Fixed-time consensus for multi-agent systems with objective optimization on directed detail-balanced networks

This paper investigates the distributed control of multi-agent systems (MASs) with objective optimization on directed detail-balanced networks, in which the global optimization function is expressed as a convex combination of local objectives of agents. First, a directed and detail-balanced network depending on the weights of an optimization function is constructed, and a distributed consensus protocol with gradients of local objectives is proposed over the designed network. Using Lyapunov stability theory and a projection technique, we prove that the proposed protocol not only makes all agents achieve consensus in a fixed-time interval but can also solve the global optimization problem asymptotically. Moreover, the optimization problem with box constraints is studied, and a δ-exact penalty method is employed to eliminate the constraints. Similarly, a distributed fixed-time consensus protocol with gradient measurement is developed, and we prove that the optimal solution can be reached asymptotically. Finally, two examples are presented to show the efficacy of the theoretical results.