scholarly journals Cucker-Smale Flocking with Bounded Cohesive and Repulsive Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Qiang Song ◽  
Fang Liu ◽  
Jinde Cao ◽  
Jianlong Qiu
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Initial Energy ◽  
Second Order ◽  
Initial State ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Two Agents ◽  
Repulsive Forces

This paper proposes two Cucker-Smale-type flocking models by introducing both cohesive and repulsive forces to second-order multiagent systems. Under some mild conditions on the initial state of the flocking system, it is shown that the velocity consensus of the agents can be reached independent of the parameter which describes the decay of communication rates. In particular, the collision between any two agents can always be avoided by designing an appropriate bounded repulsive function based on the initial energy of the flock. Numerical examples are given to demonstrate the effectiveness of the theoretical analysis.

On the Convexity Correction Approximation in Pricing Volatility Swaps and VIX Futures

2018 ◽  
Vol 14 (03) ◽  
pp. 383-401
Author(s):  
Song-Ping Zhu ◽  
Guang-Hua Lian
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Second Order ◽  
Approximation Technique ◽  
Third Order ◽  
Numerical Examples ◽  
Taylor Expansions ◽  
Vix Futures ◽  
Validity Condition

Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second-order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

scholarly journals Second-Order Consensus in Multiagent Systems via Nonlinear Protocol

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Huan Pan ◽  
Xiaohong Nian ◽  
Ling Guo
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Invariance Principle ◽  
Lyapunov Functions ◽  
Multiagent System ◽  
Second Order ◽  
General Linear ◽  
Reference Velocity ◽  
Communication Topology ◽  
Lasalle's Invariance Principle

This paper focuses on theoretical analysis of second-order consensus in multiagent system. As an extension of the general linear protocol, a nonlinear protocol is designed for multiagent system with undirected communication topology. The nonlinear protocol is also applied to achieve reference velocity consensus. Through choosing the appropriate Lyapunov functions and using LaSalle’s invariance principle, some consensus conditions are derived. Simulation examples are provided to demonstrate the effectiveness of the proposed results.

scholarly journals Multiconsensus of Second-Order Multiagent Systems with Input Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Chen ◽  
Ming Chi ◽  
Zhi-Hong Guan ◽  
Rui-Quan Liao ◽  
Ding-Xue Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Upper Bound ◽  
Multiagent System ◽  
Second Order ◽  
Matrix Analysis ◽  
Simulation Results ◽  
Input Delays ◽  
Double Integrator

The multiconsensus problem of double-integrator dynamic multiagent systems has been investigated. Firstly, the dynamic multiconsensus, the static multiconsensus, and the periodic multiconsensus are considered as three cases of multiconsensus, respectively, in which the final multiconsensus convergence states are established by using matrix analysis. Secondly, as for the multiagent system with input delays, the maximal allowable upper bound of the delays is obtained by employing Hopf bifurcation of delayed networks theory. Finally, simulation results are presented to verify the theoretical analysis.

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

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.

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

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
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.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
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.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

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