Finite-Time Synchronization of Nonlinear Multi-Agent Systems with Prescribed Performance

In this paper, we address the finite-time synchronization tracking problem for unknown high-order nonlinear multiagent systems with prescribed performance under a directed graph. The agent is described by an n-order normal form system with unknown dynamic and an external disturbance. The prescribed performance means that the synchronization tracking error preserves within a prescribed region, whose boundary functions are chosen as exponentially decaying functions of time. A tan-type barrier Lyapunov function is employed to guarantee that the tracking error stays always within the prescribed region. A finite-time control scheme is incorporated into the control design to achieve finite-time convergence of tracking error. That is, the tracking error is forced to converge to a predefined radius centered at zero in finite time. To improve the robustness of the control systems, neural networks are employed to approximate the unknown dynamic and a decentralized parameter estimator is applied to estimate the upper bound of the external disturbance. Based on backstepping technique, barrier Lyapunov function, and finite-time control scheme, a decentralized adaptive controller is proposed to guarantee that the tracking error converges exponentially to a small neighborhood around zero in finite time with guaranteeing prescribed transient performance. An illustrative example is given to show the effectiveness of the decentralized cooperative controller.