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Containment Control of Multi-Agent Systems with Dynamic Leaders Based on a -Type Approach
This paper studies the containment control problem of multi-agent systems
with multiple dynamic leaders in both the discrete-time domain and the
continuous-time domain. The leaders' motions are described by -order
polynomial trajectories. This setting makes practical sense because given some
critical points, the leaders' trajectories are usually planned by the
polynomial interpolations. In order to drive all followers into the convex hull
spanned by the leaders, a -type ( and are short for {\it
Proportion} and {\it Integration}, respectively; implies that the
algorithm includes high-order integral terms) containment algorithm is
proposed. It is theoretically proved that the -type containment algorithm
is able to solve the containment problem of multi-agent systems where the
followers are described by any order integral dynamics. Compared with the
previous results on the multi-agent systems with dynamic leaders, the
distinguished features of this paper are that: (1) the containment problem is
studied not only in the continuous-time domain but also in the discrete-time
domain while most existing results only work in the continuous-time domain; (2)
to deal with the leaders with the -order polynomial trajectories,
existing results require the follower's dynamics to be -order integral while
the followers considered in this paper can be described by any-order integral;
and (3) the "sign" function is not employed in the proposed algorithm, which
avoids the chattering phenomenon. Furthermore, in order to illustrate the
practical value of the proposed approach, an application, the containment
control of multiple mobile robots is studied. Finally, two simulation examples
are given to demonstrate the effectiveness of the proposed algorithm