In this paper, we studied a Cucker–Smale model with continuous non-Lipschitz protocol. The methodology presented in the current work is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed time if the communication rate function is locally Lipschitz continuous and has a lower bound, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.

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In this paper, we studied some consensus algorithms for the collective rotating motions of a team of agents, which has been widely studied in different disciplines ranging from physics, networks and engineering. Both discrete and continues consensus algorithm with processing delays are investigated. There are three motion patterns determined by the information exchange topology of systems and rotation angle of rotation matrices. The asymptotic consensus appears when 0 is an simple eigenvalue of Laplacian matrix and the rotation angle is less than the critical value, and the rotating consensus achieves when the rotation angle is equal to the critical value. At this point, all agents move on circular orbits and the relative radii of orbits are equal to the relative magnitudes of the components of a right eigenvector associated with 0 eigenvalue of the non-symmetric Laplacian matrix. Finally, all agents move along logarithmic spiral curves with a fixed center when the rotation angle is larger than the critical value.

Multiagent systems are used in artificial intelligence, control theory, and social sciences. In this article, we studied a Cucker–Smale model with a continuous non-Lipschitz protocol. The methodology presented in the current paper is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed-time and collision avoiding when a singular communication function with a weighted sum of sign functions of the relative velocities among agents, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.