A Robust Adaptive Control Approach to Leader-Following Consensus of Multiple Uncertain Euler–Lagrange Systems Over Switching Networks

The leader-following consensus problem for multiple uncertain Euler–Lagrange (EL) systems has been extensively studied by two approaches: robust control approach and adaptive control approach. The adaptive control approach has the advantage that it does not require the bounds of unknown parameters be known but has the shortcoming that the control law is of high dimension as every unknown parameter has to be estimated by the local control law of every follower. On the other hand, the robust control has the advantage that every local control law is static but it needs to assume that the bounds of the uncertain parameters and the disturbances are known. Moreover, the validity of the existing robust control approaches relies on some restrictive assumptions on the communication networks and the dynamics of the EL systems. In this article, we consider the leader-following consensus problem for multiple uncertain EL systems where both the bounds of the uncertain parameters and the disturbances are unknown. We solve this problem by augmenting the robust control law with an adaptive control mechanism for estimating the unknown bound of all uncertain parameters and the unknown bound of all disturbances of each follower. As a result, regardless of the dimension of the uncertain parameters and the dimension of the disturbances of each follower, the dimension of each local control law of each follower in this article is only two, which is in contrast with the dimension of the adaptive control approach in the literature. Moreover, we consider jointly connected switching networks which can be disconnected at any time instant.