Thermalization in Feedback Controlled Fermi-Pasta-Ulam Lattice
Egor Usik, Natalia Amelina, Alexander Fradkov
A controlled version of the celebrated Fermi-Pasta-Ulam problem is studied. The speed-gradient control algorithm is analyzed by computer simulation. Approximation of the system Hamiltonian
prespeci ed value is proposed as the control goal. It is demonstrated that the control goal is achieved in the controlled system. It is shown that the controlled system tends to approximate equipartition
state (mode energies are well separated from zero) much faster than it happens in the open loop (classical) system. Such a phenomenon is observed under control with sufficiently small intensity: less than 0.5% of the total system energy.
The novelty of this paper is in that the case of feedback excitation applied to the internal node #31 is studied. It is shown that the influence of feedback is much weaker than in the case of feedback excitation applied to the boundary node #32.