Achieving Constrained Optimization Digraphs Within Preset-Time via Integral Sliding Mode Control

This work presents an estimator-based distributed preset-time algorithm that effectively addresses the equality-constrained optimization problem on directed graphs (digraphs). Initially, we propose an innovative distributed preset-time estimator to accurately estimate the global information related to the cost function. Building on this, we develop an estimator-based distributed robust preset-time optimization algorithm incorporating ISMC, which is specifically tailored for strongly connected networks. Compared with existing algorithms, the proposed algorithm features three key innovations: improved precision in convergence time, enhanced robustness against disturbances, and expanded applicability to network topologies. Finally, we validate the preset-time optimization algorithm through numerical simulations, demonstrating that its convergence rate significantly outperforms those of current finite-and fixed-time algorithms.