Abstract
This chapter extends the control protocol design and consensus analysis to the setting that there exist multiple leaders, which do not communicate with others. In this setting, the control target is to drive the follower into the convex hull spanned by the leaders.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
There is only one of such a component given that G has a directed spanning tree. It consists of the root node of G if G has only one root node, for which the leader-following framework applies and further \(\mathbf {L}_{11}=\mathbf {0}\).
- 2.
This can be deemed as a constraint on the unstable mode of \(\mathbf {A}\), which means that each isolated (i.e., uncoupled) agent cannot switch too fast [96].
- 3.
A directed graph G has a united directed spanning tree if for each of the followers, there exists at least one leader that has a directed path to the follower [99].
- 4.
The \(\bar{\delta }\)-digraph corresponding to \(\varPhi (t_1,t_0)\) refers to the \(\bar{\delta }\)-digraph associated to a Laplacian matrix constructed from \(\varPhi (t_1,t_0)\) by treating \(\varPhi (t_1,t_0)\) as an adjacency matrix neglecting its diagonal elements.
- 5.
For the definition of being strictly positive real of a state transition matrix, please refer to [26].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Qin, J., Ma, Q., Gao, H., Zheng, W.X., Kang, Y. (2022). Extensions to Containment Control. In: Consensus Over Switching Network Topology: Characterizing System Parameters and Joint Connectivity. Studies in Systems, Decision and Control, vol 393. Springer, Cham. https://doi.org/10.1007/978-3-030-85657-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-85657-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-85656-4
Online ISBN: 978-3-030-85657-1
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)