Abstract
This paper proposes a fully distributed control protocol that achieves time-varying group formation tracking for linear multiagent systems connected via a directed graph. The group formation tracking often leads to sub-formations especially when the leaders are placed far apart or they have separate control inputs. In the proposed approach, the followers are distributed into several subgroups and each subgroup attains the predefined subformation along with encompassing the leaders. Each subgroup can be assigned multiple leaders, contrary to the single-leader case considered in most existing literature, which makes the current problem nontrivial. When multiple leaders exist in a subgroup, the subformation attained by that subgroup keeps tracking a convex combination of the states of the leaders. A distributed adaptive control protocol has been introduced in this paper which uses only relative state information and, thus, avoids direct computation of the graph Laplacian matrix. Due to the virtue of this, the proposed scheme remains effective even when some of the agents get disconnected from the network due to sudden communication failure. An algorithm is provided to outline the steps to design the control law to attain time-varying group formation tracking with multiple leaders. Toward the end, a case study on multitarget surveillance operation is taken up to show an important application of the proposed adaptive control technique.
Highlights
O VER THE past two decades, cooperative as well as distributed control of multiagent systems (MAS) have drawn significant attention of researchers from multiple disciplines of engineering and mathematics because of its wide applications in multirobot cooperation [1]–[3]; distributed sensor networks [4], Manuscript received November 9, 2018; revised November 13, 2018 and February 18, 2019; accepted April 7, 2019
A distributed, adaptive, and nonlinear control protocol has been introduced in this paper to achieve time-varying group formation tracking (TGFT) for linear MAS having a directed communication topology
The control objectives include subformation and tracking, that is, the followers are divided into several subgroups depending on the positions of the leaders and each subgroup reaches individual subformations while tracking the positions of the respective leaders attached to that subgroup
Summary
O VER THE past two decades, cooperative as well as distributed control of multiagent systems (MAS) have drawn significant attention of researchers from multiple disciplines of engineering and mathematics because of its wide applications in multirobot cooperation [1]–[3]; distributed sensor networks [4], Manuscript received November 9, 2018; revised November 13, 2018 and February 18, 2019; accepted April 7, 2019. To circumvent direct computation of the eigenvalues of the graph Laplacian matrix, distributed control protocols are being widely used which depend only on the local information, that is, information from the neighbors. In this context, the work of [22] should be highlighted which proposes a fully distributed control protocol for MAS with an undirected graph. The contributions of this paper can be summarized as follows: 1) The TGFT problem for MAS with a directed communication graph is explored, where each subgroup is able to reach a desired subformation surrounding the respective leaders. M -matrix if all of its off-diagonal elements are nonpositive and all eigenvalues of A have positive real parts [21]
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