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Event-triggered zero-gradient-sum distributed convex optimisation over networks with time-varying topologies

INTERNATIONAL JOURNAL OF CONTROL 2019年第12期92卷 2829-2841页

作者： Liu, Jiayun Chen, Weisheng Dai, Hao Xidian Univ Sch Math & Stat Xian 710071 Shaanxi Peoples R China Shandong Jianzhu Univ Sch Sci Jinan 250101 Shandong Peoples R China Xidian Univ Sch Aerosp Sci & Technol Xian 710071 Shaanxi Peoples R China

This paper focuses on a distributed convex optimisation problem over networks with time-varying topologies. First, an event-triggered strategy is employed to reduce computation and communication load in the networked systems. Second, the exponential convergence of event-triggered zero-gradient-sum algorithm is guaranteed if the corresponding time-varying network topology satisfies a new connected condition, called cooperatively connected condition. This condition does not require topologies constantly connected or jointly connected but only requires the integral of the Laplacian matrix of the network topology over a period of time is connected. Hence, it is suitable for more general time-varying topologies. Third, a convergence analysis technique is developed which is based on the difference of the Lyapunov function rather than its differentiation. Finally, a simulation example is provided to verify the results obtained in this paper.

关键词： distributed convex optimisation event-triggered time-varying topologies consensus

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Relaxed hybrid consensus ADMM for distributed convex optimisation with coupling constraints

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IET CONTROL THEORY AND APPLICATIONS 2019年第17期13卷 2828-2837页

作者： Olama, Alireza Bastianello, Nicola Mendes, Paulo R. C. Camponogara, Eduardo Univ Fed Santa Catarina Dept Automat & Syst Engn Florianopolis SC Brazil Univ Padua Dept Informat Engn Via Gradenigo 6-B I-35131 Padua Italy

In this study, the solution of a convex distributed optimisation problem with a global coupling inequality constraint is considered. By using the Lagrange duality framework, the problem is transformed into a distributed consensus optimisation problem and then based on the recently proposed Hybrid Alternating Direction Method of Multipliers (H-ADMM), which merges distributed and centralised optimisation concepts problems, a novel distributed algorithm is developed. In particular, the authors offer a reformulation of the original H-ADMM in an operator theoretical framework, which exploits the known relationship between ADMM and Douglas-Rachford splitting. In addition, the authors' formulation allows us to generalise the H-ADMM by including a relaxation constant, not present in the original design of the algorithm. Moreover, an adaptive penalty parameter selection scheme that consistently improves the practical convergence properties of the algorithm is proposed. Finally, the convergence results of the proposed algorithm are discussed and moreover, in order to present the effectiveness and the major capabilities of the proposed algorithm in off-line and on-line scenarios, distributed quadratic programming and distributed model predictive control problems are considered in the simulation section.

关键词： gradient methods distributed algorithms convex programming distributed control iterative methods predictive control quadratic programming convergence of numerical methods convergence relaxed hybrid consensus ADMM distributed convex optimisation coupling constraints convex distributed optimisation problem global coupling inequality constraint Lagrange duality framework distributed consensus optimisation problem centralised optimisation concepts problems original H-ADMM operator theoretical framework Douglas-Rachford splitting adaptive penalty parameter selection scheme distributed quadratic programming distributed model predictive control problems distributed algorithm hybrid alternating direction method hybrid alternating direction method of multipliers

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distributed convex optimisation with event-triggered communication in networked systems

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2016年第16期47卷 3876-3887页

作者： Liu, Jiayun Chen, Weisheng Xidian Univ Sch Aerosp Sci & Technol Xian Peoples R China

This paper studies the distributed convex optimisation problem over directed networks. Motivated by practical considerations, we propose a novel distributed zero-gradient-sum optimisation algorithm with event-triggered communication. Therefore, communication and control updates just occur at discrete instants when some predefined condition satisfies. Thus, compared with the time-driven distributed optimisation algorithms, the proposed algorithm has the advantages of less energy consumption and less communication cost. Based on Lyapunov approaches, we show that the proposed algorithm makes the system states asymptotically converge to the solution of the problem exponentially fast and the Zeno behaviour is excluded. Finally, simulation example is given to illustrate the effectiveness of the proposed algorithm.

关键词： Zero-gradient-sum (ZGS) algorithm distributed convex optimisation event-triggered scheme consensus multi-agent systems

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distributed dynamic event-triggered algorithm with positive minimum inter-event time for convex optimisation problem

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INTERNATIONAL JOURNAL OF CONTROL 2022年第5期95卷 1363-1370页

作者： Shi, Xiasheng Lin, Zhiyun Zheng, Ronghao Wang, Xuesong China Univ Min & Technol Sch Informat & Control Engn Xuzhou Jiangsu Peoples R China Hangzhou Dianzi Univ Sch Automat Hangzhou Peoples R China Zhejiang Univ Coll Elect Engn Hangzhou Peoples R China

In this study, we investigate the distributed convex optimisation problem of the multi-agent system over an undirected network, in which the global objective function is the sum of all the local cost functions and the local cost function of each agent is only known by itself. In order to save the computation and communication resources, the above optimisation problem is addressed by designing two zero-gradient-sum algorithms with state-based dynamic event-triggered mechanism, where the information communication only occurs at some discrete triggering time instants. The Zeno behaviour of the above event-triggered control scheme is excluded by the existence of the positive minimum inter-event time (MIET). The convergence is proved based on the Lyapunov method. Finally, we illustrate and evaluate the effectiveness of the proposed event-triggered algorithms through numerical experiments on simulated.

关键词： distributed convex optimisation event-triggered zero-gradient-sum algorithm minimum inter-event time

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distributed dynamic event-triggered algorithm with minimum inter-event time for multi-agent convex optimisation

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2021年第7期52卷 1440-1451页

作者： Shi, Xiasheng Lin, Zhiyun Yang, Tao Wang, Xuesong China Univ Min & Technol Sch Informat & Control Engn Xuzhou Jiangsu Peoples R China Hangzhou Dianzi Univ Sch Automat Artificial Intelligence Inst Hangzhou Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang Peoples R China

In this paper, the distributed convex optimisation problem of the multi-agent system over an undirected network is investigated, in which the local objective function of each agent is only known by itself. To reduce the communication consumption between agents, a state-based dynamic event-triggered algorithm with positive minimum inter-event time (MIET) is provided, where the aperiodic information communication only occurs at some discrete triggering time instants. Moreover, the sampling control technology is combined into the previous event-triggered algorithm for verifying the event-triggered condition at every sampling time, instead of continuous access. Finally, several numerical simulations are presented for illustrating and verifying the proposed algorithms.

关键词： distributed convex optimisation event-triggered sampling control minimum inter-event time

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distributed zero-gradient-sum optimisation algorithm with an edge-based adaptive event-triggered mechanism

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INTERNATIONAL JOURNAL OF CONTROL 2025年第5期98卷 1191-1200页

作者： Liu, Jiayun Shandong Jianzhu Univ Fengming Rd Jinan 250101 Shandong Peoples R China

This paper addresses the continuous-time distributed optimisation problem over networks, where the global objective function is formed by a sum of convex local objective functions. To avoid continuous communication among agents, a distributed adaptive Zero-Gradient-Sum (ZGS) optimisation algorithm under a dynamic event-triggered scheme is proposed. This is achieved by dynamically adjusting the coupling strengths of adjacent agents within the network. Our analysis confirms that the proposed algorithm will exponentially converge to the optimal solution provided that the underlying communication graph is undirected and connected. Additionally, we demonstrate that our event-triggered scheme is not subject to Zeno behaviour, which is a theoretical concern in systems with frequent event triggers.

关键词： distributed convex optimisation event-triggered adaptive control multi-agent system

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Event-triggered scheme for zero-gradient-sum optimisation under directed networks with time delay

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2021年第1期52卷 47-56页

作者： Zhao, Zhongyuan Chen, Gang Nanjing Univ Informat Sci & Technol Coll Automat Nanjing 210044 Peoples R China Chongqing Univ Coll Automat Chongqing 400044 Peoples R China

The paper investigates the distributed convex optimisation problem of multi-agent systems over strongly connected and balanced digraph with time delay. To reduce the traffic among agents and the control inputs' update frequency, a sample-based distributed event-triggered zero-gradient-sum optimisation algorithm has been proposed. A sufficient stability condition with respect to the related parameters and time delay is derived via the Lyapunov function approach. Moreover, it is proved that the states of agents asymptotically converge to the global optimal point. Since the sampling control is adopted, Zeno behaviour can be naturally excluded. The results of the numerical simulation illustrate the effectiveness of the proposed algorithm.

关键词： distributed convex optimisation multi-agent systems event-triggered time delay directed networks

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Event-triggered zero-gradient-sum distributed optimisation algorithm with time-varying communication delays

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2021年第1期52卷 110-125页

作者： Liu, Jiayun Xie, Jin Shandong Jianzhu Univ Sch Sci Jinan 250101 Peoples R China Xidian Univ Sch Math & Stat Xian Peoples R China

This paper addresses an event-triggered distributed convex optimisation problem over networks with time-varying delays. The communication between agents is triggered by conditions monitored by nodes. The proposed triggering condition is decentralised and does not require continuous communications among agents to calculate the threshold. By constructing a new Lyapunov-Krasovskii function, the optimisation problem is solved, and the explicit sufficient condition for the maximum admissible time delay is derived. Moreover, the Zeno behaviour of the closed-loop system is excluded. Finally, a simulation example is provided to verify the results obtained in this paper.

关键词： distributed convex optimisation event-triggered time-varying delays consensus multi-agent system

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Event-Triggered Zero-Gradient-Sum distributed Algorithm for convex Optimization with Time-Varying Communication Delays and Switching Directed Topologies

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Journal of Applied Mathematics and Physics 2022年第4期10卷 1247-1265页

作者： Lei Ye Department of Mathematics College of Information Science and Technology Jinan University Guangzhou China

Nowadays, distributed optimization algorithms are widely used in various complex networks. In order to expand the theory of distributed optimization algorithms in the direction of directed graph, the distributed convex optimization problem with time-varying delays and switching topologies in the case of directed graph topology is studied. The event-triggered communication mechanism is adopted, that is, the communication between agents is determined by the trigger conditions, and the information exchange is carried out only when the conditions are met. Compared with continuous communication, this greatly saves network resources and reduces communication cost. Using Lyapunov-Krasovskii function method and inequality analysis, a new sufficient condition is proposed to ensure that the agent state finally reaches the optimal state. The upper bound of the maximum allowable delay is given. In addition, Zeno behavior will be proved not to exist during the operation of the algorithm. Finally, a simulation example is given to illustrate the correctness of the results in this paper.

关键词： distributed convex optimisation Zero-Gradient-Sum Algorithm Event-Triggered Time-Varying Delays Switching Network Multi-Agent System Directed Network

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QUANTISATION EFFECTS IN distributed optimisation

QUANTISATION EFFECTS IN DISTRIBUTED OPTIMISATION

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Jonkman, Joseph A. G. Sherson, Thomas Heusdens, Richard Delft Univ Technol Circuits & Syst Grp Delft Netherlands

ISBN: (纸本)9781538646588

In this paper the effects of quantisation on distributed convex optimisation algorithms are explored via the lens of monotone operator theory. Specifically, by representing transmission quantisation via an additive noise model, we demonstrate how quantisation can be viewed as an instance of an inexact Krasnosel'skii-Mann scheme. In the case of two distributed solvers, the Alternating Direction Method of Multipliers and the Primal Dual Method of Multipliers, we further demonstrate how an adaptive quantisation scheme can be constructed to reduce transmission costs between nodes. Finally for the Gaussian channel capacity maximisation problem, we demonstrate convergence even in the presence of one-bit uniform quantisation based on the aforementioned adaptive quantisation scheme.

关键词： Quantisation Monotone Operator Theory distributed convex optimisation PDMM ADMM

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