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.

[1]  Mazen Alamir,et al.  Nonlinear receding-horizon state estimation for dispersive adsorption columns with nonlinear isotherm , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[2]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[3]  Jay H. Lee,et al.  Constrained linear state estimation - a moving horizon approach , 2001, Autom..

[4]  Giorgio Battistelli,et al.  Robust receding-horizon state estimation for uncertain discrete-time linear systems , 2005, Syst. Control. Lett..

[5]  D. Dochain,et al.  On-Line Estimation and Adaptive Control of Bioreactors , 2013 .

[6]  A. Vande Wouwer,et al.  Design of a Robust Nonlinear Receding-Horizon Observer - Application to a biological system , 2008 .

[7]  Didier Dumur,et al.  Optimization of the interval approach for Chlorella vulgaris biomass estimation , 2011, IEEE Conference on Decision and Control and European Control Conference.

[8]  Raymond Hanus,et al.  On-line state estimation of bioprocesses with full horizon observers , 2001 .

[9]  Juergen Hahn,et al.  Computation of arrival cost for moving horizon estimation via unscented Kalman filtering , 2009 .

[10]  M. P. Joshi.  On-line Estimation and Adaptive Control of Bioreactors. VonG. Bastin undD. Dochain. Elsevier Science Publishers, Amsterdam - Oxford - New York - Tokyo 1990. XIV, 379 Seiten, 57 Abb., 5 Tab., geb., US-$ 146,25 , 1991 .

[11]  A. Vande Wouwer,et al.  Improving continuous–discrete interval observers with application to microalgae-based bioprocesses , 2009 .

[12]  Mazen Alamir,et al.  Nonlinear receding-horizon state estimation for dispersive adsorption columns with nonlinear isotherm , 2003 .

[13]  D. Dochain,et al.  Interval observers for biochemical processes with uncertain kinetics and inputs. , 2005, Mathematical biosciences.

[14]  Jian Li,et al.  State and parameter estimation of microalgal photobioreactor cultures based on local irradiance measurement. , 2003, Journal of biotechnology.