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Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2008-2pp.159-163

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A.P. Blinov, "Stabilization of the equilibria of dynamical systems," J. Appl. Math. Mech. 72 (2), 159-163 (2008)
Year 2008 Volume 72 Issue 2 Pages 159-163
Title Stabilization of the equilibria of dynamical systems
Author(s) A.P. Blinov (Moscow, Russia)
Abstract Based on Rumyantsev's method, a procedure is developed for stabilizing stable and unstable equilibria of dynamical systems by continuous and modulus-constrained control actions. It is shown that, when modulus constraints are imposed on the controls, and when the quadratic-form coefficients are reduced in modulus, the optimal stabilization, in terms of this method, approximates to time-optimal stabilization. A solution is obtained of the problem of stabilizing unstable equilibrium positions at which the potential energy of the system has neither a maximum nor a minimum (or, in particular, at which the potential energy is identically equal to zero).
Received 25 January 2007
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