Deep-learning based design of cascade observers for discrete-time nonlinear systems with output delay

Abstract

Looking for a proper Lyapunov-based stability analysis for nonlinear discrete-time delay systems is non-trivial, even for constant delay. This paper proposes a learning approach that relies on neural networks to compute the state transformation map involved in the design of Kazantzis-Kravaris-Luenberger (KKL) based observers. Based on this transformation, we propose a chain of observers in cascade with exponential stability guarantees through the inverse transformation mapping in the original coordinates. Finally, we provide a simulation example that includes a sensitivity analysis of the delay parameter to illustrate the performance and demonstrate the effectiveness of the proposed learning-based design of chain observers for discrete-time nonlinear systems with output measurement delay.