Controllability of Multiagent Systems with a Directed Tree

This paper addresses the controllability problem of multiagent systems with a directed tree based on the classic agreement protocol, in which the information communication topologies being a directed tree and containing a directed tree are both investigated. Different from the literatures, a new method, the star transform, is proposed to study the controllability of multiagent systems with directed topology. Some sufficient and necessary conditions are given for the controllability of such multiagent system. Numerical examples and simulations are proposed to illustrate the theoretical results.

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Controllability of Second-Order Multiagent Systems with Multiple Leaders and General Dynamics

Mathematical Problems in Engineering ◽

10.1155/2013/587569 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 8

Author(s):

Bo Liu ◽

Hongke Feng ◽

Li Wang ◽

Rong Li ◽

Junyan Yu ◽

...

Keyword(s):

Multiagent Systems ◽

Multiagent System ◽

Necessary Conditions ◽

Second Order ◽

The Other ◽

Numerical Examples ◽

General Dynamics ◽

Sufficient And Necessary Conditions ◽

Multiple Leaders ◽

Theoretical Results

This paper proposes a new second-order discrete-time multiagent model and addresses the controllability of second-order multiagent system with multiple leaders and general dynamics. The leaders play an important role in governing the other member agents to achieve any desired configuration. Some sufficient and necessary conditions are given for the controllability of the second-order multiagent system. Moreover, the speed controllability of the second-order multiagent system with general dynamics is discussed. Particularly, it is shown that the controllability of the whole system relies on the number of leaders and the connectivity between the leaders and the members. Numerical examples illustrate the theoretical results.

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Controllability of conformable differential systems

Nonlinear Analysis Modelling and Control ◽

10.15388/namc.2020.25.18135 ◽

2020 ◽

Vol 25 (4) ◽

Cited By ~ 1

Author(s):

Xiaowen Wang ◽

JinRong Wang ◽

Michal Fečkan

Keyword(s):

Fixed Point ◽

Necessary Conditions ◽

Complete Controllability ◽

Krasnoselskii’S Fixed Point Theorem ◽

Differential Systems ◽

Numerical Examples ◽

Controllability Of Systems ◽

Sufficient And Necessary Conditions ◽

Theoretical Results ◽

Controllability Result

This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.

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A JOINT EOQ MODEL FOR SUPPLIER AND RETAILER WITH DETERIORATING ITEMS

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595904000114 ◽

2004 ◽

Vol 21 (02) ◽

pp. 163-178 ◽

Cited By ~ 8

Author(s):

CHINHO LIN ◽

YIHSU LIN

Keyword(s):

Necessary Conditions ◽

Optimal Solution ◽

Planning Horizon ◽

Solution Procedure ◽

Sensitivity Analyses ◽

Mutual Cooperation ◽

Total Cost ◽

Numerical Examples ◽

Eoq Model ◽

Sufficient And Necessary Conditions

The paper studies the joint inventory model between supplier and retailer relying on mutual cooperation. Unlike other studies, the deteriorated rate and partial back-ordering are consistent with assumptions for dealing with more general cases. Since it is difficult to solve this problem directly, we derived the sufficient and necessary conditions in the planning horizon, and proposed a procedure to find the optimal solution. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, and that they also reduce the total cost.

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Linear θ-Method and Compact θ-Method for Generalised Reaction-Diffusion Equation with Delay

International Journal of Differential Equations ◽

10.1155/2018/6402576 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13

Author(s):

Fengyan Wu ◽

Qiong Wang ◽

Xiujun Cheng ◽

Xiaoli Chen

Keyword(s):

Diffusion Equation ◽

Necessary Conditions ◽

Reaction Diffusion ◽

Reaction Diffusion Equation ◽

Stability And Convergence ◽

Asymptotically Stable ◽

Sufficient And Necessary Conditions ◽

Equation Solvability ◽

Equation With Delay ◽

Theoretical Results

This paper is concerned with the analysis of the linear θ-method and compact θ-method for solving delay reaction-diffusion equation. Solvability, consistence, stability, and convergence of the two methods are studied. When θ∈[0,1/2), sufficient and necessary conditions are given to show that the two methods are asymptotically stable. When θ∈[1/2,1], the two methods are proven to be unconditionally asymptotically stable. Finally, several examples are carried out to confirm the theoretical results.

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On the Perron-Frobenius Theory of Mv-matrices and equivalent properties to eventually exponentially nonnegative matrices

Electronic Journal of Linear Algebra ◽

10.13001/ela.2019.5241 ◽

2019 ◽

Vol 35 ◽

pp. 424-440

Author(s):

Thaniporn Chaysri ◽

Dimitrios Noutsos

Keyword(s):

Necessary Conditions ◽

Nonnegative Matrix ◽

Nonnegative Matrices ◽

Numerical Examples ◽

Generalized Eigenvectors ◽

Sufficient And Necessary Conditions ◽

Left And Right ◽

Equivalent Properties

Mv−matrix is a matrix of the form A = sI −B, where 0 ≤ ρ(B) ≤ s and B is an eventually nonnegative matrix. In this paper, Mv−matrices concerning the Perron-Frobenius theory are studied. Specifically, sufficient and necessary conditions for an Mv−matrix to have positive left and right eigenvectors corresponding to its eigenvalue with smallest real part without considering or not if index0B ≤ 1 are stated and proven. Moreover, analogous conditions for eventually nonnegative matrices or Mv−matrices to have all the non Perron eigenvectors or generalized eigenvectors not being nonnegative are studied. Then, equivalent properties of eventually exponentially nonnegative matrices and Mv−matrices are presented. Various numerical examples are given to support our theoretical findings.

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Consensus of Delayed Fractional-Order Multiagent Systems Based on State-Derivative Feedback

Complexity ◽

10.1155/2018/8789632 ◽

2018 ◽

Vol 2018 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

Jun Liu ◽

Kaiyu Qin ◽

Wei Chen ◽

Ping Li

Keyword(s):

Graph Theory ◽

Multiagent Systems ◽

Fractional Order ◽

Time Delays ◽

Multiagent System ◽

Frequency Domain Analysis ◽

Consensus Control ◽

Control Protocol ◽

Analysis Theory ◽

Theoretical Results

A state-derivative feedback (SDF) is added into the designed control protocol in the existing paper to enhance the robustness of a fractional-order multiagent system (FMS) against nonuniform time delays in this paper. By applying the graph theory and the frequency-domain analysis theory, consensus conditions are derived to make the delayed FMS based on state-derivative feedback reach consensus. Compared with the consensus control protocol designed in the existing paper, the proposed SDF control protocol with nonuniform time delays can make the FMS with SDF and nonuniform time delays tolerate longer time delays, which means that the convergence speed of states of the delayed FMS with SDF is accelerated indirectly. Finally, the corresponding results of simulation are given to verify the feasibility of our theoretical results.

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Collective Coordination of High-Order Dynamic Multiagent Systems Guided by Multiple Leaders

Mathematical Problems in Engineering ◽

10.1155/2011/791052 ◽

2011 ◽

Vol 2011 ◽

pp. 1-11

Author(s):

Xin-Lei Feng ◽

Ting-Zhu Huang ◽

Jin-Liang Shao

Keyword(s):

Multiagent Systems ◽

Sufficient Conditions ◽

Second Order ◽

High Order ◽

Necessary And Sufficient Conditions ◽

Numerical Examples ◽

Necessary And Sufficient ◽

Multiple Leaders ◽

Theoretical Results

For second-order and high-order dynamic multiagent systems with multiple leaders, the coordination schemes that all the follower agents flock to the polytope region formed by multiple leaders are considered. Necessary and sufficient conditions which the follower agents can enter the polytope region by the leaders are obtained. Finally, numerical examples are given to illustrate our theoretical results.

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LQR Based Optimal Topology of Hybrid-Weighted Multiagent Systems

Mathematical Problems in Engineering ◽

10.1155/2018/5269542 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14 ◽

Cited By ~ 3

Author(s):

Shuai Liu ◽

Zhijian Ji ◽

Haisheng Yu ◽

Ting Hou

Keyword(s):

Multiagent Systems ◽

Composite Structure ◽

Information Exchange ◽

Multiagent System ◽

Linear Quadratic Regulator ◽

Optimal Topology ◽

Information Communication ◽

Linear Quadratic ◽

Control Cost ◽

First Order

In this paper, the optimal topology structure is studied for hybrid-weighted leader-follower multiagent systems (MASs). The results are developed by taking advantage of linear quadratic regulator (LQR) theory. We show that the multiagent star composite structure is the optimal topology which can enable the MAS to achieve the bipartite consensus. In particular, we prove that the optimal topology corresponding to the multiagent system with the first-order static leader and the second-order dynamic leader is, respectively, a hybrid-weighted star composite structure and an unevenly hybrid-weighted star composite structure. The results of the paper indicate that, in addition to the necessary information communication between leader and followers, the information exchange among followers increases the control cost of the system.

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A DYNAMICAL MODEL FOR THE PROCESS OF SHARING

Advances in Complex Systems ◽

10.1142/s0219525918500169 ◽

2018 ◽

Vol 21 (06n07) ◽

pp. 1850016 ◽

Cited By ~ 2

Author(s):

ULRICH KRAUSE

Keyword(s):

Multiagent Systems ◽

Necessary Conditions ◽

Opinion Dynamics ◽

Ring Structure ◽

Dynamical Model ◽

Equal Distribution ◽

Sufficient And Necessary Conditions ◽

Special Case

The paper introduces a general sharing structure and presents sufficient and necessary conditions for the agents to approach by the dynamics of sharing an equal distribution of assets. For the special case of a ring structure with a uniform sharing rate, robustness is analyzed in case the rate does change during the process of sharing. The search for an equal distribution is similar to that for consensus in opinion dynamics and multiagent systems as a result of which tools from the latter are used in proving the results.

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On the Observability of Leader-Based Multiagent Systems with Fixed Topology

Complexity ◽

10.1155/2019/9487574 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Bo Liu ◽

Ningsheng Xu ◽

Housheng Su ◽

Licheng Wu ◽

Jiahui Bai

Keyword(s):

Multiagent Systems ◽

Second Order ◽

High Order ◽

Numerical Examples ◽

First Order ◽

Leader Following ◽

Fixed Topology ◽

Agreement Protocols ◽

Theoretical Results ◽

Double Integrator

This paper investigates the observability of first-order, second-order, and high-order leader-based multiagent systems (MASs) with fixed topology, respectively. Some new algebraic and graphical characterizations of the observability for the first-order MASs are established based on agreement protocols. Moreover, under the same leader-following framework with the predefined topology and leader assignment, the observability conditions for systems of double-integrator and high-integrator agents are also obtained. Finally, the effectiveness of the theoretical results is verified by numerical examples and simulations.

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