PDE‐Based Consensus Tracking and Vibration Control of Nonlinear Mobile Vehicle‐Mounted Boom Crane Multi‐Agent Systems With Actuator Faults

ABSTRACT This paper investigates the dynamic modeling, consensus tracking, and vibration control of a class of leader‐following multi‐agent systems (MASs) subject to unknown actuator faults. Each follower agent is a nonlinear moving vehicle‐mounted boom crane system, which is composed of a mobile vehicle, a rigid boom, and a flexible cable. The desired displacement of the vehicles and angular position of the rigid booms together serve as the virtual leader's reference signals. First, by utilizing Hamilton's principle, each moving boom crane is modeled by several partial differential equations (PDEs) with the coupling of displacement, angle, and vibration. Second, an adaptive parameter update law is suggested to compensate for the influences caused by actuator failures. Third, combining the obtained PDE model and adaptive law, a fault‐tolerant distributed boundary consensus protocol is proposed for MASs under an undirected interaction topology. With the designed controller, both consensus tracking of the vehicles and booms and vibration suppression of the flexible cables are realized. Moreover, the asymptotic stability of the closed‐loop systems is established using Lyapunov's direct method and LaSalle's invariance principle. Finally, some simulation examples are presented to demonstrate the effectiveness of the developed theoretical algorithms.