State Observation of a 2D Parabolic PDE with a Time-Dependent Advection Parameter using the Modulating Function Method and the Method of Integral Operators

A novel method for the Modulatung Function based state estimation of distributed systems is extended to two spatial dimensions. Furthermore, the consideration of a time-dependent advection term is discussed by introducing the Method of Integral Operators into the framework. This makes it possible to transform the resulting auxiliary problem which eventually results in a real-time capable observer setup for parabolic PDEs