Evaluation and comparison of robust optimal experiment design criteria

This paper further develops a new approach to optimal experiment design for dynamical systems by introducing and comparing different robust optimal experiment design criteria. Until recently, solutions to the optimal experiment design problem were paradoxical in so far that the optimal experiment depended on the system parameters, i.e. the optimal experiment depended on the very thing that the experiment was aimed at finding. In a recent paper, we proposed an alternative approach, robust in nature, to the experiment design problem which, inter-alia, allowed for the possibility that the true parameters lay in a convex set. Here we further explore this robust solution. In particular, we examine the role played by different design criteria

[1]  W. J. Studden,et al.  Optimal Experimental Designs , 1966 .

[2]  S. Silvey,et al.  A sequentially constructed design for estimating a nonlinear parametric function , 1980 .

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

[4]  Changbao Wu,et al.  Asymptotic inference from sequential design in a nonlinear situation , 1985 .

[5]  A. Wald On the Efficient Design of Statistical Investigations , 1943 .

[6]  Werner G. Müller,et al.  batch sequential design for a nonlinear estimation problem , 1989 .

[7]  H. Chernoff Approaches in Sequential Design of Experiments , 1973 .

[8]  D.G. Dudley,et al.  Dynamic system identification experiment design and data analysis , 1979, Proceedings of the IEEE.

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

[10]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[11]  Thomas T. Semon,et al.  Planning of Experiments , 1959 .

[12]  H. Wynn,et al.  Maximum entropy sampling and optimal Bayesian experimental design , 2000 .

[13]  Michel Gevers,et al.  Minimizing the worst-case ν-gap by optimal input design , 2003 .

[14]  R. Gagliardi Input selection for parameter identification in discrete systems , 1966, IEEE Transactions on Automatic Control.

[15]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[16]  H. Wynn Results in the Theory and Construction of D‐Optimum Experimental Designs , 1972 .

[17]  P. Whittle Some General Points in the Theory of Optimal Experimental Design , 1973 .

[18]  K. Chaloner,et al.  Optimal Bayesian design applied to logistic regression experiments , 1989 .

[19]  Thomas R. Palfrey,et al.  Economical experiments: Bayesian efficient experimental design , 1996 .

[20]  J. Kiefer,et al.  The Equivalence of Two Extremum Problems , 1960, Canadian Journal of Mathematics.

[21]  E. Walter,et al.  Robust experiment design via maximin optimization , 1988 .

[22]  Michel Gevers Identification for Control: From the Early Achievements to the Revival of Experiment Design , 2005, CDC 2005.

[23]  O. Kempthorne The Design and Analysis of Experiments , 1952 .

[24]  Graham C. Goodwin,et al.  UTILIZING PRIOR KNOWLEDGE IN ROBUST OPTIMAL EXPERIMENT DESIGN , 2006 .

[25]  K. Chaloner,et al.  Optimum experimental designs for properties of a compartmental model. , 1993, Biometrics.

[26]  V. Levadi Design of input signals for parameter estimation , 1966 .

[27]  Graham C. Goodwin,et al.  Control System Design , 2000 .

[28]  V. Fedorov,et al.  Convex design theory 1 , 1980 .

[29]  Viatcheslav B. Melas Optimal designs for exponential regression , 1978 .

[30]  S. Arimoto,et al.  Optimum input test signals for system identification—an information-theoretical approach , 1971 .

[31]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[32]  Christopher Edwards,et al.  Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty , 2005, Eur. J. Control.

[33]  G. Goodwin,et al.  Optimal test signal design for linear S.I.S.O. system identification , 1973 .

[34]  Martin B. Zarrop,et al.  Optimal experiment design for dynamic system identification , 1977 .

[35]  D. B. Reid Optimal inputs for system identification , 1972 .

[36]  D. Titterington,et al.  Inference and sequential design , 1985 .