Containment Control of Multi-Agent Systems with Dynamic Leaders Based on a $PI^n$-Type Approach

摘要

This paper studies the containment control problem of multi-agent systemswith multiple dynamic leaders in both the discrete-time domain and thecontinuous-time domain. The leaders' motions are described by $(n-1)$-orderpolynomial trajectories. This setting makes practical sense because given somecritical points, the leaders' trajectories are usually planned by thepolynomial interpolations. In order to drive all followers into the convex hullspanned by the leaders, a $PI^n$-type ($P$ and $I$ are short for {\itProportion} and {\it Integration}, respectively; $I^n$ implies that thealgorithm includes high-order integral terms) containment algorithm isproposed. It is theoretically proved that the $PI^n$-type containment algorithmis able to solve the containment problem of multi-agent systems where thefollowers are described by any order integral dynamics. Compared with theprevious results on the multi-agent systems with dynamic leaders, thedistinguished features of this paper are that: (1) the containment problem isstudied not only in the continuous-time domain but also in the discrete-timedomain while most existing results only work in the continuous-time domain; (2)to deal with the leaders with the $(n-1)$-order polynomial trajectories,existing results require the follower's dynamics to be $n$-order integral whilethe followers considered in this paper can be described by any-order integral;and (3) the "sign" function is not employed in the proposed algorithm, whichavoids the chattering phenomenon. Furthermore, in order to illustrate thepractical value of the proposed approach, an application, the containmentcontrol of multiple mobile robots is studied. Finally, two simulation examplesare given to demonstrate the effectiveness of the proposed algorithm.