  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.
