Choosing Between Open- and Closed-Loop Experiments in Linear System Identification

This correspondence shows that open-loop experiments are optimal for a broad class of systems when the system input is constrained. In addition, we show that, for a general class of systems, when the output power is constrained, closed-loop experiments are optimal. Both results use a strong notion of optimality and use expressions for estimation accuracy which are nonasymptotic in model order but asymptotic in data length.

[1]  D. M. Titterington,et al.  Aspects of Optimal Design in Dynamic Systems , 1980 .

[2]  Brian D. O. Anderson,et al.  On the performance assessment of scalar nonminimum-phase plants , 2003, Proceedings of the 2003 American Control Conference, 2003..

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

[4]  Håkan Hjalmarsson,et al.  Input design via LMIs admitting frequency-wise model specifications in confidence regions , 2005, IEEE Transactions on Automatic Control.

[5]  Graham C. Goodwin,et al.  On the Optimality of Open and Closed Loop Experiments in System Identification , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  J. Kiefer.  Optimum Experimental Designs , 1959 .

[7]  M. Gevers,et al.  Open-loop versus closed-loop identification of Box-Jenkins models: a new variance analysis , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  P. A. Papakyriazis,et al.  Optimal experimental design in econometrics: The time series problem , 1978 .

[9]  Ts Ng,et al.  On maximal accuracy estimation with output power constraints , 1977 .

[10]  M. Siotani.  Some applications of Loewner's ordering on symmetric matrices , 1967 .

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

[12]  Alfred O. Hero,et al.  Lower bounds for parametric estimation with constraints , 1990, IEEE Trans. Inf. Theory.

[13]  Lennart Ljung,et al.  Some results on optimal experiment design , 2000, Autom..

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

[15]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

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

[17]  Tung-Sang Ng,et al.  Optimal experiment design for linear systems with input-output constraints , 1977, Autom..

[18]  Randal W. Beard,et al.  Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach , 2004 .

[19]  J. Kiefer.  General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[20]  F. Pukelsheim.  Optimal Design of Experiments , 1993 .

[21]  Dennis S. Bernstein,et al.  Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory , 2005 .

[22]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[23]  Drew Seils,et al.  Optimal design , 2007 .

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

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