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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.

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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