Geodesic
Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws
Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 222-231.

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We consider the problem of tracking the solution of a parabolic equation with an unknown right-hand side by the solution of a similar parabolic equation. To solve this problem, we propose two noise-resistant algorithms based on the extremal shift method known in guaranteed control theory. The first algorithm pertains to the case of continuous measurement of solutions to the equations, and the second, to the case of discrete measurement.
Mots-clés : parabolic equations
Keywords: tracking problem. 
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V. I. Maksimov. Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws. Informatics and Automation, Differential equations and dynamical systems, Tome 308 (2020), pp. 222-231. http://geodesic.mathdoc.fr/item/TRSPY_2020_308_a15/

[1] Barbu V., Optimal control of variational inequalities, Res. Notes Math., 100, Pitman Adv. Publ. Program, London, 1984 | MR | Zbl

[2] Bensoussan A., Da Prato G., Delfour M.C., Mitter S.K., Representation and control of infinite dimensional systems, v. 1, Birkhäuser, Boston, 1992 | MR | Zbl

[3] Blizorukova M., Maksimov V., “On an algorithm for the problem of tracking a trajectory of a parabolic equation”, Int. J. Appl. Math. Comput. Sci., 27:3 (2017), 457–465 | DOI | MR | Zbl

[4] Brézis H., “Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations”, Contributions to nonlinear functional analysis, Proc. Symp. Univ. Wis. (1971), Acad. Press, New York, 1971, 101–156 | DOI | MR

[5] H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verl., Berlin, 1974 | MR | Zbl

[6] Game-Theoretical Control Problems, Springer, New York, 1988 | MR | Zbl

[7] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969 | MR

[8] V. I. Maksimov, “On tracking solutions of parabolic equations”, Russ. Math., 56:1 (2012), 35–42 | DOI | MR | Zbl

[9] V. I. Maksimov, “Algorithm for shadowing the solution of a parabolic equation on an infinite time interval”, Diff. Eqns., 50:3 (2014), 362–371 | DOI | MR | Zbl

[10] V. I. Maksimov and Yu. S. Osipov, “Infinite-horizon boundary control of distributed systems”, Comput. Math. Math. Phys., 56:1 (2016), 14–25 | DOI | MR | Zbl

[11] Moreau J.-J., “Proximité et dualité dans un espace hilbertien”, Bull. Soc. math. France, 93 (1965), 273–299 | DOI | MR | Zbl

[12] Yu. S. Osipov, A. V. Kryazhimskii, and V. I. Maksimov, “N. N. Krasovskii's extremal shift method and problems of boundary control”, Autom. Remote Control, 70:4 (2009), 577–588 | DOI | MR | Zbl