A continuous-discrete adaptive observer with a diagonal gain matrix and sigma-modification: applications in chaos synchronization and dynamical state estimation

In this paper, we propose an improved continuous-discrete observer with enhanced convergence properties and reduced sensitivity to persistent excitations. Our approach introduces several key innovations, including a customised diagonal gain matrix which improves the convergence speed, a sigma-modification technique that relaxes the persistent excitation conditions, and a weighting factor tailored to optimise the estimation of unknown parameters. Through comprehensive numerical experiments, we illustrate the effectiveness of our observer in two distinct scenarios. Firstly, we demonstrate its application in synchronising a 4-component chaotic dynamical system. Secondly, we showcase its utility in tracking a reduced 2-component chemical engineering process. Our simulation results reveal that the proposed observer outperforms existing methods by achieving quicker convergence and higher estimation accuracy. This study contributes to the advancement of adaptive observer design, offering valuable insights for its application across diverse fields.