Predefined-Time Distributed Optimization Algorithm for Disturbed MASs With Equality Constraints

This study investigates first-order multi-agent systems under external disturbances and introduces two predefined-time algorithms designed to solve convex optimization problems with global equality constraints. First, a continuous-time disturbance-rejection optimization algorithm is proposed that suppresses disturbance signals and achieves the optimal solution under bounded external disturbances. The algorithm's convergence time does not depend on both the initial states and external disturbances, and can be arbitrarily predefined. Second, to reduce communication overhead among agents, a distributed optimization algorithm utilizing a event-triggered mechanism is further developed, where agent states are updated only at certain discrete time points. This algorithm effectively suppresses disturbance signals, prevents Zeno behavior, and ensures convergence to the optimal solution within a predefined time. Using convex optimization and Lyapunov theories, the convergence of both algorithms under bounded disturbances is rigorously proven. Finally, a case study on economic dispatch in smart grids validates the effectiveness and superiority of the proposed algorithms.