An economic objective for the optimal experiment design of nonlinear dynamic processes

State-of-the-art formulations of optimal experiment design problems are typically based on a design criterion which allows us to optimize a scalar map of the predicted variance-covariance matrix of the parameter estimate. Famous examples for such scalar objectives are the A-criterion, the E-criterion, or the D-criterion, which aim at minimizing the trace, maximum eigenvalue, or determinant of the variance-covariance matrix. In this paper, we propose a different way of deriving an economic design criterion for the optimal experiment design. Here, the corresponding analysis is based on the assumption that our ultimate goal is to solve an optimization problem with a given economic objective that depends on uncertain parameters, which have to be estimated by the experiment. We illustrate the approach by studying a fedbatch bioreactor.

[1]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[2]  Eva Balsa-Canto,et al.  An iterative identification procedure for dynamic modeling of biochemical networks , 2010, BMC Systems Biology.

[3]  J. Kiefer,et al.  Optimum Designs in Regression Problems , 1959 .

[4]  H. L. Lucas,et al.  DESIGN OF EXPERIMENTS IN NON-LINEAR SITUATIONS , 1959 .

[5]  J. I.  The Design of Experiments , 1936, Nature.

[6]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

[7]  A. Emery,et al.  Optimal experiment design , 1998 .

[8]  Lennart Ljung,et al.  Optimal experiment designs with respect to the intended model application , 1986, Autom..

[9]  Sandro Macchietto,et al.  Model-based design of experiments for parameter precision: State of the art , 2008 .

[10]  Moritz Diehl,et al.  ACADO toolkit—An open‐source framework for automatic control and dynamic optimization , 2011 .

[11]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[12]  Michael Jackson,et al.  Optimal Design of Experiments , 1994 .

[13]  Bart De Moor,et al.  A convexity‐based homotopy method for nonlinear optimization in model predictive control , 2010 .

[14]  R. Mehra.  Optimal inputs for linear system identification , 1974 .

[15]  Michel Gevers,et al.  Towards a Joint Design of Identification and Control , 1993 .

[16]  G. Oehlert.  A note on the delta method , 1992 .

[17]  Sandro Macchietto,et al.  The optimal design of dynamic experiments , 1989 .

[18]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[19]  Filip Logist,et al.  Optimal experiment design under process noise using riccati differential equations , 2013 .

[20]  Wolfgang Marquardt,et al.  On the integration of model identification and process optimization , 2013 .

[21]  S. Deshpande,et al.  On the Role of Constraints in Optimization under Uncertainty , 2012 .

[22]  A Kremling,et al.  Optimal experimental design with the sigma point method. , 2009, IET systems biology.

[23]  Håkan Hjalmarsson,et al.  From experiment design to closed-loop control , 2005, Autom..

[24]  Filip Logist,et al.  Optimal experiment design for dynamic bioprocesses: A multi-objective approach , 2012 .

[25]  Johannes P. Schlöder,et al.  Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes , 2004, Optim. Methods Softw..

[26]  Whitney K. Newey,et al.  LARGE SAMPLE ESTIMATION AND HYPOTHESIS , 1999 .

[27]  Harvey Arellano-Garcia,et al.  Simultaneous solution approach to model-based experimental design , 2013 .