System Class Extensions of the Modulating Function-Based State Reconstruction for the Advection–Diffusion–Reaction Equation

In this article, the state estimation of distributed parameter systems using the modulating function method is extended to systems of two or higher spatial dimensions with spatially varying coefficients and general boundary conditions. At the center of the state observer approach lies the construction and solvability analysis of systematically obtained kernel equations determining the modulating functions. In addition, a method for the state estimation of a class of parabolic systems with time-varying and nonlinear parameters based on Volterra integral transformations is presented. Furthermore, a linearization-based strategy to deal with nonlinear reaction terms is presented. The stability of the resulting iterative feedback algorithm is proven. Numerical simulations show the validity and robustness of the methodology in two simulated examples.