Geodesic
A general approach to the solution of the bounded control synthesis problem in a controllability problem
Sbornik. Mathematics, Tome 37 (1980) no. 4, pp. 535-557 
V. I. Korobov. A general approach to the solution of the bounded control synthesis problem in a controllability problem. Sbornik. Mathematics, Tome 37 (1980) no. 4, pp. 535-557. http://geodesic.mathdoc.fr/item/SM_1980_37_4_a3/
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Consider a system of differential equations $$ \dot x=f(x,u),\qquad u\in M, $$ where $x$ an $n$-dimensional vector, $u$ is an $r$-dimensional control, and $M$ is a subset of an $r$-dimensional space. A general approach to the solution of the following synthesis problem is proposed: construct a control $u=u(x)\in M$ such that the corresponding trajectory of the system $\dot x=f(x,u(x))$ starting at an arbitrary point $x_0$ terminates at the final time $T(x_0)$ at the point $x_1$. Bibliography: 8 titles.

[1] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mischenko, Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, Moskva, 1961

[2] V. F. Krotov, “Metody resheniya variatsionnykh zadach na osnove dostatochnykh uslovii absolyutnogo minimuma. I”, Avtomatika i telemekhanika, XXIII:12 (1962), 1571–1583 | MR

[3] R. Bellman, Dinamicheskoe programmirovanie, IL, Moskva, 1960 | MR

[4] A. M. Lyapunov, Obschaya zadacha ob ustoichivosti dvizheniya, Gostekhizdat, Moskva–Leningrad, 1950

[5] Dzh. X. Uilkinson, Algebraicheskaya problema sobstvennykh znachenii, izd-vo “Nauka”, Moskva, 1970

[6] D. G. Luenberger, IEEE Trans. Automatic Control, AC-12, 1967 | MR

[7] V. I. Korobov, Upravlyaemost, ustoichivost nekotorykh nelineinykh sistem, Diff. uravneniya, IX, no. 4, 1973 | MR

[8] V. I. Korobov, “Svedenie zadachi upravlyaemosti k granichnoi zadache”, Diff. uravneniya, XII:7 (1976), 1310–1312 | MR