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## Design and Analysis of Distributed Averaging with Quantized Communication. Research Report RR-8501, INRIA, (2014)

Citations: | 1 - 1 self |

### Citations

1980 |
Distributed Algorithms
- Lynch
- 1996
(Show Context)
Citation Context ... than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average, depending on initial conditions. In the latter case, tight bounds for the size of the neighborhood are given, and it is further shown that the error can be made arbitrarily small by adjusting the algorithm’s parameters in a distributed manner. I. INTRODUCTION There has been considerable interest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averagin... |

1284 | Coordination of groups of mobile autonomous agents using nearest neighbor rules
- Jadbabaie, Lin, et al.
- 2003
(Show Context)
Citation Context ...hown that the error can be made arbitrarily small by adjusting the algorithm’s parameters in a distributed manner. I. INTRODUCTION There has been considerable interest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links.... |

547 | Information flow and cooperative control of vehicle formations
- Fax, Murray
(Show Context)
Citation Context ...nterest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized version will be received by... |

532 | Randomized gossip algorithms
- Boyd, Ghosh, et al.
(Show Context)
Citation Context ... via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized version will be received by the neighbors. With such quantization, the precise average 1Mahmoud El Chamie is with INRIA Sophia Antip... |

149 | Distributed consensus algorithms in sensor networks: quantized data and random link failures,”
- Kar, Moura
- 2010
(Show Context)
Citation Context ...801, USA ({jiliu, basar1}@illinois.edu). Research supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial values, or lea... |

144 | Quantized consensus
- Kashyap, Basar, et al.
- 2007
(Show Context)
Citation Context .... The probabilistic algorithm in [3], called “interval consensus gossip”, causes all n agents to reach a consensus in finite time almost surely on the interval in which the average lies, for time-varying (jointly connected) undirected graphs. Stochastic quantized gossip algorithms were introduced in [20], [31] and shown to work properly. The effects of quantized communication on the randomized gossip algorithm were analyzed in [8]. Another thread of research has studied quantized consensus with the additional constraint that the value at each node is an integer. The probabilistic algorithm in [19] causes all n agents reach quantized consensus almost surely for a fixed (connected) undirected graph; convergence time of the algorithm was studied in [13], with bounds on its expected value. In [5] a probabilistic algorithm was introduced to solve the quantized consensus problem for fixed (strongly connected) directed graphs using the idea of “surplus”. II. DISTRIBUTED AVERAGING Consider a group of n > 1 agents labeled 1 to n. Each agent i has control over a real-valued scalar quantity xi called an agreement variable which the agent is able to update its value from time to time. Each agent c... |

119 |
Feedback control under data rate constraints: An overview
- Nair, Fagnani, et al.
- 2007
(Show Context)
Citation Context ...tions. However, whenever agent i sends its value xi(k) through the communication network, its neighbors will receive a quantized value of xi(k). A quantizer is a function Q : R → Z that maps a real value to an integer. In this paper we will study the performance of the distributed averaging algorithm due to deterministic quantization which entails two quantizers: a truncation quantizer Qt(x) which truncates the decimal part of a real number and keeps the integer part, and a rounding quantizer Qr(x) which rounds a real number to its nearest integer. These quantizers are defined as follows [8], [25]: Qt(x) = bxc, and Qr(x) = { bxc if x− bxc < 1/2 dxe if x− bxc ≥ 1/2 . These map R into Z and have quantization jumps of size 1. Note that quantizers having a generic real positive quantization step can be simply recovered by a suitable scaling: Q()(x) = Q(x/) [8]. Thus the results in this paper cover these generic quantizers as well. IV. PROBLEM FORMULATION Suppose that all n agents adhere to the same update rule of Eq. (1). Then with a quantizer Q(x), the network equation would be xi(k + 1) = wiixi(k) + ∑ j∈Ni wijQ(xj(k)), ∀i ∈ V. (2) Simple examples show that this algorithm can cause t... |

116 | Gossip algorithms for distributed signal processing,”
- Dimakis, Kar, et al.
- 2010
(Show Context)
Citation Context ...local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized version will be received by the neighbors. With such quantization, the precise average 1Mahmoud El Chamie is with INRIA Sophia Antipolis-M... |

51 | Distributed average consensus using probabilistic quantization
- Aysal, Coates, et al.
- 2007
(Show Context)
Citation Context ...Champaign, IL 61801, USA ({jiliu, basar1}@illinois.edu). Research supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initi... |

44 | Average consensus on networks with quantized communication.
- Frasca, Carli, et al.
- 2009
(Show Context)
Citation Context ...73. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial values, or lead all agents’ variables to cycle in a small neighborhood around the average, depending on initial conditions. In the latter case, we give tight error bou... |

33 | An overview of recent progress in the study of distributed multi-agent coordination,”
- Cao, Yu, et al.
- 2013
(Show Context)
Citation Context ...-1-0573. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial values, or lead all agents’ variables to cycle in a small neighborhood around the average, depending on initial conditions. In the latter case, we give tight err... |

33 | Gossip consensus algorithms via quantized communication
- Carli, Fagnani, et al.
- 2010
(Show Context)
Citation Context ...rom the desired average is not tightly bounded. An alternative algorithm which gets around this limitation was proposed in [18] by adding dither to the agents’ variables. The probabilistic algorithm in [3], called “interval consensus gossip”, causes all n agents to reach a consensus in finite time almost surely on the interval in which the average lies, for time-varying (jointly connected) undirected graphs. Stochastic quantized gossip algorithms were introduced in [20], [31] and shown to work properly. The effects of quantized communication on the randomized gossip algorithm were analyzed in [8]. Another thread of research has studied quantized consensus with the additional constraint that the value at each node is an integer. The probabilistic algorithm in [19] causes all n agents reach quantized consensus almost surely for a fixed (connected) undirected graph; convergence time of the algorithm was studied in [13], with bounds on its expected value. In [5] a probabilistic algorithm was introduced to solve the quantized consensus problem for fixed (strongly connected) directed graphs using the idea of “surplus”. II. DISTRIBUTED AVERAGING Consider a group of n > 1 agents labeled 1 to ... |

32 | On quantized consensus by means of gossip algorithm–Part II: convergence time,”
- Lavaei, Murray
- 2009
(Show Context)
Citation Context ...USA ({jiliu, basar1}@illinois.edu). Research supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial values, or lead all... |

31 | A distributed consensus protocol for clock synchronization in wireless sensor network,”
- Schenato, Gamba
- 2007
(Show Context)
Citation Context ...here has been considerable interest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized... |

27 | Distributed consensus with limited communication data rate. Automatic Control,
- Li, Fu, et al.
- 2011
(Show Context)
Citation Context ...hat the error can be made arbitrarily small by adjusting the algorithm’s parameters in a distributed manner. I. INTRODUCTION There has been considerable interest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With ... |

23 |
Fast linear iterations for distributed averaging,” Sys
- Xiao, Boyd
- 2004
(Show Context)
Citation Context ... (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized version will be received by the neighbors. With such quantization, the precise average 1Mahmoud El Chamie is with INRIA Sophia Antipolis-Mediterranee, 200... |

21 | Communication constraints in coordinated consensus problems.
- Carli, Fagnani, et al.
- 2008
(Show Context)
Citation Context ... feedback control design problem for coding/decoding schemes; the paper shows that with an appropriate scaling function and some carefully chosen control gain, the proposed protocol can solve the distributed averaging problem, but some spectral properties of the Laplacian matrix of the underlying fixed undirected graph have to be known in advance. More sophisticated coding/decoding schemes were proposed in [22] for time-varying undirected graphs and in [30] for time-varying directed graphs, all requiring carefully chosen parameters. Control performance of logarithmic quantizers was studied in [7] and recently a novel but complicated dynamic quantizer has been proposed in [28]. A biologically inspired algorithm was proposed in [9] which makes all agents reach some consensus with arbitrary precision, but at the cost of not preserving the desired average. Most closely related to the problem considered here is the work of [15] where a deterministic algorithm of the same form as in this paper has been only partially analyzed and the authors have approximated the system by a probabilistic model and left the design of the weights as an open problem. Over the past decade quite a few probabili... |

16 | Distributed randomized algorithms for the PageRank computation
- Ishii, Tempo
- 1987
(Show Context)
Citation Context ...ed manner. I. INTRODUCTION There has been considerable interest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be tr... |

15 | On the convergence time of asynchronous distributed quantized averaging algorithms.
- Zhu, Martınez
- 2011
(Show Context)
Citation Context ...d graphs; although the expectation of the consensus value equals the desired average, the deviation of the consensus value from the desired average is not tightly bounded. An alternative algorithm which gets around this limitation was proposed in [18] by adding dither to the agents’ variables. The probabilistic algorithm in [3], called “interval consensus gossip”, causes all n agents to reach a consensus in finite time almost surely on the interval in which the average lies, for time-varying (jointly connected) undirected graphs. Stochastic quantized gossip algorithms were introduced in [20], [31] and shown to work properly. The effects of quantized communication on the randomized gossip algorithm were analyzed in [8]. Another thread of research has studied quantized consensus with the additional constraint that the value at each node is an integer. The probabilistic algorithm in [19] causes all n agents reach quantized consensus almost surely for a fixed (connected) undirected graph; convergence time of the algorithm was studied in [13], with bounds on its expected value. In [5] a probabilistic algorithm was introduced to solve the quantized consensus problem for fixed (strongly conne... |

12 |
The distributed multiple voting problem.
- Benezit, Thiran, et al.
- 2011
(Show Context)
Citation Context ...aign, IL 61801, USA ({jiliu, basar1}@illinois.edu). Research supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial va... |

11 |
Quantized consensus and averaging on gossip digraphs.
- Cai, Ishii
- 2011
(Show Context)
Citation Context ...ing (jointly connected) undirected graphs. Stochastic quantized gossip algorithms were introduced in [20], [31] and shown to work properly. The effects of quantized communication on the randomized gossip algorithm were analyzed in [8]. Another thread of research has studied quantized consensus with the additional constraint that the value at each node is an integer. The probabilistic algorithm in [19] causes all n agents reach quantized consensus almost surely for a fixed (connected) undirected graph; convergence time of the algorithm was studied in [13], with bounds on its expected value. In [5] a probabilistic algorithm was introduced to solve the quantized consensus problem for fixed (strongly connected) directed graphs using the idea of “surplus”. II. DISTRIBUTED AVERAGING Consider a group of n > 1 agents labeled 1 to n. Each agent i has control over a real-valued scalar quantity xi called an agreement variable which the agent is able to update its value from time to time. Each agent can only communicate with its “neighbors”. Neighbor relations are described as follows: agent j is a neighbor of agent i if (i, j) ∈ E is an edge in a given undirected n-vertex graph G = (V, E) where ... |

7 |
Deterministic gossiping.
- Liu, Mou, et al.
- 2011
(Show Context)
Citation Context ...ctions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized version will be received by the neighbors. With such quantization, the precise average 1Mahmoud El Chamie is with INRIA Sophia Antipolis-Mediterrane... |

6 | A local average consensus algorithm for wireless sensor networks,”
- Avrachenkov, Chamie, et al.
- 2011
(Show Context)
Citation Context ... the largest integer not greater than the average of their initial values, or will lead all variables to cycle in a small neighborhood around the average, depending on initial conditions. In the latter case, tight bounds for the size of the neighborhood are given, and it is further shown that the error can be made arbitrarily small by adjusting the algorithm’s parameters in a distributed manner. I. INTRODUCTION There has been considerable interest recently in developing algorithms for distributing information among members of interactive agents via local interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms... |

3 | Real-valued average consensus over noisy quantized channels.
- Censi, Murray
- 2009
(Show Context)
Citation Context ...ly chosen control gain, the proposed protocol can solve the distributed averaging problem, but some spectral properties of the Laplacian matrix of the underlying fixed undirected graph have to be known in advance. More sophisticated coding/decoding schemes were proposed in [22] for time-varying undirected graphs and in [30] for time-varying directed graphs, all requiring carefully chosen parameters. Control performance of logarithmic quantizers was studied in [7] and recently a novel but complicated dynamic quantizer has been proposed in [28]. A biologically inspired algorithm was proposed in [9] which makes all agents reach some consensus with arbitrary precision, but at the cost of not preserving the desired average. Most closely related to the problem considered here is the work of [15] where a deterministic algorithm of the same form as in this paper has been only partially analyzed and the authors have approximated the system by a probabilistic model and left the design of the weights as an open problem. Over the past decade quite a few probabilistic quantized consensus algorithms have been proposed. The probabilistic quantizer in [2] ensures almost sure consensus at a common but... |

3 | Convergence time for unbiased quantized consensus.
- Etesami, Basar
- 2013
(Show Context)
Citation Context ... IL 61801, USA ({jiliu, basar1}@illinois.edu). Research supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) MURI grant FA9550-10-1-0573. cannot be achieved (except in particular cases), but some value close to it can be achieved, called quantized consensus (the formal definition is given in Section IV). A number of papers have studied this quantized consensus problem and various probabilistic quantization strategies have been proposed to cause all the agents in a network to reach a quantized consensus with probability one (or at least with high probability) [2], [3], [13], [18]–[20]. Notwithstanding this, the problem of how to design and analyze consensus algorithms with deterministic quantization effects remains open [6], [15]. In this paper, we thoroughly analyze the performance of a class of deterministic distributed averaging algorithms in which the information exchange between neighboring agents is subject to certain types of uniform quantization. It is shown that in finite time, the algorithms will either cause all agents to reach a quantized consensus where the consensus value is the largest integer not greater than the average of their initial values, ... |

2 |
Distributed consensus over digital networks with limited bandwidth and time-varying topologies.
- Li, Xie
- 2011
(Show Context)
Citation Context ...one. There are only a few publications which study deterministic algorithms for quantized consensus. In [21] the distributed averaging problem with quantized communication is formulated as a feedback control design problem for coding/decoding schemes; the paper shows that with an appropriate scaling function and some carefully chosen control gain, the proposed protocol can solve the distributed averaging problem, but some spectral properties of the Laplacian matrix of the underlying fixed undirected graph have to be known in advance. More sophisticated coding/decoding schemes were proposed in [22] for time-varying undirected graphs and in [30] for time-varying directed graphs, all requiring carefully chosen parameters. Control performance of logarithmic quantizers was studied in [7] and recently a novel but complicated dynamic quantizer has been proposed in [28]. A biologically inspired algorithm was proposed in [9] which makes all agents reach some consensus with arbitrary precision, but at the cost of not preserving the desired average. Most closely related to the problem considered here is the work of [15] where a deterministic algorithm of the same form as in this paper has been on... |

2 |
Cycle analysis for deterministic finite state automata.
- Reger
(Show Context)
Citation Context ..., M(k) ≤ M(0). Similarly, we have m(k) ≥ m(0). As a consequence, bxi(k)c ∈ {m(0),m(0)+1, . . . ,M(0)−1,M(0)} is a finite set. Moreover, from equation (10), ci(k) belongs to a finite set that can have at most Bi elements. Since xi(k) = bxi(k)c + ci(k), and each of the elements in the sum belongs to a finite set, xi(k) belongs to a finite set. But from equation (6), we have x(k + 1) = f (x(k)) where the function f(.) is a deterministic function of the input state at iteration k, so the system is a deterministic finite state automata. States of deterministic automata enter a cycle in finite time [26], and therefore the system is cyclic. B. Convergence Analysis In this subsection, we will study the stability of the above system using a Lyapunov function. Equation (10) implies that there exist three fixed strictly positive constants γ1, γ2, γ3 > 0, independent of time and only dependent on initial values and the network structure, which satisfy the following: • For any i and any iteration k such that ci(k) >(∑ j∈Ni wij ) , we have: ci(k)− ∑ j∈Ni wij ≥ γ1 > 0, • For any i and any iteration k such that ci(k) >(∑ j∈Ni wij ) , we have: ci(k)− ∑ j∈Ni wij ≥ γ2 > 0, • For any i and any iteration... |

2 |
Distributed average consensus with quantization refinement. Signal Processing,
- Thanou, Kokiopoulou, et al.
- 2013
(Show Context)
Citation Context ...at with an appropriate scaling function and some carefully chosen control gain, the proposed protocol can solve the distributed averaging problem, but some spectral properties of the Laplacian matrix of the underlying fixed undirected graph have to be known in advance. More sophisticated coding/decoding schemes were proposed in [22] for time-varying undirected graphs and in [30] for time-varying directed graphs, all requiring carefully chosen parameters. Control performance of logarithmic quantizers was studied in [7] and recently a novel but complicated dynamic quantizer has been proposed in [28]. A biologically inspired algorithm was proposed in [9] which makes all agents reach some consensus with arbitrary precision, but at the cost of not preserving the desired average. Most closely related to the problem considered here is the work of [15] where a deterministic algorithm of the same form as in this paper has been only partially analyzed and the authors have approximated the system by a probabilistic model and left the design of the weights as an open problem. Over the past decade quite a few probabilistic quantized consensus algorithms have been proposed. The probabilistic quantiz... |

1 |
Distributed weight selection in consensus protocols by Schatten norm minimization.
- Chamie, Neglia, et al.
- 2012
(Show Context)
Citation Context ...interactions (e.g., a group of sensors [1] or mobile autonomous agents [24]), especially for the scenarios where agents or sensors are constrained by limited sensing, computation, and communication capabilities. Notable among these are algorithms intended to cause such a group to reach a consensus in a distributed manner [17], [21]. Consensus processes play an important role in many other problems such as Google’s PageRank [16], clock synchronization [27], and formation control [14]. One particular type of consensus process, distributed averaging, has received much attention lately [4], [10], [12], [23], [29]. Most existing algorithms for precise distributed averaging require that agents are able to send and receive real values with infinite precision. However, a realistic network can only allow messages with limited length to be transmitted between agents due to constraints on the capacity of communication links. With such a constraint, when a real value is sent from an agent to its neighbors, this value will be truncated and only a quantized version will be received by the neighbors. With such quantization, the precise average 1Mahmoud El Chamie is with INRIA Sophia Antipolis-Medite... |

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Quantized data-based distributed consensus under directed time-varying communication topology.
- Zhang, Zhang
- 2013
(Show Context)
Citation Context ...udy deterministic algorithms for quantized consensus. In [21] the distributed averaging problem with quantized communication is formulated as a feedback control design problem for coding/decoding schemes; the paper shows that with an appropriate scaling function and some carefully chosen control gain, the proposed protocol can solve the distributed averaging problem, but some spectral properties of the Laplacian matrix of the underlying fixed undirected graph have to be known in advance. More sophisticated coding/decoding schemes were proposed in [22] for time-varying undirected graphs and in [30] for time-varying directed graphs, all requiring carefully chosen parameters. Control performance of logarithmic quantizers was studied in [7] and recently a novel but complicated dynamic quantizer has been proposed in [28]. A biologically inspired algorithm was proposed in [9] which makes all agents reach some consensus with arbitrary precision, but at the cost of not preserving the desired average. Most closely related to the problem considered here is the work of [15] where a deterministic algorithm of the same form as in this paper has been only partially analyzed and the authors have appr... |