The fixed-time flocking of multi-agent systems with a virtual leader is investigated in this paper. The motion dynamics of the agents are assumed to be unknown and only satisfy the boundedness, which does not need to be modelled by the Lipschitz condition. To achieve the flocking and collision avoidance for all agents in the fixed time, a control protocol in the high-dimensional space is developed by using the graph theory and the theoretical properties of differential equations. Moreover, the upper bound of the settling time only depending on the control protocol and the topology of network is estimated. Numerical examples are used to verify the theoretical results, and show that the proposed method provides an applicable method for the control of the nonlinear dynamic systems.

This paper investigates the flocking control of multi-agent systems with unknown nonlinear dynamics while the virtual leader information is heterogeneous. The uncertain nonlinearity in the virtual leader information is considered, and the weaker constraint on the velocity information measurements is assumed. In addition, a bounded assumption on the unknown nonlinear dynamics is also considered. It is weaker than the Lipschitz condition adopted in the most flocking control methods. To avoid fragmentation, we construct a new potential function based on the penalty idea when the initial network is disconnected. A dynamical control law including a adjust parameter is designed to achieve the stable flocking. It is proven that the velocities of all agents approach to consensus and no collision happens between the mobile agents. Finally, several simulations verify the effectiveness of the new design, and indicate that the proposed method has high convergence and the broader applicability in practical applications with more stringent restrictions.

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The fixed-time leader-following synchronization in a non-identical delayed network via non-chattering nonlinear control is investigated. By introducing a function of control error, a continuous and differential controller is constructed without using the sign function and absolution of the error. The sufficient conditions are then established to guarantee that synchronization errors converge exactly to zero within a fixed time interval. The proposed approach provides a high convergence for the network accurately tracking the trajectory of the leader. More importantly, a tighter bound for the settling time is obtained and the chattering effects are eliminated. The numerical simulations are conducted to illustrate the effectiveness of theoretical analysis.