Distributed bipartite containment for heterogeneous fractional‐order multiagent systems with finite‐time and event‐triggered control strategies

This paper delves into distributed bipartite containment issues for heterogeneous fractional‐order multiagent systems (HFOMASs), considering cooperative and antagonistic interactions among neighbor agents. Initially, an observer‐based distributed finite‐time bipartite control algorithm is formulated, enabling the observer to estimate the convex hull formed by multiple leaders' states and the symmetric convex hull of other leaders' states. This approach ensures bipartite output containment control (BOCC) within a finite time. Subsequently, a distributed bipartite event‐triggered control strategy augmented with a compensator is introduced, where the compensator accurately estimates the convex hull and its symmetric counterpart of the leaders' states, enabling the realization of BOCC. Furthermore, the consensus condition and an associated triggering function are rigorously derived, thereby ensuring the elimination of Zeno behavior and significantly reducing the frequency of triggering events by suppressing unnecessary high‐frequency activations. To substantiate the theoretical findings, illustrative examples are presented, successfully validating the efficacy and applicability of the proposed methods.