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Feedback resonance in Fermi–Pasta–Ulam chain

Author

Listed:
  • Usik, Egor
  • Amelina, Natalia
  • Fradkov, Alexander L.

Abstract

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.

Suggested Citation

  • Usik, Egor & Amelina, Natalia & Fradkov, Alexander L., 2024. "Feedback resonance in Fermi–Pasta–Ulam chain," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002133
    DOI: 10.1016/j.chaos.2024.114661
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