Small-Gain Theorem Based Distributed Prescribed-Time Convex Optimization For Networked Euler-Lagrange Systems
<|reference_start|>Small-Gain Theorem Based Distributed Prescribed-Time Convex Optimization For Networked Euler-Lagrange Systems: In this paper, we address the distributed prescribed-time convex optimization (DPTCO) for a class of networked Euler-Lagrange systems under undirected connected graphs. By utilizing position-dependent measured gradient value of local objective function and local information interactions among neighboring agents, a set of auxiliary systems is constructed to cooperatively seek the optimal solution. The DPTCO problem is then converted to the prescribed-time stabilization problem of an interconnected error system. A prescribed-time small-gain criterion is proposed to characterize prescribed-time stabilization of the system, offering a novel approach that enhances the effectiveness beyond existing asymptotic or finite-time stabilization of an interconnected system. Under the criterion and auxiliary systems, innovative adaptive prescribed-time local tracking controllers are designed for subsystems. The prescribed-time convergence lies in the introduction of time-varying gains which increase to infinity as time tends to the prescribed time. Lyapunov function together with prescribed-time mapping are used to prove the prescribed-time stability of closed-loop system as well as the boundedness of internal signals. Finally, theoretical results are verified by one numerical example.<|reference_end|>
@article{zuo2024small-gain,
    title={Small-Gain Theorem Based Distributed Prescribed-Time Convex Optimization
  For Networked Euler-Lagrange Systems},
    author={Gewei Zuo, Mengmou Li and Lijun Zhu},
    journal={arXiv preprint arXiv:2407.19496},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.19496},
    primaryClass={math.OC cs.RO}
}