Practical Fixed-Time Bipartite Consensus of Nonlinear Incommensurate Fractional-Order Multiagent Systems in Directed Signed Networks

This paper deals with the problem of practical fixed-time bipartite consensus of a nonlinear incommensurate fractional-order multiagent system (MAS) in a general coopetition network with signed directed graph, where the signed directed graph is composed of both positive and negative interaction links. By introducing a sliding-mode manifold, the incommensurate fractional-order MAS is transformed into an integer-order MAS. Then, practical fixed-time bipartite consensus protocols with constant and adaptive gains are designed, respectively, for the obtained integer-order MAS. By artfully constructing a Lyapunov function, it is shown that the practical bipartite consensus can be achieved with a settling time. Moreover, the upper bound of the settling time can be estimated explicitly, which is irrelevant to any initial conditions. Finally, the effectiveness of the proposed practical fixed-time bipartite consensus schemes is illustrated by numerical simulation.