An Efficient Implementation of Backstepping Observers for Time-Varying Parabolic PDEs

Abstract

AbstractA new computationally efficient implementation of the backstepping-based state observer is considered for a 1-dimensional diffusion-reaction system with spatially and time varying parameters. For this, the implicit formulation for the integral kernel, which results from the application of the backstepping procedure is discretized in space and approximated by means of the composite trapezoidal rule. This results in a system of first-order ordinary differential equations governing the pointwise explicit-in-time evolution of the backstepping-kernel. The resulting system of ODEs is numerically solved by applying the backward Euler method, which drastically reduces the computing time compared to the usually applied method of successive approximation. The impact of the proposed method on the computing time and on the observer error convergence is evaluated by means of numerical simulations.