Pub Date : 2026-03-01Epub Date: 2026-01-07DOI: 10.1016/j.automatica.2026.112825
Zhaoming Qin, Alireza Karimi
In this paper, we propose a data-driven approach to robust feedback controller design for unknown linear time-invariant (LTI) dynamic systems. Using input-state trajectories and prior knowledge of unknown-but-bounded disturbances, the objective is to synthesize a state-feedback controller that achieves robust stabilization and performance while employing a common quadratic Lyapunov function. Previous works have exclusively considered bounded disturbances described by quadratic matrix inequalities (QMIs) and pointwise or constraints. In contrast, this paper introduces a more general framework that characterizes disturbance bounds using compact basic semi-algebraic (BSA) sets, thereby capturing both time-domain and frequency-domain properties. We cast the necessary and sufficient conditions for quadratic stabilization and performance as convex sum-of-squares (SOS) optimization problems. Additionally, we propose relaxation methods to reduce computational complexity by leveraging the geometric and structural properties of the polynomials defining the BSA sets. Simulation results demonstrate the efficiency and flexibility of the proposed approach.
{"title":"Efficient sum-of-squares approach to data-driven robust controller design under generalized bounded disturbances","authors":"Zhaoming Qin, Alireza Karimi","doi":"10.1016/j.automatica.2026.112825","DOIUrl":"10.1016/j.automatica.2026.112825","url":null,"abstract":"<div><div>In this paper, we propose a data-driven approach to robust feedback controller design for unknown linear time-invariant (LTI) dynamic systems. Using input-state trajectories and prior knowledge of unknown-but-bounded disturbances, the objective is to synthesize a state-feedback controller that achieves robust stabilization and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> performance while employing a common quadratic Lyapunov function. Previous works have exclusively considered bounded disturbances described by quadratic matrix inequalities (QMIs) and pointwise <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> constraints. In contrast, this paper introduces a more general framework that characterizes disturbance bounds using compact basic semi-algebraic (BSA) sets, thereby capturing both time-domain and frequency-domain properties. We cast the necessary and sufficient conditions for quadratic stabilization and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> performance as convex sum-of-squares (SOS) optimization problems. Additionally, we propose relaxation methods to reduce computational complexity by leveraging the geometric and structural properties of the polynomials defining the BSA sets. Simulation results demonstrate the efficiency and flexibility of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112825"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2026-01-10DOI: 10.1016/j.automatica.2026.112823
Yu-Ang Wang , Zidong Wang , Lei Zou , Fan Wang , Hongli Dong
In this paper, the problem of resilient recursive state estimation is addressed for a class of nonlinear cyber–physical systems operating under token bucket protocols and subject to probabilistic bit flips. Measurement signals are transmitted to the remote estimator only when the token storage surpasses the token consumption required for transmission. The communication process employs a binary encoding scheme, which quantizes measurement outputs into a bit string, transmits them through memoryless binary symmetric channels subject to probabilistic bit flips, and subsequently recovers them at the receiver. To achieve the desired estimation performance, a resilient state estimator is developed to mitigate the adverse effects of random perturbations in the estimator gain during implementation. The aim is to design a recursive state estimation algorithm that effectively manages the token bucket protocol, addresses probabilistic bit flips, and accommodates estimator gain perturbations. An upper bound for the estimation error covariance is derived, and the corresponding estimator gain is recursively calculated to minimize this bound. Finally, numerical simulations are conducted to validate the effectiveness of the proposed algorithm.
{"title":"Resilient state estimation for nonlinear cyber–physical systems under probabilistic bit flips: A token bucket protocol","authors":"Yu-Ang Wang , Zidong Wang , Lei Zou , Fan Wang , Hongli Dong","doi":"10.1016/j.automatica.2026.112823","DOIUrl":"10.1016/j.automatica.2026.112823","url":null,"abstract":"<div><div>In this paper, the problem of resilient recursive state estimation is addressed for a class of nonlinear cyber–physical systems operating under token bucket protocols and subject to probabilistic bit flips. Measurement signals are transmitted to the remote estimator only when the token storage surpasses the token consumption required for transmission. The communication process employs a binary encoding scheme, which quantizes measurement outputs into a bit string, transmits them through memoryless binary symmetric channels subject to probabilistic bit flips, and subsequently recovers them at the receiver. To achieve the desired estimation performance, a resilient state estimator is developed to mitigate the adverse effects of random perturbations in the estimator gain during implementation. The aim is to design a recursive state estimation algorithm that effectively manages the token bucket protocol, addresses probabilistic bit flips, and accommodates estimator gain perturbations. An upper bound for the estimation error covariance is derived, and the corresponding estimator gain is recursively calculated to minimize this bound. Finally, numerical simulations are conducted to validate the effectiveness of the proposed algorithm.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112823"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145939236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.automatica.2025.112785
Hao Yu , Zhe Guan , Toru Yamamoto , Junzheng Wang
This paper studies sampled-data tracking control problems for first-order nonlinear time-invariant plants. A sampled-data adaptive PI controller is developed from exact discretization and full form dynamic linearization (FFDL) methods. To ensure the uniform boundedness of adaptive PI parameters with respect to sufficiently small sampling periods, novel lifted FFDL models and cost functions are introduced for designing controllers and adaptive rules. After establishing nonlinear closed-loop dynamics, new overall Lyapunov functions containing logarithmic operation are constructed for proving global stability and convergence. An extension to locally Lipschitz dynamics is given. Finally, two numerical examples and a practical application in longitudinal speed tracking for electrical cars are simulated to illustrate the efficiency and feasibility of the proposed results.
{"title":"FFDL-based sampled-data adaptive PI control with uniformly bounded parameters","authors":"Hao Yu , Zhe Guan , Toru Yamamoto , Junzheng Wang","doi":"10.1016/j.automatica.2025.112785","DOIUrl":"10.1016/j.automatica.2025.112785","url":null,"abstract":"<div><div>This paper studies sampled-data tracking control problems for first-order nonlinear time-invariant plants. A sampled-data adaptive PI controller is developed from exact discretization and full form dynamic linearization (FFDL) methods. To ensure the uniform boundedness of adaptive PI parameters with respect to sufficiently small sampling periods, novel lifted FFDL models and cost functions are introduced for designing controllers and adaptive rules. After establishing nonlinear closed-loop dynamics, new overall Lyapunov functions containing logarithmic operation are constructed for proving global stability and convergence. An extension to locally Lipschitz dynamics is given. Finally, two numerical examples and a practical application in longitudinal speed tracking for electrical cars are simulated to illustrate the efficiency and feasibility of the proposed results.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112785"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-19DOI: 10.1016/j.automatica.2025.112766
Yan-Jun Liu, Wenguang Zan, Li Tang
This study explores the event-triggered based output feedback consensus issue for multi-agent systems (MASs) under denial-of-service (DoS) attacks. All agents in the considered systems are governed by parabolic partial differential equations (PDEs). Faced with unpredictable system states and malicious attackers launching non-periodic DoS attacks, an event-triggered security control agreement for MASs is introduced and achieve consensus on any given undirected communication graph. The tolerable frequency and duration of DoS attacks are outlined in relation to the observer-based security consensus problem. By employing Lyapunov technique and mathematical inequalities, the sufficient conditions to ensure the global asymptotic stability of MASs under DoS attacks are given. Furthermore, a rigorous demonstration of the minimum dwell time between successive triggered events is furnished. Finally, simulation examples effectively validate the theoretical findings.
{"title":"DoS attacks in parabolic multi-agent systems: An output feedback based event-triggered control approach","authors":"Yan-Jun Liu, Wenguang Zan, Li Tang","doi":"10.1016/j.automatica.2025.112766","DOIUrl":"10.1016/j.automatica.2025.112766","url":null,"abstract":"<div><div>This study explores the event-triggered based output feedback consensus issue for multi-agent systems (MASs) under denial-of-service (DoS) attacks. All agents in the considered systems are governed by parabolic partial differential equations (PDEs). Faced with unpredictable system states and malicious attackers launching non-periodic DoS attacks, an event-triggered security control agreement for MASs is introduced and achieve consensus on any given undirected communication graph. The tolerable frequency and duration of DoS attacks are outlined in relation to the observer-based security consensus problem. By employing Lyapunov technique and mathematical inequalities, the sufficient conditions to ensure the global asymptotic stability of MASs under DoS attacks are given. Furthermore, a rigorous demonstration of the minimum dwell time between successive triggered events is furnished. Finally, simulation examples effectively validate the theoretical findings.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112766"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-16DOI: 10.1016/j.automatica.2025.112743
Tao Jiang , Yan Yan , Shuanghe Yu , Ge Guo
This paper investigates the zero-gradient-sum (ZGS) scheme, free from local minimization, to second-order multiagent systems with disturbances, achieving predefined-time distributed optimization. Therein, three time-varying functions are adopted to uniformly achieve the predefined-time convergence for agents, which is beneficial for reducing the complexity of theoretical analysis and computation. Specifically, within the sliding mode control framework, the ZGS manifold and the global optimal consensus are realized within a predefined time, which is preset by a single parameter and independent of the initial conditions. Finally, the theoretical results are validated through simulation.
{"title":"Predefined-time distributed optimization for second-order multiagent systems: Zero-gradient-sum scheme","authors":"Tao Jiang , Yan Yan , Shuanghe Yu , Ge Guo","doi":"10.1016/j.automatica.2025.112743","DOIUrl":"10.1016/j.automatica.2025.112743","url":null,"abstract":"<div><div>This paper investigates the zero-gradient-sum (ZGS) scheme, free from local minimization, to second-order multiagent systems with disturbances, achieving predefined-time distributed optimization. Therein, three time-varying functions are adopted to uniformly achieve the predefined-time convergence for agents, which is beneficial for reducing the complexity of theoretical analysis and computation. Specifically, within the sliding mode control framework, the ZGS manifold and the global optimal consensus are realized within a predefined time, which is preset by a single parameter and independent of the initial conditions. Finally, the theoretical results are validated through simulation.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112743"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2026-01-05DOI: 10.1016/j.automatica.2025.112748
Mario Di Ferdinando , Alessandro Borri , Stefano Di Gennaro , Pierdomenico Pepe
In this paper, the digital event-based stabilization problem under safety constraints is studied for nonlinear systems with state delays. In particular, a methodology for the design of quantized sampled-data event-triggered safe stabilizers is provided for nonlinear systems affected by state delays. The proposed design procedure relies on the notion of Safe Steepest Descent Feedback (SSDF) which is based on the combination of Steepest Descent Feedbacks and Barrier functions. The stabilization in the sample-and-hold sense theory is used as a tool to show the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of SSDFs, updated through a proposed event-triggered mechanism, ensures the semi-global practical safe stability property of the related closed-loop system with arbitrarily small final target ball of the origin. A first order spline approximation is used to cope with the possible unavailability in the buffer of required past values of the state measurements. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. The proposed theoretical results are validated through an application concerning the plasma glucose regulation problem in Type-2 diabetic patients via artificial pancreas.
{"title":"Safety constrained digital control of nonlinear systems with state delays","authors":"Mario Di Ferdinando , Alessandro Borri , Stefano Di Gennaro , Pierdomenico Pepe","doi":"10.1016/j.automatica.2025.112748","DOIUrl":"10.1016/j.automatica.2025.112748","url":null,"abstract":"<div><div>In this paper, the digital event-based stabilization problem under safety constraints is studied for nonlinear systems with state delays. In particular, a methodology for the design of quantized sampled-data event-triggered safe stabilizers is provided for nonlinear systems affected by state delays. The proposed design procedure relies on the notion of Safe Steepest Descent Feedback (SSDF) which is based on the combination of Steepest Descent Feedbacks and Barrier functions. The stabilization in the sample-and-hold sense theory is used as a tool to show the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of SSDFs, updated through a proposed event-triggered mechanism, ensures the semi-global practical safe stability property of the related closed-loop system with arbitrarily small final target ball of the origin. A first order spline approximation is used to cope with the possible unavailability in the buffer of required past values of the state measurements. In the theory here developed, time-varying sampling periods and the non-uniform quantization of both input/output channels are allowed. The proposed theoretical results are validated through an application concerning the plasma glucose regulation problem in Type-2 diabetic patients via artificial pancreas.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112748"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-15DOI: 10.1016/j.automatica.2025.112740
Tenglong Kang , Ding Liu , Zhiwu Li
This paper addresses the verification of prognosability under attack in discrete event systems modeled with finite state automata. A sensor attacker is able to launch attacks on the observations sent from sensors to an operator for monitoring a system. We provide the notion of robust prognosability against attacks, which captures the features that the occurrence of any fault can still be predicted prior to its occurrence in the case of sensor attacks. To verify it, we propose a verifier under attack, from which a necessary and sufficient condition for robust prognosability verification is presented. It is shown that the verification requires polynomial time with respect to the number of states and events of a system.
{"title":"Robust prognosability of discrete event systems against stealthy sensor attacks","authors":"Tenglong Kang , Ding Liu , Zhiwu Li","doi":"10.1016/j.automatica.2025.112740","DOIUrl":"10.1016/j.automatica.2025.112740","url":null,"abstract":"<div><div>This paper addresses the verification of prognosability under attack in discrete event systems modeled with finite state automata. A sensor attacker is able to launch attacks on the observations sent from sensors to an operator for monitoring a system. We provide the notion of robust prognosability against attacks, which captures the features that the occurrence of any fault can still be predicted prior to its occurrence in the case of sensor attacks. To verify it, we propose a verifier under attack, from which a necessary and sufficient condition for robust prognosability verification is presented. It is shown that the verification requires polynomial time with respect to the number of states and events of a system.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112740"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-26DOI: 10.1016/j.automatica.2025.112808
Hai-Tao Zhang , Jiayu Zou , Xingjian Liu
It has long been a challenging task for optimal coverage control of multi-agent systems (MASs) in non-convex surface environments often encountered in real coordinated detection applications. To this end, this paper develops a surface cooperative control scheme for MASs to perform coverage operations. First, a coverage surface partition protocol is devised to divide a non-convex surface into multiple sectorial sub-surfaces. Accordingly, a performance index in surface coverage is established considering the curvature spatial evolution of the surface environments. Thereby, a random-initial-point algorithm is designed to minimize the performance index, and a surface-constrained optimal control law is developed to deploy MASs at niche positions. Significantly, sufficient conditions are derived to guarantee the asymptotical stability of the present scheme. Finally, numerical simulations are conducted to verify the effectiveness of the present surface coverage design.
{"title":"Cooperative optimal surface coverage control of multi-agent systems in non-convex surface environments","authors":"Hai-Tao Zhang , Jiayu Zou , Xingjian Liu","doi":"10.1016/j.automatica.2025.112808","DOIUrl":"10.1016/j.automatica.2025.112808","url":null,"abstract":"<div><div>It has long been a challenging task for optimal coverage control of multi-agent systems (MASs) in non-convex surface environments often encountered in real coordinated detection applications. To this end, this paper develops a surface cooperative control scheme for MASs to perform coverage operations. First, a coverage surface partition protocol is devised to divide a non-convex surface into multiple sectorial sub-surfaces. Accordingly, a performance index in surface coverage is established considering the curvature spatial evolution of the surface environments. Thereby, a random-initial-point algorithm is designed to minimize the performance index, and a surface-constrained optimal control law is developed to deploy MASs at niche positions. Significantly, sufficient conditions are derived to guarantee the asymptotical stability of the present scheme. Finally, numerical simulations are conducted to verify the effectiveness of the present surface coverage design.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112808"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-22DOI: 10.1016/j.automatica.2025.112783
Linghuan Kong , Wei He , Carlos Silvestre
This paper proposes a novel two-layer prescribed performance control strategy for underactuated unmanned aerial vehicles (UAVs) with unknown mass. Unlike conventional approaches that heavily rely on barrier functions—often producing large control signals and potential instability due to actuator limitations—the proposed method introduces soft and hard performance bounds on position and velocity errors. A smooth switching mechanism selectively activates the barrier function, thereby reducing its usage and enhancing system robustness. To accommodate these bounds, a new integral-multiplicative barrier-like (IMBL) Lyapunov function is developed to determine the desired thrust. Second-order linear systems are employed as low-pass filters in the backstepping design, lowering computational complexity and improving robustness against disturbances. An adaptive law is integrated into the framework for real-time mass estimation, and torque inputs are derived accordingly. Simulation results demonstrate the effectiveness of the method and validate the theoretical analysis.
{"title":"A two-layer adaptive control framework for prescribed performance in unmanned aerial vehicles","authors":"Linghuan Kong , Wei He , Carlos Silvestre","doi":"10.1016/j.automatica.2025.112783","DOIUrl":"10.1016/j.automatica.2025.112783","url":null,"abstract":"<div><div>This paper proposes a novel two-layer prescribed performance control strategy for underactuated unmanned aerial vehicles (UAVs) with unknown mass. Unlike conventional approaches that heavily rely on barrier functions—often producing large control signals and potential instability due to actuator limitations—the proposed method introduces soft and hard performance bounds on position and velocity errors. A smooth switching mechanism selectively activates the barrier function, thereby reducing its usage and enhancing system robustness. To accommodate these bounds, a new integral-multiplicative barrier-like (IMBL) Lyapunov function is developed to determine the desired thrust. Second-order linear systems are employed as low-pass filters in the backstepping design, lowering computational complexity and improving robustness against disturbances. An adaptive law is integrated into the framework for real-time mass estimation, and torque inputs are derived accordingly. Simulation results demonstrate the effectiveness of the method and validate the theoretical analysis.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112783"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2026-03-01Epub Date: 2025-12-22DOI: 10.1016/j.automatica.2025.112796
Fatemeh Fardno , S. Rasoul Etesami
Motivated by applications in job scheduling, queuing networks, and load balancing in cyber–physical systems, we develop and analyze a game-theoretic framework to balance the load among servers in static and dynamic settings. In these applications, jobs/tasks are held by selfish entities that do not want to coordinate with each other, yet the goal is to balance the load among servers in a distributed manner. First, we provide a static game formulation in which each player holds a job with a specific processing requirement and wants to schedule it fractionally among a set of heterogeneous servers to minimize its average processing time. We show that this static game is a potential game with a pure Nash equilibrium (NE). In particular, the best-response dynamics converge to such an NE after iterations, where is the number of players. Additionally, we bound the price of anarchy (PoA) of the static game in terms of game parameters. We then extend our results to a dynamic game setting, where jobs arrive and get processed, and players observe the load on the servers to decide how to schedule their jobs. In this setting, we show that if the players update their strategies using dynamic best-response, the system eventually becomes fully load-balanced and the players’ strategies converge to the pure NE of the static game. In particular, we show that the convergence time scales only polynomially with respect to the game parameters. Finally, we provide numerical results to evaluate the performance of our proposed algorithms.
{"title":"A game-theoretic framework for distributed load balancing: Static and dynamic game models","authors":"Fatemeh Fardno , S. Rasoul Etesami","doi":"10.1016/j.automatica.2025.112796","DOIUrl":"10.1016/j.automatica.2025.112796","url":null,"abstract":"<div><div>Motivated by applications in job scheduling, queuing networks, and load balancing in cyber–physical systems, we develop and analyze a game-theoretic framework to balance the load among servers in static and dynamic settings. In these applications, jobs/tasks are held by selfish entities that do not want to coordinate with each other, yet the goal is to balance the load among servers in a distributed manner. First, we provide a static game formulation in which each player holds a job with a specific processing requirement and wants to schedule it fractionally among a set of heterogeneous servers to minimize its average processing time. We show that this static game is a potential game with a pure Nash equilibrium (NE). In particular, the best-response dynamics converge to such an NE after <span><math><mi>n</mi></math></span> iterations, where <span><math><mi>n</mi></math></span> is the number of players. Additionally, we bound the price of anarchy (PoA) of the static game in terms of game parameters. We then extend our results to a dynamic game setting, where jobs arrive and get processed, and players observe the load on the servers to decide how to schedule their jobs. In this setting, we show that if the players update their strategies using dynamic best-response, the system eventually becomes fully load-balanced and the players’ strategies converge to the pure NE of the static game. In particular, we show that the convergence time scales only polynomially with respect to the game parameters. Finally, we provide numerical results to evaluate the performance of our proposed algorithms.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112796"},"PeriodicalIF":5.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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