Leader-following consensus with connectivity preservation of uncertain Euler-lagrange multi-agent systems

The leader-following consensus problem for multiple Euler-lagrange systems has been extensively studied for various scenarios. Under the assumption that the communication graph is jointly connected, one of our recent papers gave the solution for the case where the leader system can generate a combination of arbitrary step signal, arbitrary ramp signal, and arbitrary sinusoidal signals. In practice, it is desirable to enable the control law the capability of maintaining the connectivity of the communication graph, thus achieving the leader-following consensus without assuming the connectivity of the communication graph. We call such a problem as leader-following consensus with connectivity preservation. By combining the adaptive control technique and potential function technique, we will show that such a problem is solvable. By employing different potential functions, our approach may also lead to the solution of such problems as flocking, and swarming.