Abstract

In this paper, the distributed containment control problem is studied for continuous-time fractional-order multi-agent systems. A distributed containment control protocol with nonlinear projection algorithm is designed for each follower. Besides, a novel approach is proposed to show the effectiveness of the proposed containment control protocol. The main idea is to obtain the L 1 interpolation approximation of the investigated system based on piecewise linear interpolation, and then by using the property of the convex hull and the Mittag-Leffler function, we demonstrate that by taking the distributed containment control protocol, all followers can converge to the convex hull spanned by multiple leaders asymptotically. Finally, a numerical simulation is implemented to illustrate the effectiveness of the obtained theoretical results.

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