Abstract
We consider minimax estimation of the state of semi-infinite elastic beams under uncertainty using initial, boundary, and external dynamic inputs (concentrated and distributed forces, bending and torsional moments) and state observations. The errors of all measurements and observations are assumed to be in a given ellipsoidal region. The problems are solved using standard classical solutions of elastoplastic beams, Lur'e's symbolic method, and the theory of minimax filtering of noise in linear dynamic systems.
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References
B. N. Bublik, N. F. Kirichenko, and A. G. Nakonechnyi, Minimax Estimators and Regulators in Dynamic Systems [in Russian], Kiev (1978).
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V. A. Stoyan and A. Abduzhabborov, "Maximum state estimation of one-dimensional systems with distributed parameters," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1039–1042 (1979).
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Additional information
Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 64–70, 1991.
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Stoyan, V.A. Dynamic analysis of elastic beams under uncertainty. J Math Sci 72, 3099–3104 (1994). https://doi.org/10.1007/BF01259479
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DOI: https://doi.org/10.1007/BF01259479