Distributed fixed-time control under directed graph using input shaping

This paper presents novel fixed-time controllers for the distributed tracking of multi-agent systems with double-integrator dynamics based on the input shaping technique under directed graphs. It is assumed that there is no cycle in the directed graph with a globally reachable leader. Distributed fixed-time controllers are designed for cases with various initial conditions by placing input shapers in all communication edges in the graph. Numerical simulations and experimental studies are conducted to verify the effectiveness of the proposed controllers.