Abstract
Minimax optimization of the estimate of parameters of a nonlinear observation model containing random errors with unknown covariance matrices is investigated. An iteration algorithm for computing the minimax estimate is designed and its convergence is demonstrated. Theoretical results are tested by concrete examples.
Similar content being viewed by others
REFERENCES
Pankov, A.R. and Semenikhin, K.V., Minimax Identification of the Generalized Uncertain Stochastic Model, Avtom.Telemekh., 1998, no. 11, pp. 158-171.
Pankov, A.R., Platonov, E.N., and Semenikhin, K.V., Minimax Quadratic Optimization and Its Application to Investment Planning, Avtom.Telemekh., 2001, no. 12, pp. 55-73.
Pankov, A.R. and Popov, A.S., Minimax Estimation of the Parameters of Motion of a Flying Vehicle under a priori Stochastic Uncertainty, Trudy Mosk.Aviat.Inst., 2002, no. 7 (www.mai.ru).
Ermakov, S.M. and Zhiglyavskii, A.A., Matematicheskaya teoriya optimal'nogo eksperimenta (Mathematical Theory of the Optimal Experiment), Moscow: Nauka, 1987.
Demidenko, E.Z., Lineinaya i nelineinaya regressii (Linear and Nonlinear Regressions),Moscow: Finansy i Statistika, 1981.
Tsypkin, Ya.Z., Osnovy informatsionnoi teorii identifikatsii (Elements of Information Theory of Identification), Moscow: Nauka, 1984.
Zangwill, W.I., Nonlinear Programming.A Unified Approach, Englewood Cliffs: Prentice-Hall, 1969. Translated under the tile Nelineinoe programmirovanie.Edinyi podkhod, Moscow: Sovetskoe Radio, 1973.
Fedorov, V.V., Regression Parameter Estimation for Observation Vectors, in Regressionnye eksperimenty (Regression Experiments), Nalimov, V.V., Ed., Moscow: Mosk. Gos. Univ., 1977, pp. 112-122.
Eaves, B. and Zangwill, W., Generalized Cutting Plane Algorithms, SIAM.J.Control, 1971, no. 9, pp. 529-542.
Handbook on Semidefinite Programming and Applications, Saigal, R., Vandenberghe, L., and Wolkowicz, H., Eds., Dordrecht: Kluwer Academic, 2000.
Pankov, A.R. and Siemenikhin, K.V., Minimax Estimation of Random Elements with Application to Infinite-Dimensional Statistical Linearization, Trudy II Mezhdunar.konf.“dentificatsiya sistem i zadachi upravleniya” (Proc. II Int. Conf. System Identification and Control Problems), Moscow, 2003, pp. 1277-1291
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pankov, A.R., Popov, A.S. Minimax Identification of a Nonlinear Dynamic Observation System. Automation and Remote Control 65, 291–298 (2004). https://doi.org/10.1023/B:AURC.0000014726.04297.31
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000014726.04297.31