Observer design for a class of parabolic systems with arbitrarily delayed measurements

Abstract

An observer is designed for a class of nonlinear parabolic PDEs with delayed point measurements. The novelty lies is that the delay size is arbitrary. To compensate for this arbitrary delay effect, the observer consists of several chained sub-observers. Each sub-observer compensates a fraction of the global delay. The resulting estimation error system is shown to be exponentially stable provided that a sufficient number of sub-observers is used. The stability analysis is based on a specific Lyapunov-Krasovskii functional and the stability conditions are expressed in terms of LMIs.

Sampled-data observers for 1-D parabolic PDEs with non-local outputs

“…The first class includes observers which require as output a vector formed by a finite number of measurements provided physical sensors, each one providing the measurements of the PDE state at the point where it is placed on the domain. The observers in this class are observers which use point, local or sampled in space measurements; see for instance [3,7,11]. A special case is the case where the sensors are placed at the domain boundary (providing the PDE state or its time-derivative at the boundary); the resulting observer is termed as boundary observer.…”

“…Accordingly, the innovation term is updated at each sampling time, using the output measurement sample, and kept unchanged between two successive sampling times. Observers for PDEs belonging to this category are those proposed in [7,8,11,10,10,13]. Many more observers of this type have been proposed for ODEs.…”