Leader-Following Containment Control of Hybrid Fractional-Order Networked Agents With Nonuniform Time Delays

Time delays, such as transmission delays or measurement delays, are common phenomena in practical networked control systems. These delays directly threaten the effective completion of cooperative tasks. In this study, the leader-following containment control problem of hybrid fractional-order networked agents with nonuniform time delays is addressed. The position and velocity loops of each double-integrator agent are modeled by fractional-order calculus equations of different orders, which is also called the hybrid fractional-order networked agent system. At first, the mathematical expressions for the upper bound of allowable time delays with respect to the system parameters, such as fractional order, topological structure properties, and controller gains, are given explicitly considering both the directed and undirected graph conditions. Then, this paper obtains the maximum allowable upper bounds of time delays for achieving leader-following containment tracking control in the case of fractional order mismatch. Based on this, it is convenient to calculate the delay margin directly and to judge the stability of the networked agent systems with nonuniform time delays. Finally, some simulation results are given to verify the effectiveness of the delay margin for networked agent systems. The results show that the system stability can be directly judged by calculating the critical time delay condition; meanwhile, the system robustness can also be improved by actively adjusting the controller parameters to increase the delay margin.