An adaptive gain-based fixed-time distributed algorithm for constrained optimization problems

This letter presents a novel adaptive gain-based fixed-time distributed algorithm for solving constrained optimization problems in continuous-time multi-agent systems (MASs). The proposed approach first introduces a sliding mode control scheme with an adaptive control parameter to ensure the satisfaction of coupled equality constraints within a fixed time, regardless of the initial state. Based on this scheme, an innovative node-based distributed optimization algorithm is developed, incorporating a nonlinear adaptive consensus scheme to achieve the optimal solution within a fixed time. The theoretical upper bound for the convergence time is determined by the first positive zero point of a sine function. Furthermore, the algorithm is extended to an edge-based distributed optimization scheme to reduce communication burden, albeit with increased memory consumption. Lyapunov technique is employed to confirm the stability of both the node-based and edge-based methods. To address the singularity issues encountered in the adaptive fixed-time algorithms, the saturation function and the power-ball method are introduced. Finally, the effectiveness and superior convergence performance of the proposed methods are demonstrated through three simulation cases, particularly highlighting their advantages in scenarios with sparse communication networks.