Adaptive consensus tracking of linear multi-agent systems with matching nonlinear uncertainties

This paper addresses a leader-following problem for a class of multi-agent systems modeled as general linear systems with matching nonlinear uncertainties under undirected communication topology. The state of the leader is only available to a subset of the followers and the input of the leader is unknown to any of the follower. By parameterizing the unknown dynamics and the input of the leader with some basis functions, we design adaptive control laws for each follower to estimate the parameters and ensure consensus tracking. Parameter convergence is also guaranteed when the regressor matrix satisfies the persistently excitation (PE) condition. Moreover, due to the adaptive tuning of the control gains, no information about the structure of the communication topology, such as the eigenvalues of the Laplacian matrix, is needed in the control design process which makes the controller easier to implement in practice. A simulation example is provided to illustrate the theoretical results.