Adaptive leader-follower control for nonlinear uncertain multi-agent systems with an uncertain leader and unknown tracking paths.

With unknown leader parameters and false or immeasurable tracking paths, the leader-follower tracking problem via adaptive control becomes more complex and challenging. Different from the existing work in the literature and in line with real-world applications, this challenging issue is solved in this paper for multi-agent networks with different kinds of unknown uncertainties in the followers such as partially known parameters, nonlinearities, external disturbances, communication weights, and sensor faults. The solution of this challenging issue is obtained in three steps. Firstly, the tracking path is estimated by designing distributed adaptive observers at all agents that have direct communication edges with the leader. Next, by designing local adaptive observers for all followers, the estimates of all followers' states can be obtained. Then, distributed adaptive controllers for all followers are designed using the estimated states of both followers and their neighbors in addition to the estimated tracking path. The tracking performances are provided via sufficient conditions for both the adaptive observers and the adaptive controllers. The proposed methods are evaluated through two examples that are commonly used in the literature. The obtained results prove the efficacy of the recommended adaptive approaches.