Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events

By Ming Cao, A. Stephen Morse, B.D.O. Anderson. SIAM Journal of Control and Optimization, 2008

673 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/c8cb556b5cb996e9bab3745aa889c4b4608faba9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Guanrong Chen
2. Wenwu Yu
3. Wei Ren
4. Yongcan Cao
5. Francesco Bullo
6. Jinde Cao
7. Ming Cao
8. Z. Duan

In Mechanical Engineering

1. Francesco Bullo
2. Ming Cao
3. Guanrong Chen
4. Jing Zhou
5. Wenwu Yu
6. Jorge Cortés
7. Wei Ren
8. David Angeli

Citations in the corpus

• Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems (2011, background): “Most existing reports on the consensus problem focus on the case where agents are governed by first-order dynamics [4], [13], [18], [23], [24] or second-order dynamics [9], [10], [21].”
• Distributed Control of Robotic Networks (2009, background): “, 2006; Zhu and Mart́ınez, 2008a), characterization of convergence rates and time complexity (Landau and Odlyzko, 1981; Olshevsky and Tsitsiklis, 2009; Cao et al., 2008; Carli et al., 2008).”
• Consensus in Directed Networks of Agents With Nonlinear Dynamics (2011, background): “A broader class of directed graphs that may lead to consensus are those that contain spanning trees [8], [11], which are also called rooted graphs [9], [12].”
• A survey of distributed optimization (2019, methodology): “…approach for convergence analysis is to use the augmented graph idea originated from Tsitsiklis (1984) , which has also been used in the literature on distributed consensus ( Cao, Morse, & Anderson, 2008; Charalambous et al., 2015; Hadjicostis & Charalambous, 2014; Nedi ´c & Ozdaglar, 2010 ).”
• Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems (2010, background): “…that consensus in a network with a dynamically changing topology can be reached if and only if the time-varying network topology contains a spanning tree frequently enough as the network evolves with time (Cao, Morse, & Anderson, 2008; Jadbabaie et al., 2003; Olfati-Saber, 2004; Ren & Beard, 2005).”
• Global analysis of multi-agent systems based on Vicsek’s model (2007, background): “¥ (Lemma 4 can be proved based on the existing results in [14]) Write the matrix C(t) as C(t) = C(t)+∆C(t).”
• Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization (2015, background): “of this convex hull [5], [6] or relevant results on convergence of infinite products of stochastic matrices [1], [2], [7], stability properties of contracting iterations were examined intensively with special attention on the effect of time-varying interaction topologies.”
• Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees (2006, methodology): “Taking into account the fact that the coefficients are greater or equal to min{1/3, 2/3− ε, ε} = ε, methods in [9, 8, 29] yield an upper estimate of ρ equal to 1− ε(2), or even 1− ε ≥ 2/3 (taking into account the fact that the system under study is neighbor shared [9, 8] and adapting [9, Lemma 2 and”
• Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities (2010, background): “Based on the algebraic graph theory [27,28], it has been shown that network connectivity is the key in reaching consensus [1,2,4,5,7,8].”
• Asynchronous Consensus Protocols Using Nonlinear Paracontractions Theory (2008, methodology): “Therefore, Theorem 2 can be used to study multiagent systems with nonlinear couplings, applicable to a wider range of applications than those of its linear counterparts in [4], [19].”
• Gradient clock synchronization in wireless sensor networks (2009, background): “It is well-known that the product of row stochastic matrices converges if the graph corresponding to matrices A(t) is strongly connected [26, 4].”
• Consensus in multi‐agent systems with communication constraints (2012, background): “Recently, considerable effort has been made to study the emergence of consensus behaviors in multi-agent systems, with many profound results established [9–32].”
• Global Analysis of Multi-Agent Systems Based on Vicsek's Model (2009, background): “By Proposition 4 in [1], we have has all its entries positive.”
• Convergence speed in distributed consensus over dynamically switching random networks (2009, methodology): “…the corresponding matrix In − L(k) could have negative elements and thus it is not a stochastic matrix; therefore, the classical results in Blondel et al. (2005), Cao et al. (2008) and Tahbaz-Salehi and Jadbabaie (2008) can not be directly applied to prove the almost sure asymptotic stability.”