 | | 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
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| In English (Mech. Solids): | | 4810 |
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| B.N. Sokolov, "On the Efficiency of a Linear Controller under Additional Geometric Constraints," Mech. Solids. 44 (5), 659-662 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
659-662 |
| DOI |
10.3103/S002565440905001X |
| Title |
On the Efficiency of a Linear Controller under Additional Geometric Constraints |
| Author(s) |
B.N. Sokolov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia) |
| Abstract |
One heuristic approach to taking into account geometric constraints on the controls in stabilization problems is to use controls obtained by truncation (at the constraint values) of a control signal linear in the phase variables. With the introduction of the truncated control, the originally linear system becomes substantially nonlinear, which complicates the analysis. In numerous papers, the phase plane method was used to analyze the control defined as the sign of a control signal linear in the phase variables. In [1, 2], the asymptotic stability of linear dynamical systems with nonlinear controls of special type different from that considered below was studied. The problem of stabilization of a mechanical system by a geometrically constrained control was considered in [3]. The asymptotic stability of an arbitrary linear system with a truncated control was studied in [4], where some estimates for the attraction domain of the trivial solution of the system were obtained and necessary and sufficient conditions under which this domain can be made arbitrarily large were given. In the present paper, we solve the problem of ensuring the asymptotic stability of a mechanical system with arbitrarily many degrees of freedom and with componentwise geometric constraints on the control. |
| Keywords |
asymptotic stability, geometrically constrained control |
| References |
| 1. | A. I. Lurie,
Several Nonlinear Problems in Automatic Control Theory
(Gostekhizdat, Moscow-Leningrad, 1951)
[in Russian]. |
| 2. | A. M. Letov,
Stability in Nonlinear Control Systems
(Fizmatgiz, Moscow, 1962)
[in Russian]. |
| 3. | E. S. Pyatnitskiy and N. V. Dunskaya,
"Stabilization of Mechanical and Electromechanical Systems,"
Avtomat. Telemekh.,
No. 12, 40-51 (1989)
[Automat. Remote Control (Engl. Transl.)
49 (12), 1565-1574 (1989)]. |
| 4. | B. N. Sokolov
"Stabilization of Dynamical Systems with Geometrically Constrained Control,"
Prikl. Mat. Mekh.
55 (1), 48-53 (1991)
[J. Appl. Math. Mech. (Engl. Transl.)
55 (1), 42-48 (1991)]. |
|
| Received |
24 May 2007 |
| Link to Fulltext |
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