Optimal experiment design under process noise using Riccati differential equations

• Published in: Journal of process control 2013-04, Vol.23 (4), p.613-629
• Main Authors: Telen, D., Houska, B., Logist, F., Van Derlinden, E., Diehl, M., Van Impe, J.
• Format: Article
• Language: English
• Subjects: Biochemical processes; Dynamic optimization; Optimal experiment design; Process noise; Variance–covariance matrix
• ISSN: 0959-1524; 1873-2771
• DOI: 10.1016/j.jprocont.2012.11.005

► Novel numerical method for computing variance–covariance matrix with Riccati-based ordinary differential equations. ► Process noise is taken into account in nonlinear dynamic models. ► Method allows for exploitation of structure in order to generate sensitivities. ► Illustrated on fed-batch bioreactors. In this paper, we present a numerical method for optimal experiment design of nonlinear dynamic processes. Here, we suggest to optimize an approximation of the predicted variance–covariance matrix of the parameter estimates, which can be computed as the solution of a Riccati differential equation. In contrast to existing approaches, the proposed method allows us to take process noise into account and requires less derivative states to be computed compared to the traditional Fisher information matrix based approach. This process noise is assumed to be a time-varying random disturbance which is not known at the time when the experiment is designed. We illustrate the technique by solving an optimal experiment design problem for a fed-batch bioreactor benchmark case study. Here, we concentrate on how the optimal input design and associated accuracy of the parameter identification is influenced when process noise is present.