Distributed fixed-time optimization for multi-agent systems over a directed network

This paper proposes some distributed algorithms to solve the multi-agent optimization problem with equality constraints, in which the team objective is a sum of local convex objective functions. Firstly, a directed network related to equality constraints is constructed before converting the constrained optimization problem into an unconstrained one. Secondly, a continuous algorithm is designed by using local information of agents, and the objective function converges to the global optimum in a fixed-time interval. Moreover, in order to reduce the communication cost, an event-triggered algorithm with sign function is devised. It is found that the optimal value can be achieved in a fixed-time interval, but the sign function can cause high-frequency chattering when the sate variables converge to the optimal value. Therefore, an event-triggered algorithm with saturation function is proposed, which can effectively overcome this disadvantage. Finally, the proposed algorithms are verified by some numerical simulations.