A controlled version of the celebrated Fermi–Pasta–Ulam problem is introduced. The feedback control algorithm based on Speed-gradient approach is proposed and analyzed by extensive computer simulation. It is demonstrated that the feedback controlled system tends to approximate equipartition state much faster than it happens in the open loop (classical) system. Apparently a substantial change in system behavior is achieved with a small intensity control: less than 0.5% of the total system energy. Such a behavior has been observed and analyzed previously for oscillators with one degree-of-freedom (DOF) under the name of feedback resonance (Fradkov A.L., Physica D, 128(1999), 159-168. The results of this paper suggest that feedback resonance phenomenon may be observed in multi-DOF oscillator chains, particularly in FPU chain.

中文翻译：

---

费米-帕斯塔-乌拉姆链中的反馈共振

引入了著名的费米-帕斯塔-乌拉姆问题的受控版本。提出了基于速度梯度方法的反馈控制算法，并通过大量计算机仿真进行了分析。结果表明，反馈控制系统倾向于比开环（经典）系统更快地接近均分状态。显然，系统行为的重大变化是通过小强度控制实现的：小于系统总能量的 0.5%。以前已经在反馈共振的名义下对具有一个自由度 (DOF) 的振荡器观察和分析了这种行为（Fradkov AL, Physica D, 128(1999), 159-168。本文的结果表明：在多自由度振荡器链中，特别是在FPU链中，可以观察到反馈共振现象。