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Dynamical Primal-Dual Nesterov Accelerated Method and Its Application to Network Optimization

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第3期68卷 1760-1767页

作者： Zeng, Xianlin Lei, Jinlong Chen, Jie Beijing Inst Technol Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Dept Control Sci & Engn Shanghai 200070 Peoples R China

This article develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This article analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is O((1)/(t)2 ) by choosing suitable parameters. As far as we know, this is the first continuous-time primal dual accelerated method that can obtain the optimal rate. Then, this article applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.

关键词： Convergence Convex functions Cost function distributed algorithms Gradient methods Damping Trajectory Continuous-time algorithm Nesterov's accelerated method network optimization primal-dual method

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Detecting the Most Vital Articulation Points in Wireless Multi-Hop Networks

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IEEE-ACM TRANSACTIONS ON NETWORKING 2023年第5期31卷 2389-2402页

作者： Akram, Vahid Khalilpour Ugurlu, Onur Ege Univ Int Comp Inst TR-35100 Izmir Turkiye Izmir Bakircay Univ Fac Engn & Architecture TR-35665 Izmir Turkiye

An articulation point is a node whose removal partitions the network into disconnected segments. The articulation points may affect the reliability and efficiency of wireless multi hop networks from different aspects. Although all articulation points destroy the connectivity of the network, their negative impact on the network is not equal. Removing some articulation points may disconnect a large subset of nodes or generate a large number of partitions, while removing some other articulation points may only disconnect a few nodes. In this paper, we present two novel problems for identifying the most vital articulation points that significantly impact the network. The first problem is finding the p most important articulation points that minimize the largest connected component in the remaining network. The second problem is finding the p most important articulation points whose removal maximizes the number of partitions in the network. We prove that both problems are NP-Hard and propose a distributed algorithm to identify the vital articulation points in both problems. The proposed algorithm establishes a distributed depth-first search tree to identify the articulation points, assigns a score to each articulation point, and selects the prominent articulation points based on their scores. We compare the proposed algorithm with a brute force-based exact algorithm. The simulation result shows that after removing the detected prominent articulation points by the proposed algorithm, the maximum difference between the largest partition size and the number of partitions with the optimal solutions are less than 27.6% and 28.2%, respectively, while the sent bytes of the proposed algorithm can be 89.9% lower.

关键词： distributed algorithms articulation points connected components critical nodes

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Federated Consensus-Based Algorithm for Stable Recovery of Sparse Signals

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2023年第12期72卷 15719-15731页

作者： Qian, Rongrong Qi, Yuan Xue, Yue Zhou, Tianzhi Zhang, Jiyan Beijing Univ Posts & Telecommun Sch Artificial Intelligence Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun Beijing Key Lab Work Safety Intelligent Monitoring Beijing 100876 Peoples R China Beijing Univ Posts & Telecommun Sch Elect Engn Beijing 100876 Peoples R China

In this article, we develop a new algorithm, named federated consensus-based algorithm (FCB), for sparse recovery, and show its performance in terms of both support recovery and signal recovery. Specifically, FCB is designed on the basis of the federated computational architecture, to increase the computational parallelism and accelerate the convergence. The algorithm design is realized by integrating accelerated projection-based consensus (APC) with greedy techniques. Then, the conditions of exact support recovery and an upper bound of signal recovery error are derived for FCB in the noisy case. From the explicit expression of the signal recovery error bound, it is confirmed that FCB can stably recover sparse signals under appropriate conditions using the coherence statistic of the measurement matrix and the minimum magnitude of nonzero elements of the signal. Experimental results illustrate the performance of FCB, validating our derived conditions of exact support recovery and upper bound of signal recovery error. In summary, FCB utilizes the federated computational architecture, enabling high parallelism and fast convergence, and uses greedy techniques to guarantee stable recovery performance.

关键词： Stable sparse recovery distributed algorithms federated computational architecture performance analysis

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Adaptive Synchronization for Networked Parabolic PDE Systems With Uncertain Nonlinear Actuator Dynamics

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2023年第5期70卷 2167-2178页

作者： Zheng, Yukan Li, Yuan-Xin Ahn, Choon Ki Qingdao Univ Sch Automat Shandong Key Lab Ind Control Technol Qingdao 266071 Peoples R China Liaoning Univ Technol Coll Sci Jinzhou 121001 Peoples R China Korea Univ Sch Elect Engn Seoul 136701 South Korea

This article focuses on the synchronization control of networked uncertain parabolic partial differential equations (PDEs) with uncertain nonlinear actuator dynamics. Compared to existing networked PDE systems, control input occurs in ordinary differential equation (ODE) subsystems rather than in PDE ones. Compared to existing results, where the exact system parameters must be known for the entire system, this paper further considers parabolic PDE-ODE systems with unknown parameters affecting the interior of the PDE domain. Due to the unknown parameters and uncertain nonlinear actuator dynamics, the existing distributed algorithms and stability analysis tools cannot be utilized to solve the synchronization problem of cascaded parabolic systems. To address this difficulty, this study designs a novel passive identifier to estimate the states and unknown parameters. Subsequently, based on the passive identifier and Lyapunov function method, a synchronization controller is presented for cascaded parabolic PDE systems to ensure that the synchronization control and the boundedness of all the closed-loop signals are achieved. Lastly, the effectiveness of the obtained results is illustrated using simulation.

关键词： Synchronization Actuators Mathematical models Heating systems Uncertainty Lyapunov methods distributed algorithms parabolic PDE multi-agent systems actuator dynamics nonlinearity uncertainty

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Pricing Electricity in Residential Communities Using Game-Theoretical Billings

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IEEE TRANSACTIONS ON SMART GRID 2023年第2期14卷 1621-1631页

作者： Hupez, Martin Toubeau, Jean-Francois Atzeni, Italo De Greve, Zacharie Vallee, Francois Univ Mons Dept Elect Power Engn B-7000 Mons Belgium Univ Oulu Ctr Wireless Commun Oulu 90014 Finland

By sharing common assets such as the power grid, prosumers are closely interrelated by their actions and interests. Game theory provides powerful tools for increased coordination among the prosumers to optimize the energy resources. However, depending on the prosumer profiles and the market rules, the individual bills may notably differ and prove to be unfair. In this work, we analyze the outcomes of three relevant game-theoretical billing methods, which are innovatively transposed to the day-ahead scheduling of energy exchange within a liberalized residential community dominated by distributed energy resources. The first two approaches rely on a (static) daily billing scheme, while the third considers a multi-temporal (continuous) billing. The Nash equilibria are computed using distributed algorithms, hence ensuring individual decision-making and avoiding third-party dependencies. The cost distributions are assessed using both a qualitative and a quantitative comparison based on various prosumer profiles in a modern smart grid. It is shown that, depending on the billing option, either the contribution towards the entity (i.e., the ability to improve the global solution) or the individual empowerment (i.e., the ability to bargain) can be preferentially incentivized.

关键词： Costs Resource management Load modeling Scheduling Low voltage Games Game theory Billing distributed algorithms energy efficiency energy communities fairness game theory renewable energy smart grid energy storage Vickey-Clarke-Groves

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UNDERSTANDING A CLASS OF DECENTRALIZED AND FEDERATED OPTIMIZATION algorithms: A MULTIRATE FEEDBACK CONTROL PERSPECTIVE*

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SIAM JOURNAL ON OPTIMIZATION 2023年第2期33卷 652-683页

作者： Zhang, Xinwei Hong, Mingyi Elia, Nicola Univ Minnesota ECE Dept Minneapolis MN 55455 USA

distributed algorithms have been playing an increasingly important role in many applications such as machine learning, signal processing, and control. Significant research efforts have been devoted to developing and analyzing new algorithms for various applications. In this work, we provide a fresh perspective to understand, analyze, and design distributed optimization algorithms. Through the lens of multirate feedback control, we show that a wide class of distributed algorithms, including popular decentralized/federated schemes, can be viewed as discretizing a certain continuous-time feedback control system, possibly with multiple sampling rates, such as decentralized gradient descent, gradient tracking, and federated averaging. This key observation not only allows us to develop a generic framework to analyze the convergence of the entire algorithm class, but, more importantly, it also leads to an interesting way of designing new distributed algorithms. We develop the theory behind our framework and provide examples to highlight how the framework can be used in practice.

关键词： distributed algorithms convergence analysis control perspective

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A General Framework to Distribute Iterative algorithms With Localized Information Over Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第12期68卷 7358-7373页

作者： Timoudas, Thomas Ohlson Zhang, Silun Magnusson, Sindri Fischione, Carlo RISE Res Inst Sweden Div Digital Syst Comp Sci S-16440 Molndal Sweden MIT Lab Informat & Decis Syst Cambridge MA 02139 USA Stockholm Univ Dept Comp & Syst Sci S-11419 Stockholm Sweden KTH Royal Inst Technol Digital Futures S-10044 Stockholm Sweden

Emerging applications in the Internet of Things (IoT) and edge computing/learning have sparked massive renewed interest in developing distributed versions of existing (centralized) iterative algorithms often used for optimization or machine learning purposes. While existing work in the literature exhibits similarities, for the tasks of both algorithm design and theoretical analysis, there is still no unified method or framework for accomplishing these tasks. This article develops such a general framework for distributing the execution of (centralized) iterative algorithms over networks in which the required information or data is partitioned between the nodes in the network. This article furthermore shows that the distributed iterative algorithm, which results from the proposed framework, retains the convergence properties (rate) of the original (centralized) iterative algorithm. In addition, this article applies the proposed general framework to several interesting example applications, obtaining results comparable to the state of the art for each such example, while greatly simplifying and generalizing their convergence analysis. These example applications reveal new results for distributed proximal versions of gradient descent, the heavy ball method, and Newton's method. For example, these results show that the dependence on the condition number for the convergence rate of this distributed heavy ball method is at least as good as that of centralized gradient descent.

关键词： Agents and autonomous systems communication networks distributed algorithms optimization algorithms

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Semi-Decentralized Generalized Nash Equilibrium Seeking in Monotone Aggregative Games

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第1期68卷 140-155页

作者： Belgioioso, Giuseppe Grammatico, Sergio ETH Automatic Control Lab Swiss Fed Inst Technol CH-8092 Zurich Switzerland Delft Univ Technol Delft Ctr Syst & Control NL-2628CD Delft Netherlands

We address the generalized Nash equilibrium seeking problem for a population of agents playing aggregative games with affine coupling constraints. We focus on semi-decentralized communication architectures, where there is a central coordinator able to gather and broadcast signals of aggregative nature to the agents. By exploiting the framework of monotone operator theory and operator splitting, we first critically review the most relevant available algorithms and then design two novel schemes: 1) a single-layer, fixed-step algorithm with convergence guarantee for general (noncocoercive, nonstrictly) monotone aggregative games and 2) a single-layer proximal-type algorithm for a class of monotone aggregative games with linearly coupled cost functions. We also design novel accelerated variants of the algorithms via (alternating) inertial and over-relaxation steps. Finally, we show via numerical simulations that the proposed algorithms outperform those in the literature in terms of convergence speed.

关键词： distributed algorithms multi-agent systems optimization methods scalability

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Bilateral Peer-to-Peer Energy Trading via Coalitional Games

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2023年第5期19卷 6814-6824页

作者： Raja, Aitazaz Ali Grammatico, Sergio Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

In this article, we propose a bilateral peer-to-peer (P2P) energy trading scheme under single-contract and multi-contract market setups, both as an assignment game, a special class of coalitional games. The proposed market formulation allows for efficient computation of a market equilibrium while keeping the desired economic properties offered by the coalitional games. Furthermore, our market model allows buyers to have heterogeneous preferences (product differentiation) over the energy sellers, which can be economic, social, or environmental. To address the problem of scalability in coalitional games, we design a novel distributed negotiation mechanism that utilizes the geometric structure of the equilibrium solution to improve the convergence speed. Our algorithm enables market participants (prosumers) to reach a consensus on a set of "stable" and "fair" bilateral contracts which encourages prosumer participation. The negotiation process is executed with virtually minimal information requirements on a time-varying communication network that in turn preserves privacy. We use operator-theoretic tools to rigorously prove its convergence. Numerical simulations illustrate the benefits of our negotiation protocol and show that the average execution time of a negotiation step is much faster than the benchmark.

关键词： Games Contracts Peer-to-peer computing Informatics Game theory Stability analysis Costs distributed algorithms mechanism design multi-agent systems smart grids transactive energy

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Arbitrary pattern formation on infinite regular tessellation graphs

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THEORETICAL COMPUTER SCIENCE 2023年 942卷 1-20页

作者： Cicerone, Serafino Di Fonso, Alessia Di Stefano, Gabriele Navarra, Alfredo Comp Sci & Math Univ Aquila Dept Informat Engn Via Vetoio I-67100 Laquila Italy Comp Sci Univ Perugia Dept Math Via Vanvitelli 1 I-06123 Perugia Italy

Given a set R of robots, each one located at a different vertex of an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF) problem. Given a multiset F of grid vertices such that |R| = |F|, APF asks for a distributed algorithm that moves robots so as to reach a configuration similar to F. Similarity means that robots must be disposed as F regardless of translations, rotations, reflections. So far, as possible graph discretizing the Euclidean plane only the standard square grid has been considered in the context of the classical OBLOT model. However, it is natural to consider also the other regular tessellation graphs, that are triangular and hexagonal grids. In particular, the former can be considered as the most general in terms of possible symmetries and *** provide a resolution algorithm for APF when the initial configuration is asymmetric and the considered topology is any regular tessellation graph. The algorithm and its correctness are based on a rigorous methodology.(c) 2022 Elsevier B.V. All rights reserved.

关键词： distributed algorithms Mobile robots Asynchrony Pattern formation Graph

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