On motion stabilization of nonstationary controlled system. (English. Russian original) Zbl 1145.93043
Autom. Remote Control 68, No. 8, 1309-1321 (2007); translation from Avtom. Telemekh. 2007, No. 8, 18-31 (2007).
Summary: In this paper, a solution to the problem of optimal motion stabilization of nonstationary controlled system basing on the constant-positive Lyapunov function is represented.
MSC:
| 93D99 | Stability of control systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
References:
| [1] | Letov, A.M., Analytic Design of Controllers, Avtom. Telemekh., 1960, no. 4, pp. 436–441; no. 5, pp. 561–568; no. 6, pp. 660–665; 1961, no. 4, pp. 425–435; 1962, no. 11, pp. 1405–1413. |
| [2] | Rumyantsev, V.V., Developing the Theory of Motion Stability in the USSR, Diff. Uravn., 1983, vol. 19, no. 5, pp. 739–776. |
| [3] | Kirillova, F.M., The Problem of Analytic Design of Controllers, Prikl. Mat. Mekh., 1961, vol. 25, no. 3, pp. 433–439. |
| [4] | Krasovskii, N.N., Problems of Controlled Motion Stabilization, Supplement 4, in Teoriya ustoichivosti dvizheniya (Theory of Motion Stability), Malkin, I.G., Ed., Moscow: Nauka, 1966, pp. 475–514. |
| [5] | Krasovskii, N.N., Theory of Optimal Controlled Systems, in Mekhaniki v SSSR za 50 let (Mechanics in the USSR during 50 Years), Moscow: Nauka, 1986, vol. 1, pp. 179–244. |
| [6] | Al’brekht, E.G., On Optimal Stabilization of Nonlinear Systems, Prikl. Mat. Mekh., 1961, vol. 25, no. 5, pp. 831–844. |
| [7] | Krasovskii, N.N., On Stabilization of Unstable Motions by Additional Forces in the Presence of Incomplete Feedback, Prikl. Mat. Mekh., 1963, vol. 27, no. 4, pp. 641–663. |
| [8] | Rumyantsev, V.V., On Optimal Stabilization of Controlled Systems, Prikl. Mat. Mekh., 1970, vol. 34, no. 3, pp. 440–456. · Zbl 0215.59903 |
| [9] | Rumyantsev, V.V. and Oziraner, A.S., Ustoichivost’ i stabilizatsiya dvizheniya po otnosheniyu k chasti peremennykh (Stability and Stabilization of Motion Regarding a Part of Variables), Moscow: Nauka, 1987. · Zbl 0626.70021 |
| [10] | Vorotnikov, V.I. and Rumyantsev, V.V., Ustoichivost’ i upravlenie po chasti koordinat fazovogo vektora dinamicheskikh sistem: teoriya, metody i prilozheniya (Stability and Control by a Part of the Phase Vector Coordinates in Dynamic Systems: Theory, Methods, and Applications), Moscow: Nauchnyi Mir, 2001. · Zbl 1016.34052 |
| [11] | Andreev, A.S. and Bezglasnyi, S.P., Controlled Systems Stabilization with the Guaranteed Estimate of Control Performance, Prikl. Mat. Mekh., 1997, vol. 61, no. 1, pp. 44–51. · Zbl 1040.93532 |
| [12] | Roitenberg, Ya.N., Avtomaticheskoe upravlenie (Automatic Control), Moscow: Nauka, 1971. · Zbl 0229.93004 |
| [13] | Bulgakov, N.G., Znakopostoyannye funktsii v teorii ustoichivosti (Constant-Sign Functions in the Stability Theory), Minsk: Belarus. Gos. Univ., 1984. · Zbl 0634.34038 |
| [14] | Andreev, A.S. and Boikova, T.A., Constant-Sign Lyapunov Functions in Problems of Stability, Mekh. Tverdogo Tela, 2002, no. 32, pp. 109–116. |
| [15] | Rouche, N., Habets, P., and Laloy, M., Stability Theory by Liapunov’s Direct Method, New York: Springer-Verlag, 1977. Translated under the title Pryamoi metod Lyapunova v teorii ustoichivosti, Moscow: Mir, 1980. · Zbl 0364.34022 |
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