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Control of the Duffing oscillator under non-Gaussian external excitation. (English) Zbl 1027.70032

Summary: The problem of suboptimal linear feedback control laws with mean-square criteria for the linear oscillator and Duffing oscillator under external non-Gaussian excitations is considered. The input process is modeled as a polynomial of a Gaussian process or as a renewal driven impulse process. To determine the suboptimal control, a modified iterative procedure is proposed, where four criteria of statistical linearization are combined with an optimal control strategy. The results indicate that the obtained minima do not depend on the linearization criterion. The nonlinearity tends to reduce this minimum.

MSC:

70Q05 Control of mechanical systems
70K40 Forced motions for nonlinear problems in mechanics
74H50 Random vibrations in dynamical problems in solid mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
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