Lag Output Consensus for Second-Order Nonlinear Multiagent Systems Under PID Control

Based on PD and PI control methods, the lag output consensus problem for second-order nonlinear multiagent systems (MASs) without and with external disturbances is addressed, which generalizes the existing lag consensus results for MASs. Firstly, a lag output consensus condition is derived for the MAS by designing a proper PD control scheme. Furthermore, a PI control strategy is developed to ensure that the MAS realizes the lag output consensus. In addition, two lag ${\mathcal {H}}_{\infty } $ output consensus criteria are also established on the basis of PD and PI control schemes for the MAS with external disturbances. Lastly, two examples are utilized to verify the correctness and effectiveness of the devised control schemes. Note to Practitioners—Recently, virtual leader-based approach has been widely utilized to address the output consensus control problem for various MASs. Practically, each agent receiving its own output information may be later than the virtual leader. Therefore, it is more reasonable and meaningful to discuss the lag output consensus for MASs. Furthermore, considering that PID control is very simple and easy to implement, some PD and PI control strategies are developed to tackle the lag output consensus for MASs. In addition, since external disturbances are ubiquitous and may destroy the lag output consensus, the lag ${\mathcal {H}}_{\infty } $ output consensus for MASs is also investigated. Multiple single-link robot systems experiments verify that the approaches given in this paper are feasible and valid.