 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| S.A. Reshmin, "Estimate of the Control Threshold Value in the Problem on a Time-Optimal Satellite Attitude Transition Maneuver," Mech. Solids. 52 (1), 9-17 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
1 |
Pages |
9-17 |
| DOI |
10.3103/S0025654417010022 |
| Title |
Estimate of the Control Threshold Value in the Problem on a Time-Optimal Satellite Attitude Transition Maneuver |
| Author(s) |
S.A. Reshmin (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, reshmin@ipmnet.ru) |
| Abstract |
The time-optimal problem is considered for a nonlinear Lagrangian system with one degree of freedom. The system is controlled by a force bounded in absolute value, and all noncontrol forces are potential. We study the properties of optimal synthesis on the phase cylinder and indicate the conditions under which it has the simplest structure, namely, involves at most one switching for any initial conditions. The approach is used to specify the structure of the well-known solution in the classical problem on the time-optimal satellite attitude transition maneuver in the orbit plane. |
| Keywords |
time-optimal problem, number of switchings, second-order system, Lagrangian system, satellite |
| References |
| 1. | V. V. Beletskii,
"Optimal Transfer of an Earth Satellite to a Gravitationally Stable Position,"
Kosmich. Isseld.
9 (3), 366-375 (1971)
[Cosmic Res. (Engl. Transl.)
9 (3), 337-344 (1971)]. |
| 2. | A. A. Anchev, "Equilibrium Attitude Transitions of a Three-Rotor Gyrostat in a Circular Orbit," AIAA J. 11 (4), 467-472 (1973). |
| 3. | A. P. Markeev,
Theoretical Mechanics
(NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2007)
[in Russian]. |
| 4. | S. A. Reshmin and F. L. Chernous'ko,
"A Time-Optimal Control Synthesis for a Nonlinear Pendulum,"
Izv. Ross. Akad. Nauk. Teor. Sist. Upr.,
No. 1, 13-22 (2007)
[J. Comp. Syst. Sci. Int. (Engl. Transl.)
46 (1), 9-18 (2007)]. |
| 5. | S. A. Reshmin,
"Finding the Principal Bifurcation Value of the Maximum Control Torque
in the Problem of Optimal Control Synthesis for a Pendulum,"
Izv. Ross. Akad. Nauk. Teor. Sist. Upr.,
No. 2, 5-20 (2008)
[J. Comp. Syst. Sci. Int. (Engl. Transl.)
47 (2), 163-178 (2008)]. |
| 6. | L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko,
The Mathematical Theory of Optimal Processes
(Fizmatgiz, Moscow, 1961; Gordon & Breach Sci. Publ., New York, 1986). |
| 7. | R. Isaacs,
Differential Games
(Wiley, New York, 1965; Mir, Moscow, 1967). |
| 8. | E. B. Lee and L. Markus,
Foundations of Optimal Control Theory
(Wiley, New York, 1967; Nauka, Moscow, 1972). |
| 9. | B. Friedland and P. Sarachik,
"Indifference Regions in Optimum Attitude Control,"
IEEE Trans. Automatic Control
9 (2), 180-181 (1964). |
| 10. | J. L. Garcia Almuzara and I. Flügge-Lotz,
"Minimum Time Control of a Nonlinear System,"
J. Differen. Equations
4 (1), 12-39 (1968). |
| 11. | S. A. Reshmin,
"Bifurcation in a Time-Optimal Problem for a Second-Order Non-Linear System,"
Prikl. Mat. Mekh.
73 (4), 562-572 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (4), 403-410 (2009)]. |
| 12. | S. A. Reshmin and F. L. Chernousko,
"Properties of the Time-Optimal Feedback Control for a Pendulum-Like System,"
J. Optimiz. Theory Appl.
163 (1), 320-252 (2014). |
|
| Received |
22 December 2014 |
| Link to Fulltext |
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