This paper is concerned with the finite-time containment control for a second-order nonlinear multi-agent system in the presence of external disturbances. First, two finite-time containment control protocols are skillfully developed, of which one is based on a terminal sliding mode and the other is based on a non-singular terminal sliding mode. Second, criteria for designing desired containment control protocols are derived such that the containment performance of the resulting closed-loop leader-following multi-agent system can be guaranteed within a finite time horizon. It is shown that the settling time of the closed-loop system convergence can be estimated under the proposed protocols. Furthermore, finite-time containment control in the scenario of general switching and directed topology is also addressed and the corresponding result is derived. Finally, three illustrative examples are given to verify the effectiveness of the proposed finite-time containment control method.
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