Multilayer proportional-integral consensus of heterogeneous multi-agent systems

A distributed proportional-integral multilayer strategy is proposed, to achieve consensus in networks of heterogeneous first-order linear systems. The closed-loop network can be seen as an instance of so-called multiplex networks currently studied in network science. The strategy is able to guarantee consensus, even in the presence of constant disturbances and heterogeneous node dynamics. Contrary to previous approaches in the literature, the proportional and integral actions are deployed here on two different layers across the network, each with its own topology. Explicit expressions for the consensus values are obtained together with sufficient conditions guaranteeing convergence. The effectiveness of the theoretical results are illustrated via numerical simulations using a power network example

Multilayer proportional-integral consensus of heterogeneous multi-agent systems

A distributed proportional-integral multilayer strategy is proposed, to achieve consensus in networks of heterogeneous first-order linear systems. The closed-loop network can be seen as an instance of so-called multiplex networks currently studied in network science. The strategy is able to guarantee consensus, even in the presence of constant disturbances and heterogeneous node dynamics. Contrary to previous approaches in the literature, the proportional and integral actions are deployed here on two different layers across the network, each with its own topology. Explicit expressions for the consensus values are obtained together with sufficient conditions guaranteeing convergence. The effectiveness of the theoretical results are illustrated via numerical simulations using a power network example

Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents

In this paper, we propose a multiplex proportional-integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Sufficient conditions for convergence are derived that depend upon the structure of the network, the parameters characterizing the control layers and the node dynamics. The effectiveness of the theoretical results is illustrated using a power network model as a representative example.Comment: 13 pages, 6 Figures, Preprint submitted to Automatic

Opinion dynamics in social networks: From models to data

Opinions are an integral part of how we perceive the world and each other. They shape collective action, playing a role in democratic processes, the evolution of norms, and cultural change. For decades, researchers in the social and natural sciences have tried to describe how shifting individual perspectives and social exchange lead to archetypal states of public opinion like consensus and polarization. Here we review some of the many contributions to the field, focusing both on idealized models of opinion dynamics, and attempts at validating them with observational data and controlled sociological experiments. By further closing the gap between models and data, these efforts may help us understand how to face current challenges that require the agreement of large groups of people in complex scenarios, such as economic inequality, climate change, and the ongoing fracture of the sociopolitical landscape.Comment: 22 pages, 3 figure

다층레이어 네트워크 구조를 가지는 선형 시불변 다개체 시스템의 상태일치

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·정보공학부, 2021. 2. 심형보.전통적으로 다 개체 시스템의 상태 일치 문제는 한 가지의 네트워크 상에서 한 가지의 정보를 주고받는 경우에 대해서 주로 연구가 되었다. 하지만 최근에는 이러한 가정은 보다 복잡한 상호작용을 나타내는 데 한계가 있기 때문에 새로운 접근법이 필요한 상황이다. 본 논문에서는 각 개체가 서로 다른 정보를 서로 다른 네트워크 상에서 주고받는 경우를 고려한다. 이러한 관계를 표현하기 위해 다층레이어 네트워크 (multilayer network)라는 개념을 도입하였다. 이때 동적인 제어기로 방향성이 없는 네트워크에서 상태 일치를 이루는 새로운 필요충분조건을 제시한다. 특히 제시한 조건은 그래프 이론적인 조건과 시스템 이론적인 조건을 결합하였으며, 통신 네트워크와 주고받는 정보의 상호작용을 강조한다. 더 나아가 제시한 조건을 사용하여 방향성이 없는 네트워크상에서 상태 일치를 이루는 관측기 기반 동적 제어기를 제시한다. 주요 결과는 방향성이 있는 네트워크 상에서 출력 일치를 이루는 문제로 확장한다. 아쉽게도 이 상황에서는 제시한 조건은 더 이상 필요충분조건이 되지 못하며 이런 어려움들을 다양한 예제를 통해서 설명한다. 그럼에도 불구하고, 개체의 동역학에 추가적인 조건을 가함으로써 방향성이 없는 네트워크에서 필요충분조건을 회복한다. 또한 방향성이 있는 네트워크에서 출력 일치 문제를 푸는 충분조건을 제시하고 이를 이루는 제어기를 제안한다. 본 논문의 효용성은 여러 가지 적용 예제를 통해 보인다. 첫 번째로 분산 관측 문제를 다층 레이어 네트워크 상의 상태 일치 문제로 표현한다. 제시된 방법을 사용하면 주변 개체와의 통신량을 기존 결과들 보다 줄이는 새로운 분산 관측기를 제시한다. 두번째로 논문의 결과를 사용해 편대 제어 문제를 푼다. 특히, 원하는 편대의 모양이 개체의 상대적인 위치와 상대적인 각도로 주어진 경우를 고려한다. 제시한 방법을 사용하여 원하는 편대를 이루는 동적 제어기를 제시하였고, 편대의 크기를 유기적으로 조절하는 알고리즘을 제시한다. 마지막으로 다층 레이어 네트워크를 분산 최적화 문제에 적용을 한다. 이를 통해 매시간 결정 변수의 일부분만을 통신하는 통신적으로 더 효율적인 알고리즘을 제시한다.Traditionally, the consensus of multi-agent systems is often studied by assuming that there is a single network consisting of a single type of interaction. Recently, such an assumption is being challenged due to its limitation in representing more complex interactions. In this thesis, we consider the case where each agent is interacting using multiple, different types of output information. In order to model such interactions, the concept of a multilayer graph is employed. A novel necessary and sufficient condition is proposed for the existence of a dynamic coupling law to achieve state consensus for a multi-agent system over an undirected network. Specifically, the proposed condition couples graph theoretic conditions with system theoretic conditions and highlights the interplay between the communication network and information exchange between agents. Furthermore, based on the proposed condition, an observer-based dynamic controller is designed to achieve state consensus over an undirected network. The main results are then extended to output consensus problem over a directed network. Unfortunately, the proposed conditions are no longer necessary and sufficient and the challenge is illustrated through various examples. Nevertheless, additional assumptions are made on the dynamics of the agent to recover the equivalence for output consensus over the undirected multilayer network. A sufficient condition is also given for output consensus problem over the directed network and the corresponding controller design is presented. The effectiveness of the work is shown by a series of applications of the main results. First, the distributed state estimation problem is formulated into a consensus problem over a multilayer network. The proposed approach allowed us to develop a novel design for a distributed observer that communicates less information with its neighbors compared to existing designs. Secondly, the main results are applied to the formation control problem. Specifically, we consider the case when the desired formation is given by a combination of relative positional constraint and bearing constraint. Using the proposed approach, a dynamic controller is designed to achieve the desired formation while organically scaling the overall size of the formation. Finally, a multilayer network is also applied to the distributed optimization problem. Through multilayer networks, a communication-efficient algorithm is proposed which only communicates a part of the decision vector at each time instant.ABSTRACT i List of Figures ix List of Tables ix Notation and Symbols xi 1 Introduction 1 1.1 Research Background 1 1.2 Contributions and Outline of Dissertation 7 2 Preliminaries on Graph Theory and Convex Optimization 13 2.1 Graph Theory and Consensus Problem 13 2.1.1 Basic Definitions 13 2.1.2 Connectedness of the Graph 14 2.1.3 Laplacian Matrix and Its Properties 17 2.2 Multilayer Graph Theory 22 2.3 Convex Optimization 24 2.3.1 Convex Functions and Useful Properties 24 2.3.2 Optimization Algorithms 28 3 Consensus Problem over the Multilayer Network 41 3.1 Problem Formulation 41 3.2 A Necessary and Sufficient Condition for State Consensus 45 3.3 Proof of Necessity 51 3.4 Proof of Sufficiency 58 3.4.1 Additional Considerations for the Controllers 63 4 Extension to Output Consensus over Directed Network 67 4.1 Necessary Conditions for the Output Consensus Problem 67 4.2 Challenges for the Output Consensus over Directed Networks 71 4.3 Controller Design for the Output Consensus Problem 74 4.3.1 Controller Design under System Theoretic Constraint 74 4.3.2 Controller Design under Information Structural Constraint 82 4.4 Static Output Diffusive Coupling 84 4.5 Summary of Results 86 4.5.1 Comparison with Single-layer Consensus Problem 86 4.5.2 Relation between Necessary and Sufficient Conditions 87 5 Application to the Distributed State Estimation Problem 89 5.1 Problem Formulation 89 5.2 Distributed State Estimation over Static Network 92 5.2.1 Design Procedures 100 5.3 Distributed State Estimation over Switching Network 103 5.4 Simulation Results 111 6 Application to the Formation Control Problem 115 6.1 Problem Formulation 115 6.2 Formation Control Problem using Multilayer Network 117 6.3 Simulation Results 119 6.3.1 Achieving a Static Formation 119 6.3.2 Scaling Formation via Multilayer Network 123 7 Application to the Distributed Optimization Problem 127 7.1 Problem Formulation 127 7.2 Distributed PI Algorithm 129 7.2.1 Distributed PI Algorithm under Static Network 129 7.2.2 State Transformation for Analysis 132 7.3 Convergence Analysis for the PI Algorithm 136 7.3.1 Convergence with Weak Coupling 136 7.3.2 Convergence with Strong Coupling 139 7.3.3 Convergence under Fast Switching 153 7.4 Construction of Distributed Algorithms 158 7.4.1 Distributed Gradient Descent Method 158 7.4.2 Distributed Heavy-ball Method 160 7.4.3 Distributed Heavy-ball Method with Cyclic Coordinate Descent 166 7.5 Numerical Experiments 170 7.5.1 Distributed PI Algorithm 170 7.5.2 Distributed Heavy-ball Algorithm 172 7.6 Remark on the Study of Continuous-time Algorithms 175 8 Conclusions and Further Issues 177 APPENDIX 183 A.1 Technical Lemmas 183 A.2 Comparisons with Existing Consensus Problems 185 A.2.1 Consensus Problem of Homogeneous Agents over Singlelayer Network 186 A.2.2 Consensus Problem of Heterogeneous Agents over Singlelayer Network 188 A.2.3 Consensus Problem over Matrix-weighted Network 190 A.3 Detectability Interpretation of the Necessary Conditions 191 BIBLIOGRAPHY 195 국문초록 209Docto

Distributed frequency regulation system for interconnected microgrids based on heterogeneous agent theory

Abstract. The increase in the use of distributed energy resources such as photovoltaic panels and wind turbines and the development of most efficient energy storage systems has allowed the implementation of microgrids. This concept includes a geographical area in which storage, generation, and loads can be operated connected or islanded of the distribution network. A microgrid can be AC or DC according to the current in the common bus. In an AC microgrid inverters are required due to the nature of some distributed energy resources; this implies the regulation of voltage and frequency. It can be done either using a centralized method which involves the use of a very reliable communication system or using an entirely decentralized model in which each agent (in this case each inverter) do not communicate with the others. An intermediate approach allows each agent communicate with its neighbors without the needing of a complex communication network. Frequency regulation must guaranty the same value for the whole system, for this purpose consensus equation is used. This method is used to regulate not only the frequency and the voltage for the inverters inside a microgrid but the frequency in several interconnected microgrids. This consensus approach supposes that each agent is identical to the others without having into account the particularities of each one. A frequency regulation method for a microgrids cluster is simulated and verified using a non-identical agent approach.Resumen El aumento en el uso de fuentes distribuidas de energía y recursos de almacenamiento distribuido en las últimas décadas tales como paneles solares, turbinas de viento y bancos de baterias, ha permitido el desarrollo del concepto de Microrred. Una microrred, que agrupa generadores y almacenamiento distribuidos, puede funcionar en AC o DC dependiendo del su bus común. La microrred es definida por un área geográfica capaz de suplir su propia demanda incluso cuando funciona desconectada del sistema de potencia convencional. En un escenario futuro, varias microrredes en modo isla, podrán conectarse entre ellas formando un grupo o 'cluster'. En este trabajo se presenta un sistema de regulación de frecuencia para un grupo de microrredes. Se propone un control jerárquico distribuido basado en teoría de agentes heterogéneos, es decir, agentes no-idénticos. Este control permite la conexión y desconexión de microrredes en el nivel más alto, o la conexión y desconexión de inversores en un nivel inferior. El sistema y sus controladores son verificados por simulación.Maestrí

Multiagent-Based Control for Plug-and-Play Batteries in DC Microgrids with Infrastructure Compensation

The influence of the DC infrastructure on the control of power-storage flow in micro- and smart grids has gained attention recently, particularly in dynamic vehicle-to-grid charging applications. Principal effects include the potential loss of the charge–discharge synchronization and the subsequent impact on the control stabilization, the increased degradation in batteries’ health/life, and resultant power- and energy-efficiency losses. This paper proposes and tests a candidate solution to compensate for the infrastructure effects in a DC microgrid with a varying number of heterogeneous battery storage systems in the context of a multiagent neighbor-to-neighbor control scheme. Specifically, the scheme regulates the balance of the batteries’ load-demand participation, with adaptive compensation for unknown and/or time-varying DC infrastructure influences. Simulation and hardware-in-the-loop studies in realistic conditions demonstrate the improved precision of the charge–discharge synchronization and the enhanced balance of the output voltage under 24 h excessively continuous variations in the load demand. In addition, immediate real-time compensation for the DC infrastructure influence can be attained with no need for initial estimates of key unknown parameters. The results provide both the validation and verification of the proposals under real operational conditions and expectations, including the dynamic switching of the heterogeneous batteries’ connection (plug-and-play) and the variable infrastructure influences of different dynamically switched branches. Key observed metrics include an average reduced convergence time (0.66–13.366%), enhanced output-voltage balance (2.637–3.24%), power-consumption reduction (3.569–4.93%), and power-flow-balance enhancement (2.755–6.468%), which can be achieved for the proposed scheme over a baseline for the experiments in question.</p

Multilayer event‐based distributed control system for DC microgrids with non‐uniform delays and directional communication

The secondary control layer of microgrids is often modelled as a multi-agent distributed system, coordinated based on consensus protocols. Convergence time of consensus algorithm significantly affects transient stability of microgrids, due to changes in communication topology, switching of distributed generations (DGs), and uncertainty of intermittent energy sources. To minimise convergence time in consensus protocol, this work proposes a multilayer event-based consensus control framework, which is resilient to communication delays and supports plug-and-play (P&P) addition or removal of DGs in DC microgrids of cellular energy systems. A novel bi-layer optimisation algorithm minimises convergence time by selecting an optimal communication topology graph and then adjusts controllers' parameters. Average consensus is achieved among distributed controllers using an event-based consensus protocol, considering non-uniform delays between agents. A realisation method has also been introduced using the directional beamforming technique for topology assignment algorithm based on modern telecommunication technologies. Provided feasibility case study has been implemented on a real-time hardware-in-the-loop (HIL) experimental testbed, to validate the performance of the proposed framework for key purposes of voltage stabilisation and balanced power-sharing in DC microgrids

On the assessment of cyber risks and attack surfaces in a real-time co-simulation cybersecurity testbed for inverter-based microgrids

The integration of variable distributed generations (DGs) and loads in microgrids (MGs) has made the reliance on communication systems inevitable for information exchange in both control and protection architectures to enhance the overall system reliability, resiliency and sustainability. This communication backbone in turn also exposes MGs to potential malicious cyber attacks. To study these vulnerabilities and impacts of various cyber attacks, testbeds play a crucial role in managing their complexity. This research work presents a detailed study of the development of a real-time co-simulation testbed for inverter-based MGs. It consists of a OP5700 real-time simulator, which is used to emulate both the physical and cyber layer of an AC MG in real time through HYPERSIM software; and SEL-3530 Real-Time Automation Controller (RTAC) hardware configured with ACSELERATOR RTAC SEL-5033 software. A human–machine interface (HMI) is used for local/remote monitoring and control. The creation and management of HMI is carried out in ACSELERATOR Diagram Builder SEL-5035 software. Furthermore, communication protocols such as Modbus, sampled measured values (SMVs), generic object-oriented substation event (GOOSE) and distributed network protocol 3 (DNP3) on an Ethernet-based interface were established, which map the interaction among the corresponding nodes of cyber-physical layers and also synchronizes data transmission between the systems. The testbed not only provides a real-time co-simulation environment for the validation of the control and protection algorithms but also extends to the verification of various detection and mitigation algorithms. Moreover, an attack scenario is also presented to demonstrate the ability of the testbed. Finally, challenges and future research directions are recognized and discussed