Nonlinear Time-Delayed Quorum Sensing System: State Estimation Via a Robust Observer

Abstract

This paper proposes an innovative method to estimate the states in a nonlinear time-delayed quorum sensing (QS) model using an extended Kalman filter (EKF) observer. By addressing the inherent time delays in QS system which arise as a delayed response of bacteria to population fluctuations, the study introduces variable structure dynamical estimators, specifically the EKF, to approximate missing states based on available measurements. The EKF observer is applied to estimate four out of five internal non-measurable nonlinear states in a time-delayed QS model. This is the first attempt to utilize the EKF state estimation in nonlinear time delay QS models. The research contributes to the understanding of QS systems, provides insights into the communication dynamics inside biological systems, and offers a practical solution for estimating states in realistic scenarios.