Fixed-time cluster optimization of multi-agent systems on directed detail-balanced networks

Abstract

This paper investigates the fixed-time cluster optimization problem of first-order multi-agent systems (MASs) under directed detail-balanced networks, in which the optimization objective is a linear combination of local objective functions. Two piecewise distributed control protocols are proposed to solve the optimization problem with time-invariant and time-varying objective functions, respectively. Under the two proposed piecewise control protocols, the fixed-time cluster optimization problem can be solved on the basis of maintaining the cluster consensus unchanged. Furthermore, the initial states of all the agents need not be restricted to the minimum of their local cost functions. Finally, we provide two examples to illustrate the effectiveness of the proposed control protocols.