scholarly journals Stability Switches of Arbitrary High-Order Consensus in Multiagent Networks with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Bo Yang
Keyword(s):  
Time Delays ◽  
Cooperative Control ◽  
High Order ◽  
Frequency Domain Method ◽  
Stability Switches ◽  
Third Order ◽  
Consensus Algorithms ◽  
Communication Time ◽  
Multiagent Networks ◽  
The Stability

High-order consensus seeking, in which individual high-order dynamic agents share a consistent view of the objectives and the world in a distributed manner, finds its potential broad applications in the field of cooperative control. This paper presents stability switches analysis of arbitrary high-order consensus in multiagent networks with time delays. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology, communication time-delays, and feedback gains. Particularly, our results provide a general and a fairly precise notion of how increasing communication time-delay causes the stability switches of consensus. Furthermore, under communication constraints, the stability and robustness problems of consensus algorithms up to third order are discussed in details to illustrate our central results. Numerical examples and simulation results for fourth-order consensus are provided to demonstrate the effectiveness of our theoretical results.

scholarly journals Heterogeneous and Competitive Multiagent Networks: Couple-Group Consensus with Communication or Input Time Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Nanxiang Yu ◽  
Lianghao Ji ◽  
Fengmin Yu
Keyword(s):  
Upper Bound ◽  
Time Delays ◽  
Matrix Theory ◽  
Cooperative Networks ◽  
Frequency Domain Method ◽  
Control Parameters ◽  
Group Consensus ◽  
Communication Time ◽  
Multiagent Networks ◽  
Input Time

This paper discusses the couple-group consensus problems for a class of heterogeneous multiagent networks including the following two cases: with communication and input time delays, respectively. Different from the related cooperative networks, two novel delayed group consensus protocols are designed based on the competitive relationship between the agents. Furthermore, we absolutely relax the in-degree balance and other restrictive preconditions which existed in the relevant works. Some sufficient algebraic criteria for the achievement of couple-group consensus and the upper bound of the input time delays are technically obtained via the frequency domain method and matrix theory, respectively. The results show that the achievement of the couple-group consensus depends on the second-order agents’ in-degree and the control parameters of the systems, whereas it is independent of the communication time delays. Meanwhile, the upper bound of the input time delay is determined by the control parameters and the in-degree of the first-order agents. Finally, the validity of the proposed results is verified by several simulated examples.

High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems

2006 ◽  
Vol 129 (5) ◽  
pp. 678-688 ◽  
Author(s):  
Wei Ren ◽  
Kevin L. Moore ◽  
Yangquan Chen
Keyword(s):  
Cooperative Control ◽  
Sufficient Conditions ◽  
Higher Order ◽  
High Order ◽  
Order Model ◽  
Model Reference ◽  
Consensus Algorithms ◽  
Necessary And Sufficient ◽  
Control Application ◽  
Information Variable

In this paper we study ℓth-order (ℓ⩾3) consensus algorithms, which generalize the existing first-order and second-order consensus algorithms in the literature. We show necessary and sufficient conditions under which each information variable and its higher-order derivatives converge to common values. We also present the idea of higher-order consensus with a leader and introduce the concept of an ℓth-order model-reference consensus problem, where each information variable and its high-order derivatives not only reach consensus, but also converge to the solution of a prescribed dynamic model. The effectiveness of these algorithms is demonstrated through simulations and a multivehicle cooperative control application, which mimics a flocking behavior in birds.

scholarly journals Resilient cooperative control of AC microgrids considering relative state‐dependent noises and communication time‐delays

2020 ◽  
Vol 14 (8) ◽  
pp. 1321-1331 ◽  
Author(s):  
Amir Afshari ◽  
Mehdi Karrari ◽  
Hamid Reza Baghaee ◽  
Gevork B. Gharehpetian
Keyword(s):  
Time Delays ◽  
Cooperative Control ◽  
Relative State ◽  
State Dependent ◽  
Communication Time

scholarly journals Consensus Conditions for High-Order Multiagent Systems with Nonuniform Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mengji Shi ◽  
Kaiyu Qin ◽  
Ping Li ◽  
Jun Liu
Keyword(s):  
Multiagent Systems ◽  
Time Delays ◽  
Second Order ◽  
High Order ◽  
Sixth Order ◽  
Multiple Time ◽  
State Variables ◽  
Third Order ◽  
First Order ◽  
The Third

Consensus of first-order and second-order multiagent systems has been wildly studied. However, the convergence of high-order (especially the third-order to the sixth-order) state variables is also ubiquitous in various fields. The paper handles consensus problems of high-order multiagent systems in the presence of multiple time delays. Obtained by a novel frequency domain approach which properly resolves the challenges associated with nonuniform time delays, the consensus conditions for the first-order and second-order systems are proven to be nonconservative, and those for the third-order to the sixth-order systems are provided in the form of simple inequalities. The method revealed in this article is applicable to arbitrary-order systems, and the results are less conservative than those based on Lyapunov approaches, because it roots in sufficient and necessary criteria of stabilities. Simulations are carried out to validate the theoretical results.

scholarly journals Dynamic Models of Pollution Penalties and Rewards with Time Delays

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Akio Matsumoto ◽  
Ferenc Szidarovszky
Keyword(s):  
Dynamic Systems ◽  
Time Delays ◽  
Dynamic Models ◽  
Nonpoint Pollution ◽  
Asymptotically Stable ◽  
Total Emission ◽  
Stability Switches ◽  
Delay Models ◽  
Price Functions ◽  
The Stability

In cases of nonpoint pollution sources, the regulator can observe the total emission but unable to distinguish between the firms. The regulator then selects an environmental standard. If the total emission level is higher than the standard, then the firms are uniformly punished, and if lower, then uniformly awarded. This environmental regulation is added to n-firm dynamic oligopolies, and the asymptotical behavior of the corresponding dynamic systems is examined. Two particular models are considered with linear and hyperbolic price functions. Without delays, the equilibrium is always (locally) asymptotically stable. It is shown how the stability can be lost if time delays are introduced in the output quantities of the competitors as well as in the firms’ own output levels. Complete stability analysis is presented for the resulting one- and two-delay models including the derivations of stability thresholds, stability switching curves, and directions of the stability switches.

scholarly journals Adaptive cooperative control for high-order nonlinear multiagent time-delay systems using barrier functions

2020 ◽  
Vol 53 (2) ◽  
pp. 4044-4051
Author(s):  
Jiacheng Song ◽  
Yongfeng Ju ◽  
Maode Yan ◽  
Panpan Yang ◽  
Lei Zuo
Keyword(s):  
Time Delay ◽  
Cooperative Control ◽  
High Order ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Barrier Functions

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability
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