Sampled-Data Feedback Control of Nonlinear Parabolic PDE Systems with Measurement Errors

Abstract

This work presents a model-based approach for feedback control of spatially-distributed systems described by nonlinear parabolic PDEs subject to discretely-sampled state measurements, bounded measurement errors, and bounded model uncertainty. The controller is designed based on a suitable finite-dimensional approximation that captures the dominant dynamics of the infinite-dimensional system, and includes an inter-sample model predictor that compensates for the unavailability of continuous state measurements. The state of the model predictor is updated using the available state measurements at the sampling times. The sampled-data closed-loop system is analyzed and a sufficient condition for closed-loop stability is derived. The analysis leads to an explicit characterization of the closed-loop stability region in terms of the sampling period, the measurement error bound, the parametric uncertainty bounds, and the controller design parameters. A simulation case study is presented to demonstrate how the results can be used to mitigate the impact of measurement errors on closed-loop stability.