Nonlinear estimation in a class of gene transcription process

In this work the Goodwin model applied to gene transcription is employed as a benchmark system for estimation purposes, considering two dynamic behaviors, monotone decreasing and sustained oscillations, each one under a specific parameter's set. The preceding observability analysis of the Goodwin model was done via linear observability and the differential-algebraic framework, where is proved that the system is fully observable from mRNA concentration measurements. Therefore a class of nonlinear observer which considers a class of sigmoid and linear functions of the output feedback, considering model uncertainties, is proposed and a sketch of proof of the observer's convergence is provided under the background of the Lyapunov theory, in order to demonstrate asymptotic convergence. Numerical experiments are carrying out in order to show the performance of the proposed methodology which is compared with a standard Luenberger (Proportional) observer and a proportional sliding-mode observer (PSMO).