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distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

AUTOMATICA 2015年 55卷 254-264页

作者： Kia, Solmaz S. Cortes, Jorge Martinez, Sonia Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92717 USA Univ Calif San Diego Dept Mech & Aerosp Engn San Diego CA 92103 USA

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Cooperative control distributed convex optimization Weight-balanced digraphs Event-triggered communication

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Attack-Resilient distributed convex optimization of Cyber-Physical Systems Against Malicious Cyber-Attacks Over Random Digraphs

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IEEE INTERNET OF THINGS JOURNAL 2023年第1期10卷 458-472页

作者： Feng, Zhi Hu, Guoqiang Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore

This article addresses a resilient exponential distributed convex optimization problem for a heterogeneous linear multiagent system under Denial-of-Service (DoS) attacks over random digraphs. The random digraphs are caused by unreliable networks and the DoS attacks, allowed to occur aperiodically, refer to an interruption of the communication channels carried out by the intelligent adversaries. In contrast to many existing distributed convex optimization works over a perfect communication network, the global optimal solution might not be sought under the adverse influences that result in performance degradations or even failures of optimization algorithms. The aforementioned setting poses certain technical challenges to optimization algorithm design and exponential convergence analysis. In this work, several resilient algorithms are presented such that a team of agents minimizes a sum of local nonquadratic cost functions in a safe and reliable manner with the global exponential convergence. Numerical simulation results are further presented to validate the effectiveness of the proposed distributed approaches.

关键词： Denial-of-Service (DoS) attack distributed convex optimization heterogeneous network linear multiagent system random digraph

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Finite-Time distributed convex optimization for Continuous-Time Multiagent Systems With Disturbance Rejection

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2020年第2期7卷 686-698页

作者： Feng, Zhi Hu, Guoqiang Cassandras, Christos G. Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Boston Univ Div Syst Engn Boston MA 02446 USA Boston Univ Ctr Informat & Syst Engn Boston MA 02446 USA

This paper presents continuous distributed algorithms to solve the finite-time distributed convex optimization problems of multiagent systems in the presence of disturbances. The objective is to design distributed algorithms such that a team of agents seeks to minimize the sum of local objective functions in a finite-time and robust manner. Specifically, a distributed optimization algorithm, combined with a continuous integral sliding-mode control scheme, is proposed to solve this finite-time optimization problem, while rejecting local disturbance signals. The developed algorithm is further applied to solve economic dispatch and resource allocation problems, and proven that under proposed schemes, the optimal solution can be achieved in finite time, while satisfying both global equality and local inequality constraints. Examples and numerical simulations are provided to show the effectiveness of the proposed methods.

关键词： distributed convex optimization disturbance rejection finite-time convergence multiagent system

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Finite-Time Average Consensus Based Approach for distributed convex optimization

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ASIAN JOURNAL OF CONTROL 2020年第1期22卷 323-333页

作者： Ma, Wenlong Fu, Minyue Cui, Peng Zhang, Huanshui Li, Zhipeng Shandong Univ Sch Control Sci & Engn Jinan 250061 Peoples R China Univ Newcastle Sch Elect Engn & Comp Callaghan NSW 2308 Australia Guangdong Unvers Technol Sch Automat Guangzhou Peoples R China

In this paper, we consider a distributed convex optimization problem where the objective function is an average combination of individual objective function in multi-agent systems. We propose a novel Newton Consensus method as a distributed algorithm to address the problem. This method utilises the efficient finite-time average consensus method as an information fusion tool to construct the exact Newtonian global gradient direction. Under suitable assumptions, this strategy can be regarded as a distributed implementation of the classical standard Newton method and eventually has a quadratic convergence rate. The numerical simulation and comparison experiment show the superiority of the algorithm in convergence speed and performance.

关键词： Newton method finite-time average consensus distributed convex optimization multi-agent systems quadratic convergence

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Zero-Gradient-Sum Algorithms for distributed convex optimization: The Continuous-Time Case

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2012年第9期57卷 2348-2354页

作者： Lu, Jie Tang, Choon Yik Univ Oklahoma Sch Elect & Comp Engn Norman OK 73019 USA

This technical note presents a set of continuous-time distributed algorithms that solve unconstrained, separable, convex optimization problems over undirected networks with fixed topologies. The algorithms are developed using a Lyapunov function candidate that exploits convexity, and are called Zero-Gradient-Sum (ZGS) algorithms as they yield nonlinear networked dynamical systems that evolve invariantly on a zero-gradient-sum manifold and converge asymptotically to the unknown optimizer. We also describe a systematic way to construct ZGS algorithms, show that a subset of them actually converge exponentially, and obtain lower and upper bounds on their convergence rates in terms of the network topologies, problem characteristics, and algorithm parameters, including the algebraic connectivity, Laplacian spectral radius, and function curvatures. The findings of this technical note may be regarded as a natural generalization of several well-known algorithms and results for distributed consensus, to distributed convex optimization.

关键词： distributed consensus distributed convex optimization multi-agent systems networked dynamical systems

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Continuous-Time Coordination Algorithm for distributed convex optimization Over Weight-Unbalanced Directed Networks

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2019年第7期66卷 1202-1206页

作者： Zhu, Yanan Yu, Wenwu Wen, Guanghui Ren, Wei Southeast Univ Sch Math Nanjing 210096 Jiangsu Peoples R China Nantong Univ Dept Elect Engn Nantong Peoples R China RMIT Univ Sch Engn Melbourne Vic 3000 Australia Univ Calif Riverside Dept Elect & Comp Engn Riverside CA 95251 USA

A distributed convex optimization problem over a weight-unbalanced directed network is studied in this brief, where the global objective function is equal to the sum of strongly convex objective functions with globally Lipschitz gradients. With respect to the optimization problem, a new continuous-time coordination algorithm is proposed to compute its optimal solution in a distributed manner. The asymptotical convergence of the proposed algorithm is guaranteed by resorting to the direct sum decomposition technique, Kronecker matrix algebra, the stability of perturbed systems, and input-to-state stability. Finally, some simulations are performed to illustrate the theoretical result.

关键词： distributed convex optimization continuous-time coordination algorithm directed network

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Sampled-data Based distributed convex optimization with Event-triggered Communication

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2016年第6期14卷 1421-1429页

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

This paper studies the distributed convex optimization problem for multi-agent systems over undirected and connected networks. Motivated by practical considerations, we propose a new distributed optimization algorithm with event-triggered communication. The proposed event detection is decentralized, sampled-data and not requires periodic communications among agents to calculate the threshold. Based on Lyapunov approaches, we show that the proposed algorithm is asymptotically converge to the unknown optimizer if the design parameters are chosen properly. We also give an upper bound on the convergence rate. Finally, we illustrate the effectiveness of the proposed algorithm by a numerical simulation.

关键词： distributed convex optimization event-triggered scheme multi-agent systems sampled-data control zero-gradient-sum (ZGS) algorithm

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Continuous-time distributed Heavy-ball Algorithm for distributed convex optimization over Undirected and Directed Graphs

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Machine Intelligence Research 2022年第1期19卷 75-88页

作者： Hao-Ran Yang Wei Ni School of Science Nanchang UniversityNanchang 330031China

This paper proposes second-order distributed algorithms over multi-agent networks to solve the convex optimization problem by utilizing the gradient tracking strategy, with convergence acceleration being achieved. Both the undirected and unbalanced directed graphs are considered, extending existing algorithms that primarily focus on undirected or balanced directed graphs. Our algorithms also have the advantage of abandoning the diminishing step-size strategy so that slow convergence can be avoided. Furthermore, the exact convergence to the optimal solution can be realized even under the constant step size adopted in this paper. Finally, two numerical examples are presented to show the convergence performance of our algorithms.

关键词： distributed convex optimization second-order distributed algorithm multi-agent systems gradient tracking directed graph

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Online Learning Algorithm for distributed convex optimization With Time-Varying Coupled Constraints and Bandit Feedback

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第2期52卷 1009-1020页

作者： Li, Jueyou Gu, Chuanye Wu, Zhiyou Huang, Tingwen Chongqing Normal Univ Sch Math Sci Chongqing 400047 Peoples R China Cutin Univ Dept Math & Stat Perth WA 6845 Australia Texas A&M Univ Qatar Dept Sci Doha Qatar

This article focuses on multiagent distributed-constrained optimization problems in a dynamic environment, in which a group of agents aims to cooperatively optimize a sum of time-changing local cost functions subject to time-varying coupled constraints. Both the local cost functions and constraint functions are unrevealed to an individual agent until an action is submitted. We first investigate a gradient-feedback scenario, where each agent can access both values and gradients of cost functions and constraint functions owned by itself at the chosen action. Then, we design a distributed primal-dual online learning algorithm and show that the proposed algorithm can achieve the sublinear bounds for both the regret and constraint violations. Furthermore, we extend the gradient-feedback algorithm to a gradient-free setup, where an individual agent has only attained the values of local cost functions and constraint functions at two queried points near the selected action. We develop a bandit version of the previous method and give the explicitly sublinear bounds on the expected regret and expected constraint violations. The results indicate that the bandit algorithm can achieve almost the same performance as the gradient-feedback algorithm under wild conditions. Finally, numerical simulations on an electric vehicle charging problem demonstrate the effectiveness of the proposed algorithms.

关键词： Cost function Linear programming convex functions Resource management Cybernetics Heuristic algorithms Bandit feedback distributed convex optimization online learning regret analysis time-varying constraint

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Stability analysis of distributed convex optimization under persistent attacks: A hybrid systems approach

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AUTOMATICA 2020年 111卷 108607-000页

作者： Wang, Xue-Fang Teel, Andrew R. Liu, Kun-Zhi Sun, Xi-Ming Dalian Univ Technol Minist Educ Key Lab Intelligent Control & Optimizat Ind Equip Dalian 116024 Peoples R China Univ Calif Santa Barbara Dept Elect & Comp Engn Santa Barbara CA 93106 USA

In this paper, a distributed convex optimization algorithm under persistent attacks is investigated in the framework of hybrid dynamical systems. The existence of attacks may influence the behavior of an algorithm that solves the optimization problem. In this case, an interesting question is under what conditions the optimal solution can be found. To explore this problem, we first use differential inclusions to model attack modes and then use an average dwell-time automaton and time-ratio monitor to constrain attacks. Then based on these constraints, an inequality condition is given to ensure exponential stability of the optimal solution. Finally, a switched algorithm is modeled as a hybrid dynamical system and a Lyapunov function is constructed to show the optimal solution can be achieved exponentially under persistent attacks. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： distributed convex optimization Networked attacks Hybrid dynamical systems

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