Adaptive Cooperative Tracking and Parameter Estimation of an Uncertain Leader over General Directed Graphs

This paper studies the cooperative tracking problem of heterogeneous Euler-Lagrange systems with an uncertain leader. Different from most existing works, system dynamic knowledge of the leader node is unaccessible to any follower node in our paper. Distributed adaptive observers are designed for all follower nodes, simultaneously estimate the state and parameters of the leader node. The observer design does not rely on the frequency knowledge of the leader node, and the estimation errors are shown to converge to zero exponentially. Moreover, the results are applied to general directed graphs, where the symmetry of Laplacian matrix does not hold. This is due to two newly developed Lyapunov equations, which solely depend on communication network topologies. Interestingly, using these Lyapunov equations, many results of multi-agent systems over undirected graphs can be extended to general directed graphs. Finally, this paper also advances the knowledge base of adaptive control systems by providing a main tool in the analysis of parameter convergence for adaptive observers.