Linear Consensus Algorithm Research Articles

Deep Learning-Based Average Consensus

In this study, we analyzed the problem of accelerating the linear average consensus algorithm for complex networks. We propose a data-driven approach to tuning the weights of temporal (i.e., time-varying) networks using deep learning techniques. Given a finite-time window, the proposed approach first unfolds the linear average consensus protocol to obtain a feedforward signal-flow graph, which is regarded as a neural network. The edge weights of the obtained neural network are then trained using standard deep learning techniques to minimize consensus error over a given finite-time window. Through this training process, we obtain a set of optimized time-varying weights, which yield faster consensus for a complex network. We also demonstrate that the proposed approach can be extended for infinite-time window problems. Numerical experiments revealed that our approach can achieve a significantly smaller consensus error compared to baseline strategies.

Scalability and Fragility in Bounded-Degree Consensus Networks

We investigate the performance of linear consensus algorithms subject to a scaling of the underlying network size. Specifically, we model networked systems with nth order integrator dynamics over families of undirected, weighted graphs with bounded nodal degrees. In such networks, the algebraic connectivity affects convergence rates, sensitivity, and, for high-order consensus [n ≥ 3), stability properties. This connectivity scales unfavorably in network size, except in expander families, where consensus performs well regardless of network size. We show, however, that consensus over expander families is fragile to a grounding of the network (resulting in leader-follower consensus). We show that grounding may deteriorate system performance by orders of magnitude in large networks, or cause instability in high-order consensus. Our results, which we illustrate through simulations, also point to a fundamental limitation to the scalability of consensus networks with leaders, which does not apply to leaderless networks.

Consensus Algorithms and the Decomposition-Separation Theorem

Convergence properties of time inhomogeneous Markov chain based discrete and continuous time linear consensus algorithms are analyzed. Provided that a so-called infinite jet-flow property is satisfied by the coupling chain, necessary conditions for both consensus and multiple consensus are established. A recent extension by Sonin of the classical Kolmogorov–Doeblin decomposition-separation for homogeneous Markov chains to the inhomogeneous case is then employed to show that the obtained necessary conditions are also sufficient when a discrete time chain is in Class $\mathcal{P}^{\ast}$ , as defined by Touri and Nedic. It is also shown that Sonin's D-S Theorem leads to a rediscovery and generalization of the existing related consensus results in the literature. Finally, a geometric approach first developed by Shen is taken to extend the results of the discrete time case to the continuous time case.

Sparc: a sparsity-based consensus algorithm for long erroneous sequencing reads.

Motivation. The third generation sequencing (3GS) technology generates long sequences of thousands of bases. However, its current error rates are estimated in the range of 15–40%, significantly higher than those of the prevalent next generation sequencing (NGS) technologies (less than 1%). Fundamental bioinformatics tasks such as de novo genome assembly and variant calling require high-quality sequences that need to be extracted from these long but erroneous 3GS sequences.Results. We describe a versatile and efficient linear complexity consensus algorithm Sparc to facilitate de novo genome assembly. Sparc builds a sparse k-mer graph using a collection of sequences from a targeted genomic region. The heaviest path which approximates the most likely genome sequence is searched through a sparsity-induced reweighted graph as the consensus sequence. Sparc supports using NGS and 3GS data together, which leads to significant improvements in both cost efficiency and computational efficiency. Experiments with Sparc show that our algorithm can efficiently provide high-quality consensus sequences using both PacBio and Oxford Nanopore sequencing technologies. With only 30× PacBio data, Sparc can reach a consensus with error rate <0.5%. With the more challenging Oxford Nanopore data, Sparc can also achieve similar error rate when combined with NGS data. Compared with the existing approaches, Sparc calculates the consensus with higher accuracy, and uses approximately 80% less memory and time.Availability. The source code is available for download at https://github.com/yechengxi/Sparc.

Linear Consensus Algorithms Based on Balanced Asymmetric Chains

Multi-agent consensus algorithms, with update steps based on so-called balanced asymmetric chains, are analyzed. For such algorithms, it is shown that: (i) the empirical distribution of state values converges asymptotically and (ii) the occurrence of consensus or multiple consensus is directly related to the property of absolute infinite flow of the underlying update chain. An example is provided to illustrate the novelty of the results.

Synchronization of Networks of Heterogeneous Agents With Common Nominal Behavior

This paper deals with the problem of synchronization in networks of heterogeneous agents with common nominal behavior. The agents are modeled as (possibly nonlinear) perturbed versions of a common SISO nominal LTI operator, and they are interconnected via a sparse memoryless interconnection operator, coherent with the communication graph underlying the network. The network is said to synchronize if the outputs of the agents tend to align along given directions, the most important case being consensus, or agreement. The paper provides a general result, based on IQCs, that ensures synchronization of the network with robustness w.r.t. uncertainties in the interconnection and in each agent's dynamics. Scalability issues are discussed in the scenario where the interconnection operator is a constant normal matrix, yielding the generalization of the very popular linear consensus algorithm. The wide range of applicability of the proposed criterion is shown by providing synchronization conditions in some important examples. Whenever possible, graphical criteria are proposed for checking the required conditions.

A Reputation-Based Secure Distributed Control Methodology in D-NCS

Distributed networked control systems (D-NCSs) are more vulnerable to malicious attacks with the adoption of distributed control strategies. The misbehaving agents in the D-NCS can disrupt the distributed control algorithms and gradually compromise the entire system. In this paper, a multirobot system using the linear consensus algorithm for formation control is studied where parts of the robots are compromised. A reputation-based secure distributed control methodology with built-in defense is proposed to achieve accurate consensus computation in the presence of misbehaving robots. It embeds four phases (i.e., detection, mitigation, identification, and update) into the distributed control process. The effectiveness of the proposed method is illustrated through simulation analysis and experimental results.

Network Clock Synchronization Based on the Second-Order Linear Consensus Algorithm

In this paper a distributed algorithm for clock synchronization is proposed. This algorithm is based on an extension of the linear consensus algorithm which is able to synchronize a family of identical double integrators. Since in reality the various clocks may have different drifts, the algorithm needs to be designed in such a way that it works correctly also in case of heterogeneous double integrators. We start by reviewing an unrealistic synchronous implementation of the clock synchronization algorithm, that has been recently proposed in the context of noisy double integrators. The main contribution of this paper is to propose a realistic pseudo-synchronous implementation of this algorithm. This pseudo-synchronous algorithm is shown to be a perturbation of the synchronous one and so, through arguments related to the center manifold theorem, it is proved to be locally convergent under the assumption of absence of process noise, measurement noise and propagation delays. However, through numerical simulations, the performance of this algorithm is evaluated also in the case the communication delays are not negligible, the clock drifts are time-varying and the communication channels are unreliable. Moreover, again through numerical simulations, the strategy we propose in this paper is compared with other fully distributed strategies recently proposed in the literature. While being slightly slower to reach the asymptotic synchronization, our strategy seems to significantly outperform the other strategies in terms of robustness to process and measurement noises and time-varying clock drifts.

Non-Linear Distributed Average Consensus Using Bounded Transmissions

A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable whose expectation is the desired sample average of the initial observations with a variance that depends on the step size of the algorithm and the variance of the communication noise. The asymptotic performance is characterized by deriving the asymptotic covariance matrix using results from stochastic approximation theory. It is shown that using bounded transmissions results in slower convergence compared to the linear consensus algorithm based on the Laplacian heuristic. Simulations corroborate our analytical findings.

Resistance-Based Performance Analysis of the Consensus Algorithm over Geometric Graphs

The performance of the linear consensus algorithm is studied by using a linear quadratic (LQ) cost. The objective is to understand how the communication topology influences this algorithm. This is achieved by exploiting the analogy between Markov chains and electrical resistive networks. Indeed, this allows us to uncover the relation between the LQ performance cost and the average effective resistance of a suitable electrical network and, moreover, to show that if the communication graph fulfills some local properties, then its behavior can be approximated by that of a grid, which is a graph whose associated LQ cost is well known.

A simple consensus algorithm for distributed averaging in random geographical networks

Random geographical networks are realistic models for wireless sensor networks which are used in many applications. Achieving average consensus is very important in sensor networks and the faster the consensus is, the durable the sensors’ life, and thus, the better the performance of the network. In this paper we compared the performance of a number of linear consensus algorithms with application to distributed averaging in random geographical networks. Interestingly, the simplest algorithm – where only the degree of receiving nodes is needed for the averaging – had the best performance in terms of the consensus time. Furthermore, we proved that the network has guaranteed convergence with this simple algorithm.

基于决策级融合的高光谱遥感影像分类

To apply decision level fusion to hyperspectral remote sensing (HRS) image classification, three decision level fusion strategies are experimented on and compared, namely, linear consensus algorithm, improved evidence theory, and the proposed support vector machine (SVM) combiner. To evaluate the effects of the input features on classification performance, four schemes are used to organize input features for member classifiers. In the experiment, by using the operational modular imaging spectrometer (OMIS) II HRS image, the decision level fusion is shown as an effective way for improving the classification accuracy of the HRS image, and the proposed SVM combiner is especially suitable for decision level fusion. The results also indicate that the optimization of input features can improve the classification performance.

Optimal Linear-Consensus Algorithms: An LQR Perspective

Laplacian matrices play an important role in linear-consensus algorithms. This paper studies optimal linear-consensus algorithms for multivehicle systems with single-integrator dynamics in both continuous-time and discrete-time settings. We propose two global cost functions, namely, interaction-free and interaction-related cost functions. With the interaction-free cost function, we derive the optimal (nonsymmetric) Laplacian matrix by using a linear-quadratic-regulator-based method in both continuous-time and discrete-time settings. It is shown that the optimal (nonsymmetric) Laplacian matrix corresponds to a complete directed graph. In addition, we show that any symmetric Laplacian matrix is inverse optimal with respect to a properly chosen cost function. With the interaction-related cost function, we derive the optimal scaling factor for a prespecified symmetric Laplacian matrix associated with the interaction graph in both continuous-time and discrete-time settings. Illustrative examples are given as a proof of concept.