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Asymptotically optimal feedback control for a system of linear oscillators. (English. Russian original) Zbl 1283.93132
Dokl. Math. 88, No. 2, 613-617 (2013); translation from Dokl. Akad. Nauk. 452, No. 3, 266-270 (2013).
Introduction: One of the classical achievements in control theory is an explicit construction of the minimum time damping for a single linear oscillator. In this paper, we consider the next in complexity problem of damping of an arbitrary number of oscillators under a common bounded control. Probably, in this case, an explicit construction of an optimal feedback control is impossible, and even obtaining a numerical solution is a hard problem. We are looking for a nonoptimal feedback control which brings the system to an equilibrium point. The control obtained is asymptotically optimal: the ratio of the duration of steering to zero under our control to the minimum one is close to 1, if the initial energy is large.

MSC:
93B52 Feedback control
93C15 Control/observation systems governed by ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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