Interval observer with near optimal adaptation dynamics. Application to the estimation of lipid quota in microalgae†

In this paper, the design of an interval observer with an adaptive dynamical gain is presented. The observer is formulated in the framework of robust state estimation of uncertain dynamical systems, where an interval that encloses the unknown state variables is provided. For a specific type of interval observer design, an optimal gain could provide the narrowest interval. Since this gain depends on the (unknown) state, it can however not be determined, and only intervals for this optimal gain can be estimated. Here we propose a strategy to track, with a high gain observer, the optimal gain together with the computation of its derivative. The observer performance is first illustrated with the simple case of an uncertain bioreactor model. Then, we propose the real case of the estimation of microalgal oil in the framework of biofuel production. The proposed observer design, when applied to experimental data of Isochrysis affinis galbana, appears to be a suitable robust estimation technique. Copyright c © 0000 John Wiley & Sons, Ltd.