Mechanics of Solids (about journal) Mechanics of Solids
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IssuesArchive of Issues2012-4pp.390-399

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V.I. Matyukhin, "Multimode Laws of Control of Rigid Body Motions," Mech. Solids. 47 (4), 390-399 (2012)
Year 2012 Volume 47 Number 4 Pages 390-399
DOI 10.3103/S0025654412040048
Title Multimode Laws of Control of Rigid Body Motions
Author(s) V.I. Matyukhin (Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya†65, V-342, GSP-7, Moscow, 117997 Russia,,
Abstract The problem of control of motion of a rigid body (aircraft, satellite, or landing module) is studied. A multimode control law that can stabilize not only one prescribed motion of the body but any motion in a sufficiently broad class is constructed. The problem is solved in nonlinear setting under indeterminacy conditions on the basis of Lyapunov functions. The control law is constructed in the class of bounded discontinuous laws, special zero-overshoot response modes are constructed, and the specific character of mechanical systems is used.
Keywords rigid body, control, stability, Lyapunov function, multimode control law
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2.  G. S. Byushgens, M. G. Goman, G. I. Zaiganov, et al., Method of Lyapunov Functions in Problems of Control Synthesis for Aircraft Spatial Motion, Preprint No. 4 (IPU AN SSSR, Moscow, 1992) [in Russian].
3.  G. S. Byushgens, M. G. Goman, V. I. Matyukhin, and E. S. Pyatnitskii, "Stabilizability and Universal Control Laws for the Motion of a Solid Body with Allowance for Aerodynamic Actions," Dokl. Ross. Akad. Nauk 342 (1), 49-52 (1995) [Dokl. Phys. (Engl. Transl.) 40 (5), 247-250 (1995)].
4.  M. G. Goman, V. I. Matyukhin, and E. S. Pyatnitskii, "Control over Orientation of a Solid Body Moving in an Aerodynamical Medium," Dokl. Ross. Akad. Nauk 353 (6), 751-755 (1997) [Dokl. Phys. (Engl. Transl.) 42 (4), 223-227 (1997)].
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7.  V. M. Matrosov, L. Yu. Antokolskii, and S. N. Vasiliev, Comparison Methods in Mathematical Theory of Systems (Nauka, Novosibirsk, 1980) [in Russian].
8.  N. N. Krasovskii, Several Problems of the Theory of Stability of Motion (Fizmatgiz, Moscow, 1959) [in Russian].
9.  M. A. Aizerman and E. S. Pyatnitskii, "Foundation of a Theory of Discontinuous Systems. Pts. 1 and 2," Avtomat. Telemekh., No. 7, 33-47; No. 8, 39-61 (1974) [Automat. Remote Control (Engl. Transl.) 35 (7), 1066-1079 (1974); 35 (8), 1242-1262 (1974)].
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11.  A. F. Filippov, Differential Equations with Discontinuous Right-Hand Side (Nauka, Moscow, 1985) [in Russian].
12.  V. I. Matyukhin, "Stabilization of Motions of the Descent Vehicle in the Upper Atmosphere," Avtomat. Telemekh., No. 4, 70-83 (2003) [Automat. Remote Control (Engl. Transl.) 64 (4), 576-588 (2003)].
13.  V. I. Matyukhin, "Solid Body Stabilization in Aerodynamic Medium with Regard for Delay," Avtomat. Telemekh., No. 10, 93-107 (2005) [Automat. Remote Control (Engl. Transl.) 66 (10), 1614-1627 (2005)].
14.  V. I. Matyukhin, Control of Mechanical Systems (Fizmatlit, Moscow, 2009) [in Russian].
Received 26 April 2010
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