This paper addresses a class of optimization problems with time-varying cost functions by proposing a fully distributed prescribed-time algorithm. The algorithm decomposes the overall optimization problem into three successive subproblems, which are solved sequentially. During the three stages of the algorithm, the estimation of the total cost function's average gradient information, consensus among the states, and tracking of the optimal state trajectories are achieved in turn. Given the segmentation strategy's demand for rapid convergence, the algorithm ensures convergence within a prescribed time. Using the Lyapunov method, it is shown that all three subproblems can be solved within any user-prescribed time, independent of the system's initial states or topology. To further exploit the independence of prescribed-time convergence from system states, the algorithm eliminates the reliance on system topology information in parameter settings by introducing adaptive parameters in place of traditional fixed ones, thus enabling fully distributed control. Finally, numerical simulations and an UAVs target tracking experiment are conducted to validate the effectiveness and practicality of the proposed algorithm.

In this paper, the inter-area low-frequency oscillations are restrained in the interconnected power system by making use of the delay-dependent wide-area dynamic output feedback controller (DOFC). Modal analysis is adopted to obtain the modes of inter-area oscillation to be controlled and the Schur truncation model reduction technique is represented to reduce the order of the power system. The augmented closed-loop system model, where the transmission delay and packet loss of wide-area signals are considered, is established. The sufficient conditions of exponentially mean-square stable are obtained according to Lyapunov’s stability theory. Finally, case studies are carried out on a two-area four-machine power system, where our proposed controller, a conventional controller, and the wide-area damping controller in the existing references are installed, respectively. The simulation results under different external disturbances, packet loss rates, and delays are presented to show the effectiveness and advantages of our proposed controller.