Finite-time formation control for second-order multi-agent systems

In this paper, a finite-time formation control problem is studied for second-order multi-agent systems. A control protocol is first constructed to achieve the consensus of the multi-agent systems in finite-time with the steady-state velocity being an arbitrary specific value. Then by introducing a virtual agent, called as pre-correction agent, the formation control protocol is designed, and the convergency of the control protocol is proved. Furthermore, a control protocol without velocity measurements is designed to achieve the finite-time formation with both the steady-state velocity and position being arbitrary specific values. In addition, since the obtained protocols include free communicate parameters, different performance can be achieved by assigning the free parameters. Finally, illustrative examples are solved, including an optimal formation problem with communicate parameters as selection variables, which illustrate the efficiency and potential engineering application of the proposed control methods.