Distributed fixed-time consensus algorithms for second-order multi-agent systems under directed topology: A motion-planning approach

This paper studies the distributed consensus problems for a group of second-order multi-agent systems under directed communication topology. A class of distributed fixed-time consensus protocols are designed by using motion planning approaches and Pontryagins principle. The proposed protocol only requires relative information measurements at the sampling instants, without requiring information exchanges over the sampled interval. By using stability principle and the properties of stochastic matrixes, it is proved that distributed fixed-time consensus problem can be solved in the motion planning framework. Compared with the existing consensus algorithms, one of main contributions of this paper is that by using the proposed fixed-time control algorithms, the consensus control problems are solved over directed graphs and the fixed settling time can be off-line pre-specified according to task requirements. Further, when the frequency of the oscillators is zero, the proposed fixed-time control algorithms can also solve the consensus control problems for multiple double-integrator dynamics over directed graphs. Finally, a numerical example is also given to illustrate the effectiveness of the analytical results.