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This paper proposes two novel distributed continuous-time algorithms inspired by PID control to solve distributed optimization problems. The algorithms are referred to as first-order and second-order, respectively, depend on the intrinsic dynamics of the agents in the network. Sufficient conditions are derived so that both algorithms converge exponentially over undirected connected graphs. Finally, numerical simulations illustrate the effectiveness and efficiency of the proposed algorithms., Comment: 7 pages, 3 figures, The 49th Annual Conference of the IEEE Industrial Electronics Society

For crystalline materials with long-range orders, the phonon modes involved in the phonon-assisted radiation process are generally involving one or several phonons with specific vibration frequencies 1-4. In some glassy material, the phonon modes broaden in a short range 5-7. However, the locally distinct chemical environments or mass disorder in high-entropy systems can induce an anharmonic phonon-phonon coupling and composition disorder, which leads to significant phonon broadening 8,9.The terminology of high-entropy comes from the high configuration entropy larger than 1.5R (R is the gas constant), which results from randomly distributed multiple nearly equal components in a crystal lattice 10,11. Inspired by the high-entropy strategy, we deployed a high-entropy glass system (HEGS) doped with neodymium ions, which exhibits a complex structure with tetrahedral voids filled by different ions, including, Li+, Zn2+, Si4+, P5+, S6+, etc. Phonon spectral broadening up to thousands of wavenumbers in the HEGS allows strong wide-band absorption in both the near-infrared and mid-infrared ranges and assists the system radiation, i.e., broadened phonon-assisted wide-band radiation (BPAWR). The subsequent low-threshold self-absorption coherence modulation (SACM) was also observed in the HEGS, modulated by changing excitation wavelengths, sample size, and doping concentrations. The time delay of the BPAWR signal is up to 1.66 ns relative to the zero-delay signal, while the time delay of the Raman process is typically in the order of fs to ps, rarely up to 10 ps 12-15.The BPAWR-SACM can be applied to realize signal amplification of the centered non-absorption band when dual-wavelength lasers pump the HEGS sample, and signal amplification can be up to 26.02 dB. The spectral characteristics of the BPAWR and the dynamics of the energy distribution of the excited species are investigated in detail.