Assuming agents possess sensing capabilities and dynamics relative to their body coordinate frames, this article addresses a displacement-based strategy for discrete-time formation control through attitude synchronization. Unlike the Eulerian approximation, the first challenge lies in developing discrete-time models that capture both position and attitude motions, thereby complementing existing continuous-time systems with a discretized version. Then, two leader-following control protocols are designed, incorporating a jointly connected topology to relax the connectivity requirements. The analysis of these systems often relies on the Lyapunov function, the existence of which may be hard to guarantee. Consequently, the geometric properties of several polytopes are explored under the dynamic topologies and time-varying parameters. By extending the ergodicity results to leader-following scenarios, these properties are characterized as positively invariant sets. This invariance, which is independent of the existence of the Lyapunov function or the solvability of its associated criteria, provides a beneficial tool for analyzing time-variant systems. Utilizing this invariance and some mathematical techniques, the desired formation shape can be achieved in cases where the attitudes of the followers synchronize with the leader. Finally, a numerical simulation validates the results.
{"title":"Discrete-Time Formation Control With Attitude Alignment: A Geometric Approach Under Ergodic Products","authors":"Zhen Li;Yang Tang;Wenbing Zhang;Yongqing Fan;Tingwen Huang","doi":"10.1109/TCNS.2025.3538743","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3538743","url":null,"abstract":"Assuming agents possess sensing capabilities and dynamics relative to their body coordinate frames, this article addresses a displacement-based strategy for discrete-time formation control through attitude synchronization. Unlike the Eulerian approximation, the first challenge lies in developing discrete-time models that capture both position and attitude motions, thereby complementing existing continuous-time systems with a discretized version. Then, two leader-following control protocols are designed, incorporating a jointly connected topology to relax the connectivity requirements. The analysis of these systems often relies on the Lyapunov function, the existence of which may be hard to guarantee. Consequently, the geometric properties of several polytopes are explored under the dynamic topologies and time-varying parameters. By extending the ergodicity results to leader-following scenarios, these properties are characterized as positively invariant sets. This invariance, which is independent of the existence of the Lyapunov function or the solvability of its associated criteria, provides a beneficial tool for analyzing time-variant systems. Utilizing this invariance and some mathematical techniques, the desired formation shape can be achieved in cases where the attitudes of the followers synchronize with the leader. Finally, a numerical simulation validates the results.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1793-1804"},"PeriodicalIF":4.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-04DOI: 10.1109/TCNS.2025.3538745
Zhiheng Dong;Shuang Shi;Ziyang Zhen
This article explores the control problem of integral event-triggered $mathcal {H}_{infty }$ time-varying formation tracking (TVFT) for unmanned aerial vehicle (UAV) swarm systems, featuring switching directed topologies. Employing the persistent dwell time (PDT) switching approach, the nonweighted $mathcal {H}_{infty }$ performance can be assured for the swarm system, which improves disturbance attenuation capability and has rarely been studied in the existing UAV formation control research to date. Meanwhile, a more advanced integral event-triggered mechanism (IETM) is devised to further decrease the triggering frequency compared to the static event-triggered one. In addition, the asynchronism due to the coexistence of event-triggered transmission and switching characteristics is taken into consideration. Building on these foundations, a comprehensive approach is developed, integrating the TVFT control scheme, the IETM, and the PDT switching, with simulation results validating its effectiveness and advantages.
{"title":"Asynchronously Integral Event-Triggered Formation Tracking in UAV Swarm Systems Featuring Switching Directed Topologies","authors":"Zhiheng Dong;Shuang Shi;Ziyang Zhen","doi":"10.1109/TCNS.2025.3538745","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3538745","url":null,"abstract":"This article explores the control problem of integral event-triggered <inline-formula><tex-math>$mathcal {H}_{infty }$</tex-math></inline-formula> time-varying formation tracking (TVFT) for unmanned aerial vehicle (UAV) swarm systems, featuring switching directed topologies. Employing the persistent dwell time (PDT) switching approach, the nonweighted <inline-formula><tex-math>$mathcal {H}_{infty }$</tex-math></inline-formula> performance can be assured for the swarm system, which improves disturbance attenuation capability and has rarely been studied in the existing UAV formation control research to date. Meanwhile, a more advanced integral event-triggered mechanism (IETM) is devised to further decrease the triggering frequency compared to the static event-triggered one. In addition, the asynchronism due to the coexistence of event-triggered transmission and switching characteristics is taken into consideration. Building on these foundations, a comprehensive approach is developed, integrating the TVFT control scheme, the IETM, and the PDT switching, with simulation results validating its effectiveness and advantages.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1251-1263"},"PeriodicalIF":4.0,"publicationDate":"2025-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-31DOI: 10.1109/TCNS.2025.3526701
{"title":"IEEE Control Systems Society Information","authors":"","doi":"10.1109/TCNS.2025.3526701","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3526701","url":null,"abstract":"","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"11 4","pages":"C2-C2"},"PeriodicalIF":4.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10865804","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-31DOI: 10.1109/TCNS.2025.3526702
{"title":"IEEE Control Systems Society Information","authors":"","doi":"10.1109/TCNS.2025.3526702","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3526702","url":null,"abstract":"","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"11 4","pages":"2276-2277"},"PeriodicalIF":4.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10865829","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143107205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-27DOI: 10.1109/TCNS.2025.3534281
Yahan Deng;Nachuan Yang;Yuzhe Li
The event-triggered scheme (ETS) has been widely used for sensor data scheduling in cyber-physical systems. Existing literature on the design of ETSs for packet drops deals with the issue of non-Gaussianity of the a posteriori distribution in the system state. On the one hand, the Gaussian assumption only derives an approximate result, while on the other hand, exact results can be obtained by numerical integration but with excessive computational complexity. To this end, in this article, we propose a stochastic ETS based on acknowledgment information for remote state estimation with smart sensors and packet drops. The transmission decision is jointly driven by the holding time at the remote end and the accumulated innovative information. Then, we inductively derive the exact probability density function of the augmented innovative information vector by the Bayesian rule, which is used to obtain the explicit form of the estimation error covariance. These exact theoretical results mean that the design of scheduling parameter sequences no longer relies on experience. Finally, numerical simulations are provided to demonstrate that the empirical results agree with the theoretical results.
{"title":"Stochastic Event-Triggered Estimation With Smart Sensors Over Packet-Dropping Links","authors":"Yahan Deng;Nachuan Yang;Yuzhe Li","doi":"10.1109/TCNS.2025.3534281","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3534281","url":null,"abstract":"The event-triggered scheme (ETS) has been widely used for sensor data scheduling in cyber-physical systems. Existing literature on the design of ETSs for packet drops deals with the issue of non-Gaussianity of the a posteriori distribution in the system state. On the one hand, the Gaussian assumption only derives an approximate result, while on the other hand, exact results can be obtained by numerical integration but with excessive computational complexity. To this end, in this article, we propose a stochastic ETS based on acknowledgment information for remote state estimation with smart sensors and packet drops. The transmission decision is jointly driven by the holding time at the remote end and the accumulated innovative information. Then, we inductively derive the exact probability density function of the augmented innovative information vector by the Bayesian rule, which is used to obtain the explicit form of the estimation error covariance. These exact theoretical results mean that the design of scheduling parameter sequences no longer relies on experience. Finally, numerical simulations are provided to demonstrate that the empirical results agree with the theoretical results.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1756-1768"},"PeriodicalIF":4.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-27DOI: 10.1109/TCNS.2025.3534459
Jing Zhou;Jun Shang;Tongwen Chen
This article examines the problem of optimal deception attacks against state estimation with partially secured measurements, where smart sensors transmit innovation sequences to the remote end for information fusion. Due to resource limitations or defensive countermeasures, the adversary can only modify data packets transmitted through unreliable channels. Meanwhile, the attack should be synthesized with sophistication to deceive an anomaly detector. To investigate the vulnerabilities of such estimation systems without feedback links and enhance security performance, the optimal attack policy is derived by formulating and explicitly solving a convex optimization problem, with the goal of maximizing the sum of estimation errors. Subsequently, a novel attack detection and resilient state estimation algorithm is proposed to ensure an acceptable level of estimation accuracy. The theoretical performance metrics, including false alarm rates for the proposed detector, are provided. Finally, the effectiveness of the results is confirmed through numerical examples.
{"title":"Worst-Case Integrity Attacks and Resilient State Estimation With Partially Secured Measurements","authors":"Jing Zhou;Jun Shang;Tongwen Chen","doi":"10.1109/TCNS.2025.3534459","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3534459","url":null,"abstract":"This article examines the problem of optimal deception attacks against state estimation with partially secured measurements, where smart sensors transmit innovation sequences to the remote end for information fusion. Due to resource limitations or defensive countermeasures, the adversary can only modify data packets transmitted through unreliable channels. Meanwhile, the attack should be synthesized with sophistication to deceive an anomaly detector. To investigate the vulnerabilities of such estimation systems without feedback links and enhance security performance, the optimal attack policy is derived by formulating and explicitly solving a convex optimization problem, with the goal of maximizing the sum of estimation errors. Subsequently, a novel attack detection and resilient state estimation algorithm is proposed to ensure an acceptable level of estimation accuracy. The theoretical performance metrics, including false alarm rates for the proposed detector, are provided. Finally, the effectiveness of the results is confirmed through numerical examples.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1769-1779"},"PeriodicalIF":4.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-27DOI: 10.1109/TCNS.2025.3534557
Bohang Fang;Changhong Zhao;Steven H. Low
Solving power flow is a fundamental problem in power systems. The normally radial (tree) topology of a distribution network induces a spatially recursive structure in ac power flow, which enables a class of efficient solution methods—backward/forward sweep (BFS). In this article, we revisit BFS from the perspective of its convergence, which was rarely addressed before. We introduce three variants of BFS algorithms: the first one calculates voltages and line currents in a single-phase network model; the second algorithm extends the first one to an unbalanced three-phase network with $Y$ and $Delta$ configurations; the third one calculates voltages and line power flows in the classical dist-flow model. We prove a sufficient condition, under which the first algorithm is a contraction mapping on a closed set of voltages and thus converges geometrically to a unique solution. This proof is extended to the second algorithm for three-phase networks. We then use the monotone convergence theorem to prove convergence of the third algorithm. We verify the convergence conditions, solution accuracy, and computational efficiency of BFS algorithms through simulations in IEEE test systems.
{"title":"Convergence of Backward/Forward Sweep for Power Flow Solution in Radial Networks","authors":"Bohang Fang;Changhong Zhao;Steven H. Low","doi":"10.1109/TCNS.2025.3534557","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3534557","url":null,"abstract":"Solving power flow is a fundamental problem in power systems. The normally radial (tree) topology of a distribution network induces a spatially recursive structure in ac power flow, which enables a class of efficient solution methods—backward/forward sweep (BFS). In this article, we revisit BFS from the perspective of its convergence, which was rarely addressed before. We introduce three variants of BFS algorithms: the first one calculates voltages and line currents in a single-phase network model; the second algorithm extends the first one to an unbalanced three-phase network with <inline-formula><tex-math>$Y$</tex-math></inline-formula> and <inline-formula><tex-math>$Delta$</tex-math></inline-formula> configurations; the third one calculates voltages and line power flows in the classical dist-flow model. We prove a sufficient condition, under which the first algorithm is a contraction mapping on a closed set of voltages and thus converges geometrically to a unique solution. This proof is extended to the second algorithm for three-phase networks. We then use the monotone convergence theorem to prove convergence of the third algorithm. We verify the convergence conditions, solution accuracy, and computational efficiency of BFS algorithms through simulations in IEEE test systems.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1780-1792"},"PeriodicalIF":4.0,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-10DOI: 10.1109/TCNS.2025.3528094
Yiyang Chen;Yongzhao Hua;Zhi Feng;Xiwang Dong
This article investigates the adaptive prescribed-time distributed Nash equilibrium (NE) seeking problems for networked games with heterogeneous dynamics and unknown uncertainties. The proposed algorithms are based on the two-layer structure, namely, the NE seeking part and the tracking control part. For players without uncertainties, adaptive parameters are utilized in the seeking part to avoid the use of global information. Auxiliary variables are constructed to seek the NE point within the prescribed time and serve as reference signals for the tracking control part. Then, state feedback control is designed to drive the strategies of all the players to the expected NE point in the prescribed time. Furthermore, the approximation theory is introduced to deal with unknown nonlinear uncertainties. Exponential parameters are involved in the designed estimates to accelerate the convergence rate. The Lyapunov method is utilized to show the prescribed-time convergence property of the algorithms. Besides, although the time-varying piecewise function is involved in the algorithms, the uniform boundedness of the control input can be ensured by carefully selecting the initial values of the auxiliary parameters. Finally, a simulation is given to show the effectiveness of the proposed algorithms.
{"title":"Adaptive Prescribed-Time Distributed Nash Equilibrium Seeking for Networked Games With Heterogeneous Dynamics and Unknown Uncertainties","authors":"Yiyang Chen;Yongzhao Hua;Zhi Feng;Xiwang Dong","doi":"10.1109/TCNS.2025.3528094","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3528094","url":null,"abstract":"This article investigates the adaptive prescribed-time distributed Nash equilibrium (NE) seeking problems for networked games with heterogeneous dynamics and unknown uncertainties. The proposed algorithms are based on the two-layer structure, namely, the NE seeking part and the tracking control part. For players without uncertainties, adaptive parameters are utilized in the seeking part to avoid the use of global information. Auxiliary variables are constructed to seek the NE point within the prescribed time and serve as reference signals for the tracking control part. Then, state feedback control is designed to drive the strategies of all the players to the expected NE point in the prescribed time. Furthermore, the approximation theory is introduced to deal with unknown nonlinear uncertainties. Exponential parameters are involved in the designed estimates to accelerate the convergence rate. The Lyapunov method is utilized to show the prescribed-time convergence property of the algorithms. Besides, although the time-varying piecewise function is involved in the algorithms, the uniform boundedness of the control input can be ensured by carefully selecting the initial values of the auxiliary parameters. Finally, a simulation is given to show the effectiveness of the proposed algorithms.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1744-1755"},"PeriodicalIF":4.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-10DOI: 10.1109/TCNS.2025.3528095
Shiyu Zhou;Dong Sun;Gang Feng
This article studies the fixed-time time-varying formation (TVF) tracking control problem for heterogeneous multiagent systems with a nonautonomous leader under a directed communication network. The primary objective is to design a TVF tracking protocol enabling the followers to form the desired TVF while simultaneously tracking the output of the nonautonomous leader in a fixed time. First, a distributed fixed-time observer is proposed to estimate the state of the nonautonomous leader under a directed communication network. Then, utilizing coordinate transformation and sliding mode techniques, a fixed-time observer-based TVF tracking protocol is developed without requiring the full row rank assumption on the input matrix of the follower. It is proved via the Lyapunov stability theory that the fixed-time TVF tracking problem with a nonautonomous leader can be solved under the proposed protocol. Finally, the effectiveness of the proposed fixed-time TVF tracking control protocol is demonstrated by numerical examples.
{"title":"Fixed-Time Formation Tracking for Heterogeneous Linear Multiagent Systems With a Nonautonomous Leader","authors":"Shiyu Zhou;Dong Sun;Gang Feng","doi":"10.1109/TCNS.2025.3528095","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3528095","url":null,"abstract":"This article studies the fixed-time time-varying formation (TVF) tracking control problem for heterogeneous multiagent systems with a nonautonomous leader under a directed communication network. The primary objective is to design a TVF tracking protocol enabling the followers to form the desired TVF while simultaneously tracking the output of the nonautonomous leader in a fixed time. First, a distributed fixed-time observer is proposed to estimate the state of the nonautonomous leader under a directed communication network. Then, utilizing coordinate transformation and sliding mode techniques, a fixed-time observer-based TVF tracking protocol is developed without requiring the full row rank assumption on the input matrix of the follower. It is proved via the Lyapunov stability theory that the fixed-time TVF tracking problem with a nonautonomous leader can be solved under the proposed protocol. Finally, the effectiveness of the proposed fixed-time TVF tracking control protocol is demonstrated by numerical examples.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1733-1743"},"PeriodicalIF":4.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-08DOI: 10.1109/TCNS.2025.3527255
Ali Beikmohammadi;Sarit Khirirat;Sindri Magnússon
Parallel stochastic gradient methods are gaining prominence in solving large-scale machine learning problems that involve data distributed across multiple nodes. However, obtaining unbiased stochastic gradients, which have been the focus of most theoretical research, is challenging in many distributed machine learning applications. The gradient estimations easily become biased, for example, when gradients are compressed or clipped, when data are shuffled, and in meta-learning and reinforcement learning. In this work, we establish worst-case bounds on parallel momentum methods under biased gradient estimation on both general nonconvex and $mu$-Polyak–Łojasiewicz problems. Our analysis covers general distributed optimization problems, and we work out the implications for special cases where gradient estimates are biased, i.e., in meta-learning and when the gradients are compressed or clipped. Our numerical experiments verify our theoretical findings and show faster convergence performance of momentum methods than traditional biased gradient descent.
{"title":"Parallel Momentum Methods Under Biased Gradient Estimations","authors":"Ali Beikmohammadi;Sarit Khirirat;Sindri Magnússon","doi":"10.1109/TCNS.2025.3527255","DOIUrl":"https://doi.org/10.1109/TCNS.2025.3527255","url":null,"abstract":"Parallel stochastic gradient methods are gaining prominence in solving large-scale machine learning problems that involve data distributed across multiple nodes. However, obtaining unbiased stochastic gradients, which have been the focus of most theoretical research, is challenging in many distributed machine learning applications. The gradient estimations easily become biased, for example, when gradients are compressed or clipped, when data are shuffled, and in meta-learning and reinforcement learning. In this work, we establish worst-case bounds on parallel momentum methods under biased gradient estimation on both general nonconvex and <inline-formula><tex-math>$mu$</tex-math></inline-formula>-Polyak–Łojasiewicz problems. Our analysis covers general distributed optimization problems, and we work out the implications for special cases where gradient estimates are biased, i.e., in meta-learning and when the gradients are compressed or clipped. Our numerical experiments verify our theoretical findings and show faster convergence performance of momentum methods than traditional biased gradient descent.","PeriodicalId":56023,"journal":{"name":"IEEE Transactions on Control of Network Systems","volume":"12 2","pages":"1721-1732"},"PeriodicalIF":4.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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