Weighted-average Consensus Research Articles

Distributed computation of fast consensus weights using ADMM

In time-critical multi-agent tasks, it is important for the agents to reach consensus as fast as possible. In this paper, we consider the problem of computing the weights in the weighted-average consensus protocol that achieve average consensus with an optimal per-step convergence factor. Most of the work in the literature either computes these optimal set of weights in a centralized manner, which requires global information about the network that may not be available, or computes a suboptimal set of weights, which are slow in achieving consensus. We propose an iterative, distributed algorithm to compute a set of weights that achieve an optimal convergence factor. We give theoretical guarantees of the convergence of the algorithm. Through numerical examples, we show that our method performs better than other distributed methods of computing weights for consensus, and it matches the performance of the centralized optimal method.

Distributed recursive filtering for multi-sensor networked systems with multi-step sensor delays, missing measurements and correlated noise

This paper is concerned with the distributed recursive filtering for the discrete-time nonlinear multi-sensor networked system with multi-step sensor delays, missing measurements and correlated noise. Based on the innovation statistical distance, an adaptive time delay estimation method, which belongs to the online methods, is derived to determine whether the measurement is acquired or not along with the time delay step. Then, a nonlinear system model is founded based on a set of selected Bernoulli distributed random variables to describe the multi-step sensor delays, missing measurements and correlated noise. The obtained time delay step can be used to update parameters of the proposed measurement model. Next, a distributed recursive filtering is designed based on linear fitting (LF) and weighted average consensus (WAC) to solve the nonlinear state estimation in the multi-sensor networked system. Meanwhile, a selection strategy is designed based on the innovation statistical distance for the weighted factors to improve the distributed fusion accuracy. Further, filtering errors of the distributed recursive filtering are proved to be exponentially bounded in mean square. Numerical simulations are conducted to evaluate the performance of the proposed algorithm.

Distributed cubature H-infinity information filtering for target tracking against uncertain noise statistics

The traditional Kalman-based distributed state estimation (DSE) is unable to address uncertain system noise. To this end, this paper studies robust DSE problems for nonlinear systems over wireless sensor networks (WSNs) with uncertain noise. The distributed cubature H-infinity information filter (DCHIF) is developed by exploiting the weighted average consensus technique. The DCHIF is employed for high-dimensional state estimation with uncertain system noise in WSNs. The local estimation in the DCHIF is obtained by each single sensor without being affected by the failure of non-adjacent sensors. The estimation is then transmitted to the adjacent fusion centres for information fusion according to the weighted average consensus (WAC) technique. The DCHIF has advantages, such as high precision and strong robustness that can alleviate the influence of uncertain noise statistics on the state estimation. Therefore, to guarantee the stability regardless of the number of consensus steps, a novel convergence analysis approach is presented based on innovative terms for each sensor node. Additionally, the efficiency of the proposed algorithm is demonstrated by performing a numerical simulation of a typical air-traffic control system.

Distributed Robust Cubature Information Filtering for Measurement Outliers in Wireless Sensor Networks

In wireless sensor networks (WSN), measurements are always corrupted by outliers or impulsive noise. Cubature information filtering (CIF) is founded based on minimum mean square error (MMSE) criterion, which is not applicable to non-Gaussian noise. Hence, a novel robust CIF (RCIF) is derived based on maximum correntropy criterion (MCC) to enhance the robustness of state estimation in the local node. For the information fusion, weighted average consensus (WAC) based distributed RCIF (DRCIF) is founded to improve the stability of sensor networks and the accuracy of state estimation. The estimation error of DRCIF is proved to be bounded in mean square. Numerical simulations are provided to evaluate the effectiveness of proposed algorithms.

An Advanced Cubature Information Filtering for Indoor Multiple Wideband Source Tracking With a Distributed Noise Statistics Estimator

Acoustic vector sensor (AVS) is an effective tool to tracking acoustic sources. However, for the problem of tracking multiple wideband sources using distributed AVS array (DAVS), there are still unsolved issues which include measurements-to-targets association and targets tracking under incorrect or unknown statistics of measurement noise. Joint probabilistic data association (JPDA) is an effective algorithm to solve data association between measurements and targets and JPDA based cubature information filter (MTCIF) is designed for nonlinear system. Meanwhile, noise statistics estimator (NSE) based on modified Sage-Husa maximum posterior (SHMP) is constructed to cope with incorrect or unknown statistics of measurement noise. Then, a two-step distributed information fusion based on weighted average consensus (WAC) is built for DAVS to improve the stability and accuracy of state estimator and NSE. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Improved weighted average consensus in distributed cooperative spectrum sensing networks

AbstractThis work proposes a fully distributed improved weighted average consensus (IWAC) technique applied to a cooperative spectrum sensing (CSS) problem in cognitive radio systems. This method allows the secondary users to cooperate based on only local information exchange without a fusion centre. We have compared 4 rules of average consensus (AC) algorithms. The first rule is the simple AC without weights. The AC rule presents performance comparable to the traditional CSS techniques such as the equal gain combining rule, which is a soft combining centralised method. Another technique is the weighted AC (WAC) rule, using the weights based on the SUs' channel condition. This technique results in a performance similar to that of the maximum ratio combining with soft combining (centralised CSS). Two new AC rules are analysed, namely, WAC accuracy exchange (WAC‐AE) and IWAC; the former relates the weights to the channel conditions of the SUs' neighbours, whereas the latter combines the conditions of WAC and WAC‐AE in the same rule. All methods are compared with each other and with the hard combining centralised CSS. The WAC‐AE results in a similar performance of the WAC technique but with fast convergence, whereas the IWAC can deliver suitable performance with small complexity increment. Moreover, the IWAC method results in a similar convergence rate than the WAC‐AE method but slightly higher than the AC and WAC methods. Hence, the computational complexity of IWAC, WAC‐AE, and WAC is proven to be very similar. The analyses are based on numerical Monte Carlo simulations, whereas the algorithm's convergence is evaluated for both fixed and dynamic mobile communication scenarios and under additive white Gaussian noise and Rayleigh channels.

Finite-Time Consensus with a Time-Varying Reference State and Switching Topology

The finite-time consensus problem in the networks of multiple mobile agents is comprehensively investigated. In order to resolve this problem, a novel nonlinear information exchange protocol is proposed. The proposed protocol ensures that the states of the agents are converged to a weighted-average consensus in finite time if the communication topology is a weighted directed graph with a spanning tree and each strongly connected component is detail-balanced. Furthermore, the proposed protocol is also able to solve the finite-time consensus problem of networks with a switching topology. Finally, computer simulations are presented to demonstrate and validate the effectiveness of the theoretical analysis under the proposed protocol.

Reaching consensus in unbalanced networks with coarse information communication

This paper is concerned with the problem of seeking consensus for a network of agents under a fixed or switching directed communication topology. Each agent is modeled as discrete-time first-order dynamics and interacts with its neighbors via logarithmically quantized information. We assume that the digraph is not necessarily balanced and, thus, avoiding the double stochasticity requirement for the adjacency matrix. For the case of a fixed topology that is strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse logarithmic quantization and the β-asymptotic weighted-average consensus is achieved. For the case of a switching topology that is periodically strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse quantization and the β-asymptotic consensus is achieved. Furthermore, for both cases, not only are the convergence rates for consensus specified but also the bounds on the consensus error that highlight their dependence on the sector bound β of the logarithmic quantizer are also provided. Copyright © 2015 John Wiley & Sons, Ltd.

Information weighted consensus‐based distributed particle filter for large‐scale sparse wireless sensor networks

To the problem of information fusion estimation for large-scale sparse wireless sensor networks (WSNs), a novel algorithm, named the information weighted consensus-based distributed particle filter, is presented. The proposed filter can avoid the divergence of the consensus error introduced by the naive nodes in the large-scale sparse WSNs. This is achieved by embedding an information weighted local particle filter (LPF) and a weighted-average consensus filter as the underlying filter and the top filter, respectively in each sensor node. The information weighted LPF will enable the weighted-average consensus filter to be used in the information space to communicate the information matrix and information state in a distributed fashion. And the weighted-average consensus filter will guarantee that a weighted average consensus for all initial states can be reached with some consensus error, which will not be divergent. Moreover, at the same time, the cross correlation between each pair of networked nodes can be approximately computed, which will further inhibit the divergence among the local estimated states of the filters embedded in each node. Finally, some examples are presented to illustrate the reasonability of the theoretical derivation.

Joining consensus of networked multi-agent systems with nonlinear couplings and weighting constraints

This paper studies the joining consensus of networked multi-agent systems subject to nonlinear couplings and weighted directed graphs via pinning control. A weighted-average consensus protocol is proposed to achieve the collective decision by interacting with the local information of some pinned agents. By proposing a novel joining consensus protocol, average consensus and general consensus strategies are joined to achieve an agreement for the weighting networked system. Furthermore, by calculating a proper consensus gain and using finite control Lyapunov controllers, an efficient joining consensus protocol is presented to improve the consensus speed. Sufficient conditions for achieving the consensuses asymptotically are proved. Finally, theoretical results are validated via simulations.

Consensus of sampled-data multi-agent networking systems via model predictive control

This paper presents a theoretical framework to design and analyze the consensus of a sampled-data multi-agent networking system via model predictive control (MPC). We introduce a distributed MPC weighted-average consensus protocol for a continuous-time multi-agent network in the sampled-data setting, and prove such a sampled-data multi-agent system asymptotically reaches the weighted-average consensus via the distributed MPC protocol with both fixed and switching network topologies. Numerical examples verify the effectiveness of the distributed MPC consensus protocol, which is beneficial to the convergence of consensus and the feasible range of the sampling interval.

Analysis of Decentralized Quantized Auctions on Cooperative Networks

This Technical Note considers a decentralized quantity allocation problem over networks. By employing the so-called UQ-PSP auction algorithm, distributed auctions on a two-level network are developed so as to achieve efficient resource allocations (in the sense of maximization of social welfare). In the formulation in this Technical Note, each vertex in the connected higher-level network is regarded as a supplier for a uniquely associated lower-level network, and each lower-level network consists of a set of agents which represent buyers. Each lower-level network with its associated supplier is assumed to constitute a local UQ-PSP auction, generically denoted by Al. The adjustment of the quantities supplied to any Al is via a consensus-based dynamical system which exchanges quantities depending upon the limit prices of the recursive bidding processes of the local auctions in the neighborhood of Al in the higher-level network. Such a consensus auction system is formulated as a discrete-time weighted-average consensus problem with an associated family of time-varying and asymmetric Perron matrices. Subject to continuous-valued pricing, the corresponding dynamical system converges to a global limit price which is independent of the initial data and corresponds to an efficient quantity allocation. Exponential convergence is established by using the passivity property of UQ-PSP auctions, and using the stochastic, indecomposable, and aperiodic (SIA) properties of the family of Perron matrices.