Geodesic
An estimation problem with separate constraints on initial states and disturbances
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 1, pp. 27-39 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Questions of approximation of a guaranteed estimation problem with geometrically bounded initial states and integrally bounded in the space $\mathbb{L}_2$ disturbances in the system and in the measurement equation are considered. The problem is reduced to an optimal control problem without state constraints and to the application of Pontryagin's maximum principle. A discrete multistep system is indicated for which the information set converges in the Hausdorff metric to the corresponding information set of a continuous system as the partition step converges to zero. In contrast to the general case, under the specified conditions, the information set can be constructed as a reachable set of a special system. A numerical example is given.
Keywords: guaranteed estimation, filtering, maximum principle, reachable set.
Mots-clés : information set 
@article{TIMM_2022_28_1_a1,
     author = {B. I. Anan'ev and P. A. Yurovskikh},
     title = {An estimation problem with separate constraints on initial states and disturbances},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {27--39},
     year = {2022},
     volume = {28},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_1_a1/}
}
TY  - JOUR
AU  - B. I. Anan'ev
AU  - P. A. Yurovskikh
TI  - An estimation problem with separate constraints on initial states and disturbances
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2022
SP  - 27
EP  - 39
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2022_28_1_a1/
LA  - ru
ID  - TIMM_2022_28_1_a1
ER  - 
%0 Journal Article
%A B. I. Anan'ev
%A P. A. Yurovskikh
%T An estimation problem with separate constraints on initial states and disturbances
%J Trudy Instituta matematiki i mehaniki
%D 2022
%P 27-39
%V 28
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2022_28_1_a1/
%G ru
%F TIMM_2022_28_1_a1
B. I. Anan'ev; P. A. Yurovskikh. An estimation problem with separate constraints on initial states and disturbances. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 1, pp. 27-39. http://geodesic.mathdoc.fr/item/TIMM_2022_28_1_a1/

[1] Schweppe F.C., “Recursive state estimation: unknown but bounded errors and system inputs”, IEEE Trans. on Autom. Control, 13 (1968), 22–28 | DOI

[2] Bertsecas D.P., Rhodes I.B., “Recursive state estimation for a set-memberschip description of uncertainty”, IEEE Trans. on Autom. Control, AC-16:2 (1971), 117–128 | DOI | MR

[3] Kurzhanskii A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977, 306 pp.

[4] Kurzhanski A.B., Valyi I., Ellipsoidal calculus for estimation and control, Birkhäuser, Boston, 1996 | MR

[5] Chernousko F.L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem. Metod ellipsoidov, Nauka, M., 1988, 319 pp.

[6] Kurzhanski A.B., Varaiya P., Dynamics and control of trajectory tubes: Theory and computation, SCFA, 85, Birkhäuser, Basel, 2014, 445 pp. | MR

[7] Ananyev B.I., Yurovskih P.A., “On the approximation of estimation problems for controlled systems”, AIP Conference proceedings, 2164 (2019), 110001, 9 pp. | DOI

[8] Ananev B.I., Yurovskikh P.A., “Approksimatsiya zadachi garantirovannogo otsenivaniya so smeshannymi ogranicheniyami”, Tr. Instituta matematiki i mekhaniki UrO RAN, 26:4 (2020), 48–63 | MR

[9] Ananyev B.I., “Minimax estimation of statistically uncertain systems under the choice of a feedback parameter”, J. Math. Systems, Estimation, and Control, 5:2 (1995), 1–17 | MR

[10] Loheac J., Zuazua E., “Averaged controllability of parameter dependent conservative semi-groups”, J. Diff. Eq., 262:3 (2017), 1540–1574 | DOI | MR | Zbl

[11] Loheac J., Zuazua E., “From averaged to simultaneous controllability”, Ann. Fac. Sci. Toulouse, Math. (6), 25:4 (2016), 785–828 | DOI | MR | Zbl

[12] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988, 280 pp. | MR

[13] Vasilev F.P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988, 552 pp. | MR