Discrete Consensus Research Articles

IMPROVING BYZANTINE FAULT TOLERANCE IN SWARM ROBOTICS COLLECTIVE DECISION-MAKING SCENARIO VIA A NEW BLOCKCHAIN CONSENSUS ALGORITHM

Swarm robotics applies concepts of swarm intelligence to robotics. Discrete consensus achievement is one of the major behaviors found in swarm robotics. Various algorithms have been developed for discrete consensus achievement. However, existing discrete consensus achievement algorithms are vulnerable to Byzantine robots. Blockchain has been successfully used to mitigate the negative effect of Byzantine robots. Nevertheless, since the blockchain solution uses the Proof-of-Work blockchain consensus algorithm, it is vulnerable to the 51% attack. Besides, the swarm also takes longer to achieve consensus. This research proposes a novel blockchain consensus algorithm called Proof-of-Identity—which uses a private-public key pair and a swarm controller—to create a dynamically permissioned blockchain that would negate the 51%-attack problem associated with the Proof-of-Work algorithm while also reducing the consensus time. This proposed solution was tested against the classical solution and the existing blockchain solution using the collective perception scenario. Test results show that the Proof-of-Identity algorithm prevents the 51%-attack problem while improving the consensus time in comparison to the existing blockchain solution without affecting the exit probability.

Distributed cooperative secondary control based on discrete consensus for DC microgrid

Aiming at overcoming the drawbacks of bus voltage deviation and current sharing accuracy degradation caused by conventional v-i droop control in primary control of DC microgrid, a distributed cooperative secondary control strategy is proposed in this paper. The strategy includes voltage restoration control and current sharing control. Discrete consensus is applied in the proposed method which considers the discrete nature of measurement, controller implementation, and communication. The controller on each converter exchanges data with only its neighbors on a sparse network of communication across the DC microgrid, further dynamically tracking the output voltage and current. In addition, the proposed control strategy can reduce the impact of communication noise on consensus convergence and accuracy by introducing the consistency gain function. The effectiveness of the proposed method is verified by a grid-connected DC microgrid system based on the MATLAB/Simulink.

Convergence analysis of the discrete consensus-based optimization algorithm with random batch interactions and heterogeneous noises

We present stochastic consensus and convergence of the discrete consensus-based optimization (CBO) algorithm with random batch interactions and heterogeneous external noises. Despite the wide applications and successful performance in many practical simulations, the convergence of the discrete CBO algorithm was not rigorously investigated in such a generality. In this work, we introduce a generalized discrete CBO algorithm with a weighted representative point and random batch interactions, and show that the proposed discrete CBO algorithm exhibits stochastic consensus and convergence toward the common equilibrium state exponentially fast under suitable assumptions on system parameters. For this, we recast the given CBO algorithm with random batch interactions as a discrete consensus model with a random switching network topology, and then we use the mixing property of interactions over sufficiently long time interval to derive stochastic consensus and convergence estimates in mean square and almost sure senses. Our proposed analysis significantly improves earlier works on the convergence analysis of CBO models with full batch interactions and homogeneous external noises.

DAGmap: Multi-Drone SLAM via a DAG-Based Distributed Ledger

Simultaneous localization and mapping (SLAM) in unmanned vehicles, such as drones, has great usability potential in versatile applications. When operating SLAM in multi-drone scenarios, collecting and sharing the map data and deriving converged maps are major issues (regarded as the bottleneck of the system). This paper presents a novel approach that utilizes the concepts of distributed ledger technology (DLT) for enabling the online map convergence of multiple drones without a centralized station. As DLT allows each agent to secure a collective database of valid transactions, DLT-powered SLAM can let each drone secure global 3D map data and utilize these data for navigation. However, block-based DLT—a so called blockchain—may not fit well to the multi-drone SLAM due to the restricted data structure, discrete consensus, and high power consumption. Thus, we designed a multi-drone SLAM system that constructs a DAG-based map database and sifts the noisy 3D points based on the DLT philosophy, named DAGmap. Considering the differences between currency transactions and data constructions, we designed a new strategy for data organization, validation, and a consensus framework under the philosophy of DAG-based DLT. We carried out a numerical analysis of the proposed system with an off-the-shelf camera and drones.

On Sampled-Data Consensus: Divide and Concur

This note studies the consensus problem for integrator agents under intermittent information exchange between connected neighbours at asynchronous sampling time instances. It proposes a novel sampled-data protocol, based on emulating suitable global analog consensus dynamics at each agent and using sampled centroids of these emulators to convey information between agents. We show that the closed-loop dynamics can be divided into centroid and disagreement parts. The former is completely autonomous and evolves according to time-varying discrete consensus dynamics, independent of the sampling intervals. The disagreement part evolves according to conventional analog consensus dynamics for a constant network topology and is driven by the emulator centroids. The system then asymptotically converges to agreement under mild assumptions on the persistency of connectivity and the uniform boundedness of sampling intervals. A substantially simplified and scalable implementation under a special emulated topology, namely the complete graph, is also proposed.

Multi-View clustering and discrete consensus based tri-level coordinated control of wind farm and adiabatic compressed air energy storage for providing frequency regulation service

Due to the intermittency and uncertainty natures of wind power, electrical energy storages (EESs) are often equipped in the power systems to reduce the side-effect of wind power fluctuations, and adiabatic compressed air energy storage (A-CAES) is one of EES technologies to smooth the power fluctuation of wind farms (WFs). This paper proposes a coordinated control framework of WF and A-CAES station to achieve frequency response, and discusses the active power distribution scheme among wind turbines (WTs) and A-CAES units during frequency regulation. Firstly, the models of WT and A-CAES used in frequency regulation are presented. Then, considering that the power distribution might go through a long iteration process when the number of WTs in WF is quite large, these WTs are clustered into several groups using a comprehensive multi-view grouping indicator. On the basis of the WTs grouping result and with a defined generalized energy increment (GEI), this paper proposes a discrete consensus based tri-level coordinated frequency control method, which divides the control into three levels, i.e., group level, wind farm level and coordinated level. Through the three levels’ control, the method can reasonably and rapidly distribute the frequency regulation powers among WTs and A-CAES units without being limited by the scale of WF, and the coordination of WF and A-CAES station during frequency regulation is achieved. To demonstrate the effectiveness of the proposed method, a modified WF in Inner Mongolia of China is utilized for case study. Simulation results show that the proposed method is valid in various frequency events and can reach consensus within 4 s in the studied cases, and it is well-performed with different capacities of wind powers and A-CAESs in the power systems. The common communication failures have few influences on the methods, and the frequency nadirs fluctuate lower than 0.1 Hz with time delays in the communications. Compared with centralized and multi-machine equivalent methods, the proposed distributed method can balance the computational speed and the solution accuracy, and thus is beneficial to improve the system frequency nadirs when frequency drops.

Distributed control strategy for global economic operation and bus restorations in a hybrid AC/DC microgrid with interconnected subgrids

With the increasing penetration of distributed generators (DGs) in microgrid (MG), the economic power dispatch (EPD) is a fundamental optimization problem of MG systems. This paper investigates a distributed control strategy, which is consists of local economic control (LEC) and global economic control (GEC), for a hybrid MG with multiple interconnected ac and dc subgrids. The incremental cost (IC) of each DG is selected as a discrete consensus variable and the mismatch of bus parameters, such as dc bus voltage and ac bus frequency, between measured and reference values is assigned as a feedback variable. Thus, both the economic power allocation demand for all DGs and the bus restorations within each subgrid can be simultaneously realized by the proposed LEC. This reduces implementation cost, enhances the operation reliability, and accelerates the converging speed of algorithm. Furthermore, the interconnected subgrids are connected by a set of bidirectional interlinking converters (BILCs) that play a critical role in the power flow performance. Hence, the distributed GEC makes the whole MG system is in global economic operation in accordance with the equal IC principle. The impacts of communication time delays and communication link failures are also analyzed. Finally, the effectiveness of the proposed control strategy is verified by the real-time hardware-in-loop (HIL) tests.

Optimal design for manipulation of random consensus over discrete information in networked systems

In distributed and cooperative systems, the network structure is determinant to the success of the strategy adopted to solve complex tasks. Those systems are primarily governed by consensus protocols whose convergence is intrinsically dependent on the network topology. Most of the consensus algorithms deal with continuous values and perform average-based strategies to reach cohesion over the exchanged information. However, many problems demand distributed consensus over countable values, that cannot be handled by traditional protocols. In such a context, this work presents an approach based on semidefinite programming to design the optimal weights of a network adjacency matrix, in order to control the convergence of a distributed random consensus protocol for variables at the discrete-space domain, based on the voter model. As a second contribution, this work uses Markov theory and the biological inspiration of epidemics to find out a dynamical spreading model that can predict the information diffusion over this discrete consensus protocol. Also, convergence properties and equilibrium points of the proposed model are presented regarding the network topology. Finally, extensive numerical simulations evaluate the effectiveness of the proposed consensus algorithm, its spreading model, and the approach for optimal weight design.

Hierarchical distributed control approach for multiple on-site DERs coordinated operation in microgrid

Micro grid (MG) is a self-controllable small-scale network developed to flexibly manage distributed energy resources (DERs). In this paper, an interlinked three-layer distributed control framework is proposed for the coordinated operation of multiple DERs in MG. In the bottom layer, an inner double-loop voltage and current controller is incorporated with a power droop controller for DER primary voltage and frequency regulation, which explores the fast response capability of DERs to counterbalance load fluctuations in MG. In the middle layer, a distributed secondary frequency and voltage control strategy based on the finite-time discrete consensus theory is implemented to correct the DER frequency and voltage offset in the bottom layer, and the proportional allocation of MG reactive load demands among multiple DERs is also achieved. In the upper layer, a distributed economic dispatch algorithm based on finite-time discrete consensus is implemented to minimize DERs total generation cost by optimizing DER active power reference coupled with the middle and bottom layers. Simulation results demonstrated that the proposed three-layer hierarchical distributed control approach is flexible for the plug-and-play behaviors of DERs and can achieve satisfactory reactive power share among multiple DERs; in addition, the approach effectively regulates DER voltage and frequency and ensures their low-cost operation.

Pattern formation of multi-AUV systems with the optical sensor based on displacement-based formation control

Associated with multi-autonomous underwater vehicle (AUV) systems, the optical sensors with short working range can be reconsidered, which can provide more detailed and more comprehensive descriptions of the seabed than acoustical sensors and can assist in communications among neighbouring AUVs. The typical achievable tasks for these multi-AUV systems equipped with optical sensors mainly include to study the seabed sediments, search small objects at the seabed, collect colourful biological samples, and monitor the underwater infrastructures, etc. The purpose of this research is to develop a new coordination strategy to make a fleet of AUVs build a geometrical pattern suitable for optical sensing at the seabed. This new coordination strategy includes two parts: designing a predefined pattern (a planar pyramid pattern) and proposing an associated formation control method (an improved asynchronous discrete consensus algorithm with a time-variant digraph via the displacement-based control, inspired from the fish schooling problem) to update the trajectories of AUVs in real-time and reach this pattern from a disorder distribution. Before it is tested at sea with six AUVs, the performance of this new coordination method is verified in the simulation environments constructed in Blender and Matlab respectively. The simulation results show the good convergence of this new coordination method.

An improved discrete consensus algorithm for reactive power sharing considering communication delay condition

An improved discrete consensus algorithm for reactive power sharing considering communication delay condition

Distributed control system architecture for balancing and stabilizing traffic in the network of multiple autonomous intersections using feedback consensus and route assignment method

Autonomous and intelligent system show a remarkable step in urban traffic management. Autonomous Intersection Management (AIM) is an outstanding example of using an autonomous vehicle and wireless communication technology. The traffic performance of a single AIM system has been proved in many works however, traffic in the network of multiple AIMs is waiting for an implementation. Coordination of traffic between intersections in the network is an important step of managing the overall networked traffic throughput. The authors modeled the traffic network with the multi-agents concept and used the discrete consensus algorithm to coordinate between autonomous agents and implemented the rerouting algorithm in order to distribute the excessive traffics to neighbored intersections with the optimal condition. Our target is to have a balance traffic in each intersection and reaches the equilibrium where the stability has been not compromised. The results show that reaching consensus condition will bring the networked traffic to an equilibrium state where a peak traffic will not be happened. In addition, this method shows that when traffic in a network reached consensus, it will also converge to the Nash equilibrium in the finite time.

Agreement Algorithm Based on a Trial and Error Method for the Best of Proportions Problem

The best-of-n problem (BSTn) is a collective decision-making problem in which a swarm of robots needs to make a collective decision about a set of n choices; specifically, to decide what choice offers the best alternative [1]. The BSTn captures the structure and logic of the discrete consensus achievement problems that appear in several swarm robotics scenarios. Although numerous algorithms have been proposed recently to deal with more than two choices, the number of choices that can be dealt with is not large. The bias and raising threshold (BRT) algorithm proposed by Phung et al. [2] enables swarms to deal with a large number of choices (n≫2). However, the algorithm’s goodness has not been evaluated in any practical problems, and it is necessary to evaluate the algorithm in a problem where a large number of choices exist. In this paper, we consider the best of proportions (BOP) problem; that is a version of BSTn in which a large number of choices can be dealt with by adjusting the values of different proportions. In previous research on swarms that needed to solve the BOP problem, there is only a study on the response threshold models for the division of labor. In the present study, we investigate a scenario of the BOP and apply the BRT algorithm to find the best proportion. In our previous work [3], a fixed proportion setting method has been adopted. Here, we adopt a stochastic proportion setting method to verify the relationship between the efficiency and the number of choices in a more general case. The results show that with a larger number of choices, the decision making becomes more efficient with high equality; that is a result that has not been found in [3].

Island DC Microgrid Hierarchical Coordinated Multi-Mode Control Strategy

As renewable energy sources connecting to power systems continue to improve and new-type loads, such as electric vehicles, grow rapidly, direct current (DC) microgrids are attracting great attention in distribution networks. In order to satisfy the voltage stability requirements of island DC microgrids, the problem of inaccurate load power dispatch caused by line resistance must be solved and the defects of centralized communication and control must be overcome. A hierarchical, coordinated, multiple-mode control strategy based on the switch of different operation modes is proposed in this paper and a three-layer control structure is designed for the control strategy. Based on conventional droop control, a current-sharing layer and a multi-mode switching layer are used to ensure the stable operation of the DC microgrid. Accurate load power dispatch is satisfied using a difference discrete consensus algorithm. Furthermore, virtual bus voltage information is applied to guarantee smooth switching between various modes, which safeguards voltage stability. Simulation verification is carried out for the proposed control strategy by power systems computer aided design/electromagnetic transients including DC (PSCAD/EMTDC). The results indicate that the proposed control strategy guarantees the voltage stability of island DC microgrids and accurate load power dispatch under different operation modes.

Dynamic modeling of discrete leader-following consensus with impulses

A leader-following consensus of discrete-time multi-agent systems with nonlinear intrinsic dynamics and impulses is investigated. We propose and prove conditions ensuring a leader-following consensus. Numerical examples are given to illustrate effectiveness of the obtained results. Also, the necessity and sufficiency of the obtained conditions are shown.

A clustered neighbourhood consensus algorithm for a generic agent interaction protocol

This paper significantly contributes a consensus algorithm to enhance the efficiency of existing generic interaction protocol for multiagent systems (GIPMAS). The proposed algorithm is marriage of neighbourhood algorithm and discrete time consensus protocol and the neighbourhood algorithm focuses on providing more weight to communication links/edges joining two clusters as compared to links joining two agents in a cluster, which increases rate of convergence of information. Thus, in clustered network of agents, cluster head and executive cluster head would be responsible for deriving consensus in the received information. Simulation reflects that proposed mechanism improves time of convergence of information. However, slight increase in task execution is also observed due to trade-off between quality of output and complexity of mechanism.

Distributed Piecewise Approximation Economic Dispatch for Regional Power Systems Under Non-Ideal Communication

Appropriate distributed economic dispatch (DED) strategies are of great importance to manage wide-area controllable generators in wide-area regional power systems. Compared with existing works related to ED, where dispatch algorithms are carried out by a centralized controller, a practical DED scheme is proposed in this paper to achieve the optimal dispatch by appropriately allocating the load to generation units while guaranteeing consensus among incremental costs. The ED problem is decoupled into several parallel sub-problems by the primal-dual principle to address the computational issue of satisfying power balance between the demand and the supply from the distributed regional power system. The feasibility test and an innovative mechanism for unit commitment are then designed to handle extreme operation situations, such as low load level and surplus generation. In the designed mechanism, the on/off status of units is determined in a fully distributed framework, which is solved using the piecewise approximation method and the discrete consensus algorithm. In the algorithm, the push-sum protocol is proposed to increase the system adaptation on the time-varying communication topology. Moreover, consensus gain functions are designed to ensure the performance of the proposed DED under communication noise. Case studies on a standard IEEE 30-bus system demonstrate the effectiveness of our proposed methodology.

Hierarchical Distributed Coordinated Control Strategy for Hybrid Energy Storage Array System

A hierarchical distributed control structure is proposed for the optimal operation of a hybrid energy storage array system (HESAS) composed of multiple battery units and supercapacitor units. A grouping control strategy is established for multiple battery units. The upper layer is the coordinated control layer. To realize the coordinated and safe operation of a battery energy storage system (BESS) and supercapacitor energy storage system (SCSS), a two time-scale optimization model based on model predictive control (MPC) is proposed. The long time-scale model provides reference values for the short time-scale model, whereas the short time-scale model optimizes the real-time power demand based on the reference values to ensure that the state of charge and power of the BESS and SCSS are within the safe operation region. The lower layer is the distributed control layer. To quickly decompose the power commands sent by the upper layer, the weighted discrete consensus algorithm based on MPC is used to realize the adaptive allocation of power between the units with the same energy storage. The convergence speed of the proposed algorithm is improved by shrinking the weighted matrix. The results show that the proposed control structure, model, and grouping strategy have certain advantages in terms of control performance, convergence speed, and in extending battery life.

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.

Consensus-based local information coordination for the networked control of the autonomous intersection management

Autonomous intersection management (AIM) will be a future method for improving traffic efficiency in the urban area. Instead of using the traffic signal control like nowadays, it uses wireless communication with autonomous vehicles to support the management of road traffic more safely and efficiently. A single AIM shows an exceptional performance in managing traffics at an intersection. However, it could not be represented a traffic in the real world, which is composed of multiple intersections. We show that coordination of traffic information among vehicles and infrastructures is an essential part of macroscopic traffic management. Coordination of traffic information among the network of AIMs is the key to improve the overall traffic flow throughout the network not only has an optimal flow in some intersections and very heavy traffic in others. In this paper, we introduce the distributed control to a graph-based intersection network to control traffic in a macroscopic level. Vehicle to infrastructure and infrastructure to infrastructure communication are used to exchange the traffic information between a single autonomous vehicle to the network of autonomous intersections. We implement a discrete time consensus algorithm to coordinate the traffic density of an intersection with its neighborhoods and determine the control policy to maximize a traffic throughput of each intersection as well as stabilizing the overall traffic in the network. We use the Greenshields traffic model to define the boundary condition of various traffic flows to the corresponded traffic density and velocity. Our proposed method represents the ability to maintain traffic flow rate of each intersection without having a back up traffic. As well, every intersection operates under the uncongested flow condition. The simulation results of the graph-based networked control of a multiple autonomous intersection showed that the overall traffic flow in the network achieves up to 20% higher than using traffic signal system.