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 High-Order Iterative Methods for the DMP Inverse

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Xiaoji Liu ◽  
Naping Cai
Keyword(s):  
Error Estimate ◽  
Iterative Methods ◽  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Sufficient Conditions For Convergence ◽  
Necessary And Sufficient ◽  
High Order Iterative Methods

We investigate two iterative methods for computing the DMP inverse. The necessary and sufficient conditions for convergence of our schemes are considered and the error estimate is also derived. Numerical examples are given to test the accuracy and effectiveness of our methods.

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 Switched Convergence of Second-Order Switched Homogeneous Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Carmen Pérez ◽  
Francisco Benítez
Keyword(s):  
Sufficient Conditions ◽  
Homogeneous System ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Initial Condition ◽  
Numerical Examples ◽  
Switching Law ◽  
Homogeneous Systems ◽  
Switched Convergence ◽  
Necessary And Sufficient

This paper studies the stabilization of second-order switched homogeneous systems. We present results that solve the problem of stabilizing a switched homogeneous system; that is, we establish necessary and sufficient conditions under which the stabilization is assured. Moreover, given an initial condition, our method determines if there exists a switching law under which the solution converges to the origin and, if there exists this switching law, how it is constructed. Finally, two numerical examples are presented in order to illustrate the results.

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.

The M/M/1 queue with mass exodus and mass arrivals when empty

1997 ◽  
Vol 34 (01) ◽  
pp. 192-207 ◽  
Author(s):  
Anyue Chen ◽  
Eric Renshaw
Keyword(s):  
Sufficient Conditions ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Positive Recurrence ◽  
Powerful Technique ◽  
Resolvent Approach ◽  
Necessary And Sufficient ◽  
Direct Attack

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

scholarly journals Positive 2D Discrete-Time Linear Lyapunov Systems

2009 ◽  
Vol 19 (1) ◽  
pp. 95-106 ◽  
Author(s):  
Przemysław Przyborowski ◽  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Positive 2D Discrete-Time Linear Lyapunov SystemsTwo models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

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