Average Consensus Algorithm Research Articles

Distributed Joint Cooperative Self-Localization and Target Tracking Algorithm for Mobile Networks.

Location information is a key issue for applications of the Internet of Things. In this paper, we focus on mobile wireless networks with moving agents and targets. The positioning process is divided into two phases based on the factor graph, i.e., a prediction phase and a joint self-location and tracking phase. In the prediction phase, we develop an adaptive prediction model by exploiting the correlation of trajectories within a short period to formulate the prediction message. In the joint positioning phase, agents calculate the cooperative messages according to variational message passing and locate themselves. Simultaneously, the average consensus algorithm is employed to realize distributed target tracking. The simulation results show that the proposed prediction model is adaptive to the random movement of nodes. The performance of the proposed joint self-location and tracking algorithm is better than the separate cooperative self-localization and tracking algorithms.

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.

Improved Distributed Minimum Variance Distortionless Response (MVDR) Beamforming Method Based on a Local Average Consensus Algorithm for Bird Audio Enhancement in Wireless Acoustic Sensor Networks

Currently, wireless acoustic sensor networks (WASN) are commonly used for wild bird monitoring. To better realize the automatic identification of birds during monitoring, the enhancement of bird audio is essential in nature. Currently, distributed beamformer is the most suitable method for bird audio enhancement of WASN. However, there are still several disadvantages of this method, such as large noise residue and slow convergence rate. To overcome these shortcomings, an improved distributed minimum variance distortionless response (IDMVDR) beamforming method for bird audio enhancement in WASN is proposed in this paper. In this method, the average metropolis weight local average consensus algorithm is first introduced to increase the consensus convergence rate, then a continuous spectrum update algorithm is proposed to estimate the noise power spectral density (PSD) to improve the noise reduction performance. Lastly, an MVDR beamformer is introduced to enhance the bird audio. Four different network topologies of the WASNs were considered, and the bird audio enhancement was performed on these WASNs to validate the effectiveness of the proposed method. Compared with two classical methods, the results show that the Segmental signal to noise ratio (SegSNR), mean square error (MSE), and perceptual evaluation of speech quality (PESQ) obtained by the proposed method are better and the consensus rate is faster, which means that the proposed method performs better in audio quality and convergence rate, and therefore it is suitable for WASN with dynamic topology.

Distributed Cooperative Scheme for Forced Oscillation Location Identification in Power Systems

The most effective countermeasure against forced oscillations (FOs) is to locate and isolate external disturbances from power systems. However, it is challenging for existing location identification schemes to satisfy real-time computation and communication requirements in central data concentrators. To solve this problem, we propose a distributed cooperative scheme for identifying the FO source location. Phasor data collectors (PDCs) located at local control centers are utilized to calculate local energy flows embedded in low FOs. We apply an average-consensus algorithm for exchanging the energy flow information among local PDCs which detects the cut-set energy and locate the FO source in a distributed manner. We also propose an adaptive minimum cut-set division method based on graph theory. By implementing the proposed method on central PDC, the auxiliary control data are updated automatically, which makes the location scheme adaptive to changes in grid and communication network topologies. The effectiveness of the distributed cooperative location identification scheme is verified using the results for the IEEE 39-bus and 162-bus power systems.

A novel cooperative distributed secondary controller for VSI and PQ inverters of AC microgrids

This paper proposes a novel cooperative secondary control strategy for microgrids which is fully distributed. There is a two-layered coordination, which exists between inverter based DGs of both types, i.e. Voltage Source Inverter (VSI) and Current Source Inverter (CSI), also called PQ inverter. In first layer of the proposed two-layered cooperative control strategy, VSIs will take care of the primary average voltage regulation by implementing the average consensus algorithm (ACA); then in the second layer of control, the PQ inverters will improve the voltage quality of the microgrid while maintaining the average voltage of buses at the same desired level. Zone dedication algorithm is utilized in the second layer for voltage quality purposes based on sensitivity analysis. The sensitivity analysis is based on Simplified Jacobian matrix and the result of that is used to define the zone related to each DG in the microgrid. The goal of this zone dedication is to assign loads to the DGs that can compensate their changes with less effort (generating less power) than the others. There are two major contributions in this paper; 1- PQ inverters are effectively involved to increase microgrids capacity for better power management by introducing sensitivity to the PQ inverters set-point. This is defined based on the structure of the microgrid and takes into account the location of load changes. 2- The proposed strategy not only focuses on transient response but also improves the steady state response which smooths the voltage profile of the system while keeping the average voltage at the same desired level.The algorithm has been applied to a 13 bus system with a fully distributed communication in which each VSI inverter only communicates with its immediate neighbors and each PQ inverter is only in touch with associated bordering agents. The conclusive results verify that the proposed control strategy is an effective way to control the microgrid's voltage to have a smoother and stable voltage profile. The analysis also confirms the robustness of the proposed cooperative control in presence of possible time delays.

Broadcast and Gossip Stochastic Average Consensus Algorithms in Directed Topologies

We address the problem of a set of agents reaching consensus by computing the average of their initial states. We propose two randomized algorithms over a directed communication graph where either a random node broadcast its value or a randomly selected pair of nodes communicate in a distributed fashion. The proposed algorithms guarantee convergence in three important definitions, namely: almost surely, in expectation, and in the mean-square sense. We show how the parameters of the algorithm can be optimized to improve the rate of convergence and compare its rates of convergence for directed and undirected graphs.

Accurate Privacy Preserving Average Consensus

Average consensus has significant applications in dynamic load balancing and cooperative control of vehicle formations, where all the agents receive information from neighboring agents via communication network and update their states to achieve an agreement. However, this approach would result in an undesirable disclosure on the initial states of agents to their neighbors. In this brief, we propose an accurate privacy preserving average consensus (APPAC) algorithm, where all the agents independently generate and transmit random numbers based on Paillier cryptosystem to conceal their initial states. Under the proposed APPAC algorithm, the accurate average consensus is indeed achieved. Besides, the necessary and sufficient conditions that initial states can be inferred are also discussed. Extensive simulations are conducted to demonstrate the effectiveness of the proposed algorithm.

Distributed Stopping Criterion for Consensus in the Presence of Delays

Linear consensus protocol is an iterative distributed algorithm with asymptotic convergence guarantees. This paper develops and analyzes an algorithm for agents running linear consensus iterations to detect convergence to consensus within a specified error tolerance in a distributed manner. The distributed stopping criterion allows for time-varying bounded delays in information transmission and reception between agents. The algorithm relies on distributively determining the maximum and minimum values held by the agents. This paper further develops an algorithm for average consensus that utilizes a distributive stopping criterion, based on maximum and minimum consensus, where no centralized coordination is needed on how each agent weights its neighbor's values. Here, the doubly stochastic assumption on the weight matrix is relaxed and only column stochasticity is needed. The effectiveness of the algorithms is demonstrated by simulations and a comparison with prior work in the literature. Moreover, the demonstration of the proposed algorithms on an experimental test bed of Raspberry-Pi agents communicating wirelessly validates its applicability and utility.

A multi-cast algorithm for robust average consensus over internet of things environments

The initial cloud-managed-network conceptualization of the IoT has mutated into a sparsely coupled, distributed system of interacting smart objects, or things. In this context, distributed control techniques have emerged as a tool for performing tasks locally without the support of a back-end infrastructure. Consensus algorithms are the flagship of distributed control and find application in solving problems as varied as distributed task assignment, distributed estimation, and distributed optimization. Unfortunately, typical consensus algorithms deteriorate their performance when faced with realistic communication phenomena as asynchronous communications, packet losses and channel delays. In this work, an algorithm for achieving average consensus over an IoT environment is introduced and evaluated extensively in a large-scale IoT testbed. Evaluation results show that the proposed algorithm achieves average consensus in all evaluated scenarios despite heterogeneity in the network in terms of processing and networking capabilities, packet losses and delays.

Multi-agent system for microgrids: design, optimization and performance

Smart grids are considered a promising alternative to the existing power grid, combining intelligent energy management with green power generation. Decomposed further into microgrids, these small-scaled power systems increase control and management efficiency. With scattered renewable energy resources and loads, multi-agent systems are a viable tool for controlling and improving the operation of microgrids. They are autonomous systems, where agents interact together to optimize decisions and reach system objectives. This paper presents an overview of multi-agent systems for microgrid control and management. It discusses design elements and performance issues, whereby various performance indicators and optimization algorithms are summarized and compared in terms of convergence time and performance in achieving system objectives. It is found that Particle Swarm Optimization has a good convergence time, so it is combined with other algorithms to address optimization issues in microgrids. Further, information diffusion and consensus algorithms are explored, and according to the literature, many variants of average-consensus algorithm are used to asynchronously reach an equilibrium. Finally, multi-agent system for multi-microgrid service restoration is discussed. Throughout the paper, challenges and research gaps are highlighted in each section as an opportunity for future work.

Privacy-Preserving Average Consensus: Privacy Analysis and Algorithm Design

Privacy-preserving average consensus aims to guarantee the privacy of initial states and asymptotic consensus on the exact average of the initial values. In this paper, it is achieved by adding variance-decaying and zero-sum random noises to the consensus process. However, there is lack of theoretical analysis to quantify the degree of the data privacy protection. In this paper, we introduce the maximum disclosure probability that other nodes can infer one node's initial state within a given small interval to quantify the data privacy. We utilize a novel privacy definition, named $(\alpha, \beta)$ -data-privacy, to depict the relationship between the maximum disclosure probability and the estimation accuracy. Then, we prove that the general privacy-preserving average consensus provides $(\alpha, \beta)$ -data-privacy, and obtain the closed-form expression of the relationship between $\alpha$ and $\beta$ given the noise distribution. We reveal that the added noise with a uniform distribution is optimal in terms of achieving the highest $(\alpha, \beta)$ -data-privacy. We also prove that under what condition, the data-privacy will be compromised. Finally, an optimal privacy-preserving average consensus algorithm is proposed to achieve the highest $(\alpha, \beta)$ -data-privacy. Simulations verify the analytical results.

Multiagent Newton–Raphson Optimization Over Lossy Networks

In this work, we study the problem of unconstrained convex optimization in a fully distributed multiagent setting, which includes asynchronous computation and lossy communication. In particular, we extend a recently proposed algorithm named Newton–Raphson consensus by integrating it with a broadcast-based average consensus algorithm, which is robust to packet losses. We show via the separation of time-scale principle that under mild conditions (i.e., persistency of the agents activation and bounded consecutive communication failures), the proposed algorithm is provably locally exponentially stable with respect to the optimal global solution. Finally, we complement the theoretical analysis with numerical simulations and comparisons based on real datasets.

Consensus-Based SOC Balancing of Battery Energy Storage Systems in Wind Farm

Multiple battery energy storage systems (BESSs) are used to compensate for the fluctuation in wind generations effectively. The stage of charge (SOC) of BESSs might be unbalanced due to the difference of wind speed, initial SOCs, line impedances and capabilities of BESSs, which have a negative impact on the operation of the wind farm. This paper proposes a distributed control of the wind energy conversion system (WECS) based on dynamic average consensus algorithm to balance the SOC of the BESSs in a wind farm. There are three controllers in the WECS with integrated BESS, including a machine-side controller (MSC), the grid-side controller (GSC) and battery-side controller (BSC). The MSC regulates the generator speed to capture maximum wind power. Since the BSC maintains the DC link voltage of the back-to-back (BTB) converter that is used in the WECS, an improved virtual synchronous generator (VSG) based on consensus algorithm is used for the GSC to control the output power of the WECS. The functionalities of the improved VSG are designed to compensate for the wind power fluctuation and imbalance of SOC among BESSs. The average value of SOCs obtained by the dynamic consensus algorithm is used to adjust the wind power output for balancing the SOC of batteries. With the proposed controller, the fluctuation in the output power of wind generation is reduced, and the SOCs of BESSs are maintained equally. The effectiveness of the proposed control strategy is validated through the simulation by using a MATLAB/Simulink environment.

Tight bound on parameter of surplus-based averaging algorithm over balanced digraphs

ABSTRACT We study a continuous-time surplus-based algorithm for multi-agent average consensus, and derive a tight upper bound on the key parameter included in this algorithm that ensures convergence over strongly connected and balanced digraphs. We specialise the upper bound result to undirected (connected) graphs and unweighted cyclic digraphs; in particular, for undirected graphs the algorithm converges for arbitrary positive values of the parameter, and for cyclic digraphs the upper bound on the parameter depends only on the number of agents and may be easily calculated. Moreover, it is suggested through extensive simulation that, for the same number of agents, the upper bound for cyclic digraphs be smaller than that for other strongly connected and possibly unbalanced digraphs; this implies that as long as the parameter satisfies the upper bound for cyclic digraphs, this parameter can work for other digraphs.

Distributed Integer Weight Balancing in the Presence of Time Delays in Directed Graphs

A digraph with positive weights on its edges is weight-balanced if, for each node, the sum of the weights of the incoming edges is equal to the sum of the weights of the outgoing edges. Weight-balanced digraphs play an important role in a variety of cooperative control problems, including formation control, event-triggered coordination, distributed averaging, and optimization. Classical distributed algorithms for asymptotic average consensus typically assume timely and reliable exchange of information between neighboring components of a given multicomponent system. These assumptions are not necessarily valid in practice due to varying delays that might affect computations at different nodes and/or transmissions at different links. In this paper, we propose a distributed algorithm that solves the integer weight balancing problem in the presence of arbitrary (time-varying and inhomogeneous) time delays that might affect the transmission at a particular link at a particular time. The algorithm converges after a finite number of steps (that we explicitly bound) in the presence of bounded delays and converges in finite time (with probability one) in the case of unbounded delays (packet drops). Furthermore, we show that the resulting weight-balanced digraph is unique regardless of how time delays or packet drops manifest themselves. We also analyze the computational and communication complexity of the proposed algorithm, and provide examples to illustrate its operation and performance.

Discrete-Time Distributed Extremum-Seeking Control Over Networks With Unstable Dynamics

In this paper, we propose a discrete-time version of extremum-seeking control (ESC) which can be implemented by several agents communicating over a network. We consider the problem where several agents measure a local cost and must cooperate to minimize the total cost which is the sum of the local costs. To solve this problem, we combine a dynamic average consensus algorithm with a proportional integral ESC technique in discrete time. The consensus algorithm provides each agent with an estimate of the total cost and this estimate is used by the ESC to minimize the total cost. The main contribution of this paper is to show that the distributed agents can effectively minimize the unmeasured total cost.

Consensus-Based Droop Control of Isolated Micro-Grids by ADMM Implementations

Due to low inertia, high penetration of renewable generators in isolated micro-grids may result in poor frequency and voltage response under large disturbances. In order to overcome this difficulty, the distributed average consensus algorithm has been studied recently by extending local droop control mechanisms of power converters into distributed droop control. However, its convergence rate and the resilience to noises are still not satisfactory. In this paper, two implementations of consensus-based distributed droop control by the alternating direction multipliers method are proposed. It can be shown that the closed-loop system is described by the second-order vector differential equation, and the stability of every trajectory can be analyzed by the energy function approach under certain mild conditions. Real-time digital simulations are performed to validate the effectiveness of the proposed distributed droop control mechanism.

Distributed optimal active power dispatch with energy storage units and power flow limits in smart grids

Dynamic optimal active power dispatch with energy storage units and power flow limits is an important problem in smart grids. This problem is usually described as a convex optimization model. In our model, not only the conventional equality and inequality constraints, energy storage units’ constraints and power flow constraints are considered, but also the energy storage units’ operational costs and the power price of the main grid are considered in the total costs. To solve this problem, a fully distributed algorithm based on the alternating direction method of multipliers (ADMM), the projected gradient method and the average consensus is proposed. The proposed algorithm can obtain the optimal output power settings of the energy storage units, distributed generators and the main grid for different demand loads with different initial states. In the proposed algorithm, firstly, the dispatch problem is decomposed into multiple subproblems on the basis of the alternating direction method of multipliers; then the subproblems can be solved according to the projected gradient method and the average consensus algorithm. In order to apply the projected gradient method, every bus is equipped with a bus agent which is responsible for information communication and the output power optimization calculation. Simulation studies demonstrate the effectiveness of the proposed algorithm. .

Performance and robustness of discrete and finite time average consensus algorithms

ABSTRACTIn this paper, we review some of the main discrete and finite time average consensus implementations in the literature, discussing their strengths and shortcomings from a theoretical and empirical point of view. In particular, we compare the computational characteristics of the different algorithms, their behaviour considering different underlying network topologies, their ability to withstand packet losses and their robustness to attacks where a malicious node aims to steer the result of the algorithm towards a desired value, without letting the other nodes detect the attack. Specifically, we will discuss synchronous approaches, where the nodes broadcast their messages, and asynchronous approaches, where the nodes need to be able to address their neighbours individually on a point-to-point basis (i.e. by direct communication between a specific sender and a specific receiver). With the aim to overcome some critical aspects of the considered methodologies, in this paper we present an asynchronous consensus algorithm based on a broadcast-only approach. The algorithm is characterised by a good trade-off between the robustness of synchronous approaches and to low computational demands of asynchronous methods.

Distributed Bayesian filtering using logarithmic opinion pool for dynamic sensor networks

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent’s estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.