of the approach to nonlinear systems, consists in making it applicable in the case of an arbitrarily large time-delay D. This issue is presently coped with by redesigning the cascade observer method to fit ODE–PDE systems. A new class of observers is thus obtained involving a set of cascaded high-gain state observers and output predictors. The latter are defined by PDEs that provide estimates of the system future outputs y(t+x) for all x∈[0,D]. The exponential stability of the observer is proved using a set of Lyapunov functionals and its performances are illustrated by simulation.