Leader-Follower Free-Will Arbitrary Time Consensus for Nonlinear Second-Order Multiagent Systems

In this research ,we study the leader-follower consensus at free-will arbitrary time (FWAT) for second-order multi-agent systems (MASs) with a fixed nonlinear term. Firstly, due to the existence of inherent nonlinear terms in the system, the backstepping method is used to eliminate the nonlinear terms by designing a virtual controller. Secondly, design suitable control strategy that enable arbitrary convergence of follower states and velocities at a predetermined arbitrary time, and make sure the convergence time is not impacted by the system’s original conditions and characteristics. Finally, the existence of the theory is deduced by introducing the Lyapunov function.