Geodesic
The Riccati equation for autonomous linear systems with unbounded aftereffect
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 129-137
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The problem of optimal stabilization for autonomous linear systems of differential equations with unbounded aftereffect is considered. The reduction of the solvability problem for the Riccati operator equation to the analogous problem for the Riccati functional-differential equation is proved. A class of systems of differential equations with unbounded aftereffect for which the Riccati functional-differential equation can be solved analytically is described.
Keywords: differential equations with aftereffect, optimal stabilizing control, quadratic performance index
Mots-clés : Riccati equation. 
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Yu. F. Dolgii. The Riccati equation for autonomous linear systems with unbounded aftereffect. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 129-137. http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a14/

[1] Krasovskii N.N., “Ob analiticheskom konstruirovanii optimalnogo regulyatora v sisteme s zapazdyvaniyami vremeni”, Prikl. matematika i mekhanika, 26:1 (1962), 39–51 | MR

[2] Osipov Yu.S., “O stabilizatsii upravlyaemykh sistem s zapazdyvaniem”, Differents. uravneniya, 1:5 (1965), 605–618 | Zbl

[3] Gibson J.S., “Linear-quadratic optimal control of hereditary differential systems: infinite dimensional Riccati equations and numerical approximations”, SIAM J. Control Optimiz., 21:5 (1983), 95–135 | DOI | MR

[4] Zhelonkina N.I., Lozhnikov A.B., Sesekin A.N., “Ob optimalnoi stabilizatsii impulsnym upravleniem lineinykh sistem s posledeistviem”, Avtomatika i telemekhanika, 2013, no. 11, 39–48 | MR | Zbl

[5] Dolgii Yu.F., “Tochnye resheniya zadachi optimalnoi stabilizatsii dlya sistem differentsialnykh uravnenii s posledeistviem”, Tr. instituta matematiki i mekhaniki UrO RAN, 21:4 (2015), 124–135 | MR

[6] Kolmanovskii V.B., Nosov V.R., Ustoichivost i periodicheskie rezhimy reguliruemykh sistem s posledeistviem, Nauka, M., 1981, 448 pp. | MR

[7] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984, 421 pp. | MR

[8] Dolgii Yu.F., “Analiticheskie resheniya zadachi optimalnoi stabilizatsii dlya sistem differentsialnykh uravnenii s posledeistviem”, Tr. XII Vseros. soveschaniya po problemam upravleniya, IPU RAN, M., 2014, 1349–1362