 | | 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
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| In English (Mech. Solids): | | 4810 |
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| A. V. Korostelev and O. N. Tushev, "Determination of parametric sensitivity of dynamical systems," Mech. Solids. 40 (3), 26-31 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
26-31 |
| Title |
Determination of parametric sensitivity of dynamical systems |
| Author(s) |
A. V. Korostelev (Moscow)
O. N. Tushev (Moscow) |
| Abstract |
The theory of sensitivity of dynamical systems is mostly aimed at the determination of sensitivity
functions of phase coordinates. A well-known method widely used in the literature for analyzing
the sensitivity with respect to parameters consists in differentiating the equations of motion with
respect to these parameters. As a result, one obtains chains of linked systems of differential
equations for the sensitivity functions of different order. If the number of these equations is
large, the problem becomes too cumbersome and the calculations increase drastically, especially
for second-order sensitivity functions. On the other hand, this method is excessively informative
for engineering applications, since for most practical problems one has to determine sensitivity of
only few phase coordinates, with respect to part of the parameters.
An approach without the said drawback is proposed in the present paper. This approach does not
require integration of linked systems of differential equations. In the process of derivation of
the basic relations, no simplifying assumptions are made. A vector of invariants is introduced,
these being new variables independent of the sensitivity functions. Every one of these (of the
first or the second order) can be independently expressed in an integral form through the said
variables. In order to determine these variables, a system of linear differential equations is
obtained, the dimension of the system being equal to that of the vector of phase coordinates. |
| References |
| 1. | E. N. Rosenvasser and R. M. Yusupov, Sensitivity of Automatic Control Systems [in Russian],
Energia, Leningrad, 1969. |
| 2. | C. B. Speedy, R. F. Brown, and G. C. Goodwin, Control Theory [Russian translation], Mir, Moscow, 1973. |
| 3. | F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow, 1967. |
|
| Received |
03 July 2003 |
| << Previous article | Volume 40, Issue 3 / 2005 | Next article >> |
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