Optimal experiment design with diffuse prior information

In system identification one always aims to learn as much as possible about a system from a given observation period. This has led to on-going interest in the problem of optimal experiment design. Not surprisingly, the more one knows about a system the more focused the experiment can be. Indeed, many procedures for `optimal' experiment design depend, paradoxically, on exact knowledge of the system parameters. This has motivated recent research on, so called, `robust' experiment design where one assumes only partial prior knowledge of the system. Here we go further and study the question of optimal experiment design when the a-priori information about the system is diffuse. We show that band-limited `1/f' noise is optimal for a particular choice of cost function.

[1]  L. Ljung.  Asymptotic variance expressions for identified black-box transfer function models , 1984 .

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

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

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

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

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

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

[8]  Håkan Hjalmarsson,et al.  Variance error quantifications that are exact for finite model order , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[10]  Graham C. Goodwin,et al.  Robust optimal experiment design for system identification , 2007, Autom..

[11]  Graham C. Goodwin,et al.  Good, Bad and Optimal Experiments for Identification , 2006 .

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

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

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

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

[16]  G.C. Goodwin,et al.  Evaluation and comparison of robust optimal experiment design criteria , 2006, 2006 American Control Conference.

[17]  C. Ray Smith,et al.  Maximum-entropy and Bayesian methods in science and engineering , 1988 .

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

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

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

[21]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[22]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

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

[24]  Graham C. Goodwin,et al.  Fundamental Limitations in Filtering and Control , 1997 .

[25]  J. Skilling.  The Axioms of Maximum Entropy , 1988 .

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

[27]  H. W. Bode,et al.  Network analysis and feedback amplifier design , 1945 .