Abstract
This paper considers the problem of sequentially generating test signals for parameter estimation in linear, single-input, single-output, discrete-time systems using a frequency-domain approach based on the theory of optimal experiments in regression analysis. The input signals are power constrained and are optimal in the sense that system information is maximized, where the criterion employed is the determinant of the Fisher information matrix (D-optimality). A class of algorithms is investigated, each member of which generates a sequence of input designs converging to aD-optimum. A number of these algorithms are compared computationally.
Similar content being viewed by others
References
Aoki, M., andStaley, R. M.,On Input Signal Synthesis in Parameter Identification, Automatica, Vol. 6, pp. 431–440, 1970.
Goodwin, G. C., Murdoch, J. C., andPayne, R. L.,Optimal Test Signal Design for Linear SISO System Identification, International Journal of Control, Vol. 17, pp. 45–55, 1973.
Viort, B.,D-Optimal Designs for Dynamic Models: Part 1, Theory, University of Wisconsin, Department of Statistics, Technical Report No. 314, 1972.
Kalaba, R. E., andSpingarn, K.,Optimal Inputs for Nonlinear Process Parameter Estimation, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-10, pp. 339–345, 1974.
Mehra, R. K.,Optimal Input Signals for Parameter Estimation in Dynamic Systems—A Survey and New Results, IEEE Transactions on Automatic Control, Vol. AC-19, pp. 753–768, 1974.
Mehra, R. K.,Frequency-Domain Synthesis of Optimal Inputs for Linear System Parameter Estimation, Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, Vol. 98, pp. 130–138, 1976.
Kiefer, J., andWolfowitz, J.,Optimum Designs in Regression Problems, Annals of Mathematical Statistics, Vol. 30, pp. 271–294, 1959.
Silvey, S. D.,Statistical Inference, Penguin, London, England, 1970.
Payne, R. L.,An A-Priori Estimate for the Information Matrix of a SISO Linear System, Imperial College, Department of Computing and Control, Publication No. 72/4, 1972.
Ljung, L.,Characterization of the Concept of “Persistently Exciting” in the Frequency Domain, Lund Institute of Technology, Division of Automatic Control, Report No. 7119, 1971.
Levin, M. J.,Optimal Estimation of Impulse Response in the Presence of Noise, IRE Transactions on Circuit Theory, Vol. CT-7, pp. 50–56, 1960.
Fedorov, V. V.,Theory of Optimal Experiments, Academic Press, New York, New York, 1972.
Payne, R. L., andGoodwin, G. C.,A Bayesian Approach to Experiment Design with Applications to Linear Multivariable Dynamic Systems, IMA Conference on Computational Problems in Statistics, University of Essex, Essex, England, 1973.
Martins de Carvalho, J. L.,Binary Sequences with Prescribed Autocorrelations, Imperial College, Department of Computing and Control, PhD Thesis, 1977.
Van den Bos, A.,Construction of Binary Multifrequency Test Signals, 1st IFAC Symposium on Identification, Prague, Czechoslovakia, 1967.
Rothenberg, T. J.,Identification in Parametric Models, Econometrica, Vol. 39, pp. 577–591, 1971.
Kiefer, J.,General Equivalence Theory for Optimum Designs (Approximate Theory), Annals of Mathematical Statistics, Vol. 2, pp. 849–879, 1974.
Payne, R. L., andGoodwin, G. C.,Simplification of Frequency Domain Experiment Design for SISO Systems, Imperial College, Department of Computing and Control, Publication No. 74/3, 1974.
Zarrop, M. B.,Optimal Experiment Design for Dynamic System Identification, Springer-Verlag, Berlin, Germany, 1979.
Wynn, H. P.,The sequential Generation of D-Optimum Experimental Designs, Annals of Mathematical Statistics, Vol. 41, pp. 1655–1664, 1970.
Atwood, C. L.,Sequences Converging to D-Optimal Designs of Experiments, Annals of Statistics, Vol. 1, pp. 342–352, 1970.
St. John, R. C., andDraper, N. R.,D-Optimality for Regression Designs, Technometrics, Vol. 17, pp. 15–23, 1975.
Gupta, N. K., Mehra, R. K., andHall, W. E., Jr.,Application of Optimal Input Synthesis to Aircraft Parameter Estimation, Transactions of the ASME, Journal of Dynamic System Measurement, Vol. 98, pp. 139–145, 1976.
Author information
Authors and Affiliations
Additional information
Communicated by R. E. Kalaba
Rights and permissions
About this article
Cite this article
Zarrop, M.B. Sequential generation ofD-optimal input designs for linear dynamic systems. J Optim Theory Appl 35, 277–291 (1981). https://doi.org/10.1007/BF00934581
Issue Date:
DOI: https://doi.org/10.1007/BF00934581