The control of the angular motion of a solid with interference. A game-theoretic approach / Vorotnikov V.I. // Journal of Applied Mathematics and Mechanics. - 1994. - V. 58, l. 3. - P. 457-476.

ISSN:
00218928
Type:
Article
Abstract:
A constructive method for control synthesis for the problem of the reorientation of an asymmetric solid is presented using a game-theoretic model of interference. Prescribed "geometric constraints" on the control functions are taken into account. The method is based on a choice of the structural form of control rules that enables the solution of the original non-linear problem to be reduced to solving auxiliary linear game-theoretic problems. The non-linear control rules obtained in this way are robust (stable) and ensure that the body arrives at the prescribed state in a finite time, which can be computed within the framework of the proposed solution scheme starting from the time-optimization requirement. A method of estimating the guaranteed minimum reorientation time is given. The results of a computer simulation are presented. © 1994.
Author keywords:
Index keywords:
нет данных
DOI:
10.1016/0021-8928(94)90096-5
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-0002183601&doi=10.1016%2f0021-8928%2894%2990096-5&partnerID=40&md5=1a0f3c2f538b604a7e48bc1d606cc266
Соавторы в МНС:
Другие поля
Поле Значение
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-0002183601&doi=10.1016%2f0021-8928%2894%2990096-5&partnerID=40&md5=1a0f3c2f538b604a7e48bc1d606cc266
Affiliations Nizhnii TagilUSSR
References Petrov, Bodner, Alekseyev, Analytic solution of the problem of controlling a three-dimensional rotational manoeuvre (1970) Dokl Akad. Nauk SSSR, 192 (6), pp. 1235-1238; Rumyantsev, On controlling the orientation and stabilization of a satellite by rotors (1970) Vest. Mosk. Gos. Univ. Mat. i Mekh., 2, pp. 83-96; Branets, Shmyglevskii, (1973) Application of Quaternions in Problems of Orientation of a Solid, , Nauka, Moscow; Krasovskii, (1973) Automatic Flight Control Systems and their Analytic Construction, , Nauka, Moscow; Raushenbakh, Tokar', (1974) Controlling the Orientation of a Spacecraft, , Nauka, Moscow; Beletskii, (1975) The Motion of a Satellite Relative to the Centre in a Gravitational Field, , Nauka, Moscow; Shklyar, Malyshenko, The problem of the optimal three-dimensional turn of a spacecraft relative to the centre of mass (1975) Kosmich. Issled., 13 (4), pp. 473-480; Sarychev, Problems of the orientation of artificial satellites (1978) Progress in Science and Technology. Space Exploration, 11. , VINITI, Moscow; Zubov, Ermolin, Sergeyev, Smirnov, (1978) Controlling the Rotational Motion of a Solid, , Izd. Leningrad. Gos. Univ, Leningrad; Chernous'ko, Akulenko, Sokolov, (1980) Control of Oscillations, , Nauka, Moscow; Gulyayev, Koshkin, Savilova, Time-optimal control of the triaxial orientation of a solid with restricted control parameters (1986) MTT, 5, pp. 11-15. , Izv. Akad. Nauk SSSR; Akulenko, (1987) Asymptotic Optimal Control Methods, , Nauka, Moscow; Vorotnikov, (1991) The Stability of Dynamical Systems with Respect to some of the Variables, , Nauka, Moscow; Krasovskii, (1974) Phase Space and Statistical Theory of Dynamical Systems, , Nauka, Moscow; Chernous'ko, Kolmanovskii, (1978) Optimal Control under Random Perturbations, , Nauka, Moscow; Afanas'yev, Kolmanovskii, Nosov, (1989) Mathematical Theory of the Construction of Control Systems, , Vyssh. Shkola, Moscow; Tertychnyi, Stochastic stabilization of controlled rotational motion of a solid (1989) MTT, 2, pp. 9-14. , Izv. Akad. Nauk SSSR; Isaacs, (1967) Differential Games, , Mir, Moscow; Krasovskii, (1970) Game-theoretic Problems on the Encounter of Motions, , Nauka, Moscow; Kurzhanskii, (1977) Control and Observation Under Conditions of Uncertainty, , Nauka, Moscow; Chernous'ko, Melikyan, (1978) Game-theoretic Control and Search Problems, , Nauka, Moscow; Yorotnikov, On the stabilization of the permanent rotations of a massive solid clamped at a fixed point (1985) MTT, 3, pp. 16-18. , Izv. Akad. Nauk SSSR; Vorotnikov, The control of the angular motion of a solid (1986) MTT, 6, pp. 38-43. , Izv. Akad. Nauk SSSR; Chernous'ko, Decomposition and suboptimal control in dynamical systems (1990) Prikl. Mat. Mekh., 54 (6), pp. 883-893; Chernous'ko, Decomposition and synthesis of control in dynamical systems (1990) Tekhn. Kibern., 6, pp. 64-82. , Izv. Akad. Nauk SSSR; Chernous'ko, The synthesis of the control of a non-linear dynamical system (1992) Prikl. Mat. Mekh., 56 (2), pp. 179-191; Rumyantsev, Optimal stabilization of control systems (1970) Prikl. Mat. Mekh., 34 (3), pp. 440-456; Vorotnikov, On the stability and stabilization of motion with respect to some of the variables (1982) Prikl. Mat. Mekh., 46 (6), pp. 914-923; Rumyantsev, Oziraner, (1987) Stability and Stabilization of Motion with Respect to Some of the Variables, , Nauka, Moscow; Vorotnikov, Optimal stabilization of motion with respect to some of the variables (1990) Prikl. Mat. Mekh., 54 (5), pp. 726-736; Vorotnikov, Optimal stabilization of non-linear control systems (1991) Avtom. Telemekh., 3, pp. 22-34; Vorotnikov, Problems and methods of studying the stability and stabilization of motion with respect to some of the variables: trends of research, results and features (1993) Avtom. Telemekh, 3, pp. 3-62; Brockett, Feedback invariants for non-linear systems (1978) Preprint IFAC Congress, 2, pp. 1115-1120. , Helsinki; Jakubczyk, Respondek, On linearization of control systems (1980) Bull. Acad. Polon. Sci. Ser. Sci. Math., 28 (9-10), pp. 518-522; Hunt, Meyer, Global transformations of nonlinear systems (1983) IEEE Transactions on Automatic Control, 28 AC (1), pp. 24-31; Dwyer, III, Exact nonlinear control of large angle rotational maneuvers (1984) IEEE Transactions on Automatic Control, 29 AC (9), pp. 769-774; Matrosov, Anapol'skii, Vasil'yev, (1980) Comparison Method in Mathematical Systems Theory, , Nauka, Novosibirsk; Vasil'yev, The control of non-linear systems with phase constraint and constantly acting perturbations (1993) Tekhn. Kibern., 1, pp. 77-82. , Izv. Ross. Acad. Nauk; Krasovskii, (1987) Handbook of Automatic Control Theory, , Nauka, Moscow; Atans, Falb, (1968) Optimal Control, , Mashinostroyeniye, Moscow; Pontryagin, Boltyanskii, Gamkredlidze, Mishchenko, (1983) Mathematical Theory of Optimal Processes, , Nauka, Moscow
Correspondence Address Vorotnikov, V.I.
CODEN JAMMA
Language of Original Document English
Abbreviated Source Title J. Appl. Math. Mech.
Source Scopus