Fixed-time distributed optimization algorithm for multi-agent systems with disturbance resistance

This paper presents an anti-interference distributed algorithm, which can solve the convex optimization problem of first-order multi-agent systems with the state constraint and external bounded disturbance in a fixed-time. The designed algorithm is divided into two parts. The first part makes every agent converge to consensus in a fixed-time under any initial conditions. The second part minimizes the sum of all local objective functions in a fixed-time while satisfying the constraint condition. This algorithm can restrain the bounded interference signal and finally obtain the optimal solution. The setup time can be pre-allocated off-line according to task needs, regardless of the initial states of the agents and in the presence of bounded disturbances. By means of the convex optimization and fixed-time Lyapunov theory, the convergence of the algorithm in a fixed-time is proved when the bounded disturbance exists. Finally, the effectiveness and superiority of the algorithm is verified by an example of economic dispatch in smart grid. © 2024 Northeast University. All rights reserved.