Observer-Based Adaptive Time-Varying Formation-Containment Tracking for Multiagent System With Bounded Unknown Input

In this article, the time-varying formation (TVF)-containment tracking problem is investigated for linear multiagent systems (MASs), in which the input of tracking leader is unknown and bounded. A novel kind of adaptive discontinuous TVF-containment tracking protocol for linear MAS is proposed. Based on the Lyapunov stability theory, it is shown that under the appropriate assumptions the leaders can achieve an expected TVF and track the trajectory of the tracking leader, while the follower agents can move into the convex hull formed by leader agents. Furthermore, the continuous protocols are also presented to avoid undesirable chattering from the tracking leader’s nonzero input, under which the errors are uniformly ultimately bounded and the upper bound of errors can be made arbitrarily small. In the end, simulation example verifies the feasibility of the desired theoretical results.