Robust Moving Horizon State Estimation: Application to Bioprocesses

In this paper, a robust nonlinear receding-horizon observer is proposed for the estimation of cellular concentration in a bioreactor. In the presence of uncertainties on the model parameter or on the initial state of the system, this estimation problem can lead to poor estimation performance. A min-max optimization solution can be used to increase the robustness of the observer in the presence of parameter uncertainties. This solution assumes that each model parameter belongs to an interval. The paper proposes an alternative modeling for these parameters: A Gaussian model is assumed in order to take into account the correlation between parameters. As the confidence region for the parameters is now an ellipsoid, the max step in the min-max problem is replaced by more tractable statistics. Expected value has been tested for its simplicity. For robustness requirements a statistic considering the variance of the estimation has also been developed. Numerical simulations illustrate the efficiency of the proposed estimation scheme.