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.

Partial Higher-Order Specifications1

1992 ◽  
Vol 16 (2) ◽  
pp. 101-126
Author(s):  
Egidio Astesiano ◽  
Maura Cerioli
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Important Case ◽  
Deduction System ◽  
Closure Properties ◽  
Inference System ◽  
Conditional Specification ◽  
Necessary And Sufficient

In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

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 Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients

2007 ◽  
Vol 14 (1) ◽  
pp. 81-97
Author(s):  
Alberto Cialdea
Keyword(s):  
Elliptic Equation ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Complete System ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Polynomial Solutions ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
Completeness Theorems

Abstract Let {ω𝑘 } be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚 aα 𝐷 α 𝑢 = 0, aα being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.

scholarly journals Multi-robot formation control based on high-order bilateral consensus

2020 ◽  
Vol 53 (5-6) ◽  
pp. 983-993
Author(s):  
Dejian Liu ◽  
Chengguo Zong ◽  
Detang Wang ◽  
Wenbin Zhao ◽  
Yuehua Wang ◽  
...  
Keyword(s):  
Information Exchange ◽  
Formation Control ◽  
Sufficient Conditions ◽  
Higher Order ◽  
High Order ◽  
Third Order ◽  
Control Protocol ◽  
The Third ◽  
Multi Agent ◽  
Multi Robot

A high-order bilateral consensus robot formation control protocol for multi-agent systems is proposed in this paper. Considering the relationship between the state of the information exchange topology and derivatives, a third-order bilateral consistency protocol is presented and is extended it to a higher order bilateral consensus protocol. First, sufficient conditions for the third-order multi-agent system are given to achieve the bilateral consensus control protocol, and the system’s asymptotical stability is also achieved by adjusting the feedback system gain parameters. Then, by further studying the cohesive relationship between each state variable of the third-order protocol and the gauge transformation, the sufficient conditions of the higher order system are also provided. Finally, by applying the third-order control protocol to the control of multi-robot formation, the general control scheme of robot formation is given and the control of robot formation is successfully achieved.

scholarly journals Lagrangian for Circuits with Higher-Order Elements

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1059 ◽  
Author(s):  
Zdenek Biolek ◽  
Dalibor Biolek ◽  
Viera Biolkova
Keyword(s):  
Variational Principle ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Higher Order ◽  
The State ◽  
Even Order ◽  
Independent Variable ◽  
Necessary And Sufficient ◽  
Derivatives Of ◽  
State Functions

The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or −R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table.

scholarly journals Consensus Analysis for High-Order Multi-Agent Systems without or with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhengxin Wang ◽  
Yang Cao
Keyword(s):  
Partial Information ◽  
Sufficient Conditions ◽  
High Order ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Agent Systems ◽  
Multi Agent ◽  
Necessary And Sufficient

This paper studies the consensus problem for a high-order multi-agent systems without or with delays. Consensus protocols, which only depend on the own partial information of agents and partial relative information with its neighbors, are proposed for consensus and quasi-consensus, respectively. Firstly, some lemmas are presented, and then a necessary and sufficient condition for guaranteeing the consensus is established under the consensus protocol without delays. Furthermore, communication delays are considered. Some necessary and sufficient conditions for solving quasi-consensus problem with delays are obtained. Finally, some simulations are given to verify the 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.

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