scholarly journals Containment Control of First-Order Multi-Agent Systems under PI Coordination Protocol

Algorithms ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 209
Author(s):  
Mingyang Huang ◽  
Chenglin Liu ◽  
Liang Shan
Keyword(s):  
Convex Hull ◽  
Frequency Domain Analysis ◽  
Convergence Condition ◽  
Multi Agent Systems ◽  
Containment Control ◽  
First Order ◽  
Leaders And Followers ◽  
Multi Agent ◽  
Multiple Leaders ◽  
Theoretical Results

This paper investigates the containment control problem of discrete-time first-order multi-agent system composed of multiple leaders and followers, and we propose a proportional-integral (PI) coordination control protocol. Assume that each follower has a directed path to one leader, and we consider several cases according to different topologies composed of the followers. Under the general directed topology that has a spanning tree, the frequency-domain analysis method is used to obtain the sufficient convergence condition for the followers achieving the containment-rendezvous that all the followers reach an agreement value in the convex hull formed by the leaders. Specially, a less conservative sufficient condition is obtained for the followers under symmetric and connected topology. Furthermore, it is proved that our proposed protocol drives the followers with unconnected topology to converge to the convex hull of the leaders. Numerical examples show the correctness of the theoretical results.

Formation-containment control of sampled-data second-order multi-agent systems with sampling delay

2018 ◽  
Vol 40 (16) ◽  
pp. 4369-4381 ◽  
Author(s):  
Baojie Zheng ◽  
Xiaowu Mu
Keyword(s):  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Control Problems ◽  
Sampled Data ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Multi Agent ◽  
Theoretical Results

The formation-containment control problems of sampled-data second-order multi-agent systems with sampling delay are studied. In this paper, we assume that there exist interactions among leaders and that the leader’s neighbours are only leaders. Firstly, two different control protocols with sampling delay are presented for followers and leaders, respectively. Then, by utilizing the algebraic graph theory and matrix theory, several sufficient conditions are obtained to ensure that the leaders achieve a desired formation and that the states of the followers converge to the convex hull formed by the states of the leaders, i.e. the multi-agent systems achieve formation containment. Furthermore, an explicit expression of the formation position function is derived for each leader. An algorithm is provided to design the gain parameters in the protocols. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.

Schooling for multi-agent systems via impulsive containment control algorithms with quantized information

2018 ◽  
Vol 41 (3) ◽  
pp. 828-841 ◽  
Author(s):  
Hong-Xiao Zhang ◽  
Li Ding ◽  
Zhi-Wei Liu
Keyword(s):  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Control Algorithms ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Eigenvalues Of The Laplacian ◽  
Multi Agent ◽  
Necessary And Sufficient ◽  
Theoretical Results

In the paper, schooling problems based on containment control in multi-agent systems that have static or dynamic leaders under directed and undirected communication topologies are investigated. We propose a periodic impulsive containment control algorithm to realize schooling in multi-agent systems. Both ideal and quantized relative state measurements are considered under this framework. Some necessary and sufficient conditions, which depend on the eigenvalues of the Laplacian matrix that is associated with the communication graph, the impulsive period as well as the gain parameters, are obtained to realize the containment control of schooling. Finally, some numerical simulations are illustrated to verify the theoretical results.

Fixed-time consensus of first-order multi-agent systems over signed directed graphs

2021 ◽  
pp. 014233122110019
Author(s):  
Zhentao Li ◽  
Zhengxin Wang ◽  
Yuanzhen Feng
Keyword(s):  
Directed Graphs ◽  
Fixed Time ◽  
Control Parameters ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
First Order ◽  
Strongly Connected ◽  
Multi Agent ◽  
Theoretical Results

This paper studies the fixed-time consensus problems of first-order multi-agent systems over signed directed graphs. Fixed-time consensus protocols are designed for first-order multi-agent systems without/with disturbances and first-order nonlinear multi-agent systems with disturbances, respectively. With proposed protocols, it is proved that multi-agent systems with strongly connected topologies will achieve consensus in a fixed time if the control parameters satisfy certain conditions. Finally, simulation examples are provided to verify the effectiveness of the theoretical results.

Iterative learning control for nonlinear heterogeneous multi-agent systems with multiple leaders

2020 ◽  
pp. 014233122094163
Author(s):  
Qin Fu
Keyword(s):  
Control Problem ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Time Interval ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Multi Agent ◽  
Multiple Leaders

This article investigates the iterative learning control problem for a class of nonlinear heterogeneous multi-agent systems. The main contribution of this article is to apply iterative learning control algorithm to the multi-agent systems with multiple leaders, and solve the containment control problem of multi-agent systems in the sense of iterative learning control stability. Based on the framework of communication topologies, distributed iterative learning controllers are designed. And when the iterative learning control laws are applied to the systems, the containment errors between the followers’ states and the convex hull spanned by the leaders’ states over a finite-time interval are bounded, and furthermore, the containment errors can converge to zero as the iteration index approaches to infinity in the absence of initial errors. A simulation example is finally constructed to verify the effectiveness of the theoretical method.

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