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A faster containment algorithm is also presented when the fibers of I are prime.
Under the containment algorithm (3), system (1) can solve the containment control problem in the mean square sense.
Under Markov switching topologies and the containment algorithm (17), system (15) can solve the mean square containment control problem.
The containment algorithm is proposed as follows: u_{i}(t)=sum_{jin Fcup L}a_{ij} bigl(x_{j}(t -x_{i}(t -x_{i}sum _{jin Fcup L}a_{ij}bigl(v_{j}(t bigri}(t) bigr), (17) where F and L are the same as those in Theorem 1.
The leader's dynamic is denoted as follows: begin{aligned} &x_{i} k+1) = x_{i} k)+v_{i} k T, &v_{i} k+1) = v_{i} k),quad i=M+1,ldots, N. end{aligned} (2) The containment algorithm is proposed as follows: u_{i} k)=sum_{jin Fcup L} a_{ij}bigl(x_{j} k -x_{i} k bigr),quad i=1, ldots, M, (3) where (F={1,ldots, M} k -x_{i} k bigrt of followers and (L={M+1,quads, N}) i=1the set of ldotsrs.
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Some of that was through smart detection and containment algorithms.
In this paper, containment algorithms for continuous-time and discrete-time multi-agent systems are given, respectively.
In [1], dynamic containment algorithms based on observers for the high-order continuous-time multi-agent systems were proposed under the fixed topology.
In [5], containment algorithms based on the sampled data for the second-order multi-agent systems were given, where the necessary and sufficient conditions of multi-agent systems were derived.
In the fixed directed topology, under the algorithm (3), the containment control problem for system (1) can be solved, that is, follower (1) is driven into the leaders' sets (2).
Briefly, the algorithm builds a containment tree and then performs a breadth-first traversal of the tree, retaining all top-level ESTs plus a number of ESTs from the next-highest levels based on configuration parameters.
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