Double integrator consensus in fixed time: A novel distributed algorithm for generalised networks

A novel fixed-time consensus algorithm is presented for a multi-agent system comprising of double-integrator based agents. The proposed consensus algorithm ensures that agents' states converge to that of a maneuvering target in fixed-time. Each state of the agents (position, velocity, and acceleration) is exchanged over separate communication network which are assumed to be undirected. It is assumed that there exist one agent receiving target's information (position, velocity, and acceleration). It is not necessary that agent having target's position be the same which gets target's velocity and/or acceleration. However, the target cannot access the information of the agents. Lyapunov stability theory is used to establish the global stability of the proposed algorithm. Fixed time convergence of the proposed algorithm is established by using the concept of bi-limit homogeneity of a vector field. We also show that the proposed fixed-time algorithm can be extended directly to design a multi-agent formation control law. Effectiveness of the proposed consensus algorithm is presented by numerical results.