Pub Date : 2026-01-17DOI: 10.1016/j.sysconle.2026.106358
Yuchen Yang , Kaihong Lu , Long Wang
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this problem, a distributed clipped stochastic gradient descent algorithm is proposed, and the high probability convergence of the algorithm is studied. Existing works on distributed algorithms involving stochastic gradients only consider the light-tailed noises. Different from them, we study the case with heavy-tailed settings. Under mild assumptions on the graph connectivity, we prove that the algorithm converges in high probability under a certain clipping operator. Finally, a simulation is provided to demonstrate the effectiveness of our theoretical results.
{"title":"High probability convergence of distributed clipped stochastic gradient descent with heavy-tailed noise","authors":"Yuchen Yang , Kaihong Lu , Long Wang","doi":"10.1016/j.sysconle.2026.106358","DOIUrl":"10.1016/j.sysconle.2026.106358","url":null,"abstract":"<div><div>In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this problem, a distributed clipped stochastic gradient descent algorithm is proposed, and the high probability convergence of the algorithm is studied. Existing works on distributed algorithms involving stochastic gradients only consider the light-tailed noises. Different from them, we study the case with heavy-tailed settings. Under mild assumptions on the graph connectivity, we prove that the algorithm converges in high probability under a certain clipping operator. Finally, a simulation is provided to demonstrate the effectiveness of our theoretical results.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106358"},"PeriodicalIF":2.5,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038500","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 : 2026-01-16DOI: 10.1016/j.sysconle.2025.106339
Javier F. Rosenblueth, Niels H. Wacher
This paper gives a direct and elementary proof of the Legendre–Clebsch necessary condition of optimality for a control problem of Bolza involving equality and inequality mixed constraints. The novelty of the approach consists in showing that the condition holds even if the standard rank hypothesis (or nondegeneracy condition) made on the nature of the mixed constraints is replaced with a weaker hypothesis based on the multipliers associated with the extremal under consideration, thus broadening its range of applicability.
{"title":"The Legendre–Clebsch condition for a control problem of Bolza","authors":"Javier F. Rosenblueth, Niels H. Wacher","doi":"10.1016/j.sysconle.2025.106339","DOIUrl":"10.1016/j.sysconle.2025.106339","url":null,"abstract":"<div><div>This paper gives a direct and elementary proof of the Legendre–Clebsch necessary condition of optimality for a control problem of Bolza involving equality and inequality mixed constraints. The novelty of the approach consists in showing that the condition holds even if the standard rank hypothesis (or nondegeneracy condition) made on the nature of the mixed constraints is replaced with a weaker hypothesis based on the multipliers associated with the extremal under consideration, thus broadening its range of applicability.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106339"},"PeriodicalIF":2.5,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979607","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 : 2026-01-15DOI: 10.1016/j.sysconle.2025.106340
Xuqian Ju , Qing Sun , Dario Dennstädt , Karl Worthmann , Dajun Du , Minrui Fei
This paper presents a novel data-driven predictive control strategy for discrete-time switched nonlinear systems. By leveraging the Koopman operator framework, we construct a linear surrogate model that effectively captures the systems’ nonlinear dynamics, significantly enhancing prediction accuracy over standard Koopman methods that ignore switching behavior. We then formulate a Model Predictive Control (MPC) scheme based on this linear predictor. The proposed controller is designed for systems with known switching times, incorporating the sequence into the optimization horizon. Critically, we also formulate the controller to handle cases where the switching sequence is a decision variable, thereby enabling joint optimization of both the control input and the discrete mode switching. Numerical simulations demonstrate the method’s feasibility and its significant advantages in both state prediction and control performance compared to traditional nonlinear and switched-system control strategies.
{"title":"Model predictive control for nonlinear switched systems based on Koopman theory","authors":"Xuqian Ju , Qing Sun , Dario Dennstädt , Karl Worthmann , Dajun Du , Minrui Fei","doi":"10.1016/j.sysconle.2025.106340","DOIUrl":"10.1016/j.sysconle.2025.106340","url":null,"abstract":"<div><div>This paper presents a novel data-driven predictive control strategy for discrete-time switched nonlinear systems. By leveraging the Koopman operator framework, we construct a linear surrogate model that effectively captures the systems’ nonlinear dynamics, significantly enhancing prediction accuracy over standard Koopman methods that ignore switching behavior. We then formulate a Model Predictive Control (MPC) scheme based on this linear predictor. The proposed controller is designed for systems with known switching times, incorporating the sequence into the optimization horizon. Critically, we also formulate the controller to handle cases where the switching sequence is a decision variable, thereby enabling joint optimization of both the control input and the discrete mode switching. Numerical simulations demonstrate the method’s feasibility and its significant advantages in both state prediction and control performance compared to traditional nonlinear and switched-system control strategies.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106340"},"PeriodicalIF":2.5,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979606","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 : 2026-01-15DOI: 10.1016/j.sysconle.2026.106355
Nguyen Trong Hieu , Dang Hai Nguyen
We propose and analyze a stochastic tumor–immune interaction model subject to periodic impulsive treatment, capturing the combined effects of chemotherapy and immunotherapy. The model extends previous deterministic frameworks by incorporating environmental noise and treatment-induced state-dependent impulses, leading to a hybrid stochastic differential system. We rigorously classify the long-term behavior of the system, providing sharp conditions for the extinction and persistence of tumor cells. Unlike earlier studies that treat impulses deterministically and yield limited insight, our framework accounts for random fluctuations in treatment efficacy and immune response. We derive explicit threshold conditions that determine the effectiveness of the combined therapies, offering practical guidelines for improving treatment outcomes. Our analysis framework can be extended to study a broad class of stochastic hybrid models recently introduced in tumor–immune dynamics.
{"title":"Complete classification of the long-term behavior of a tumor–immune model with impulsive therapeutic interventions","authors":"Nguyen Trong Hieu , Dang Hai Nguyen","doi":"10.1016/j.sysconle.2026.106355","DOIUrl":"10.1016/j.sysconle.2026.106355","url":null,"abstract":"<div><div>We propose and analyze a stochastic tumor–immune interaction model subject to periodic impulsive treatment, capturing the combined effects of chemotherapy and immunotherapy. The model extends previous deterministic frameworks by incorporating environmental noise and treatment-induced state-dependent impulses, leading to a hybrid stochastic differential system. We rigorously classify the long-term behavior of the system, providing sharp conditions for the extinction and persistence of tumor cells. Unlike earlier studies that treat impulses deterministically and yield limited insight, our framework accounts for random fluctuations in treatment efficacy and immune response. We derive explicit threshold conditions that determine the effectiveness of the combined therapies, offering practical guidelines for improving treatment outcomes. Our analysis framework can be extended to study a broad class of stochastic hybrid models recently introduced in tumor–immune dynamics.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106355"},"PeriodicalIF":2.5,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979540","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 : 2026-01-14DOI: 10.1016/j.sysconle.2026.106356
Liangquan Zhang , Xun Li
In this paper, we employ a Hilbert space approach based on orthogonal decomposition to investigate an optimal control problem associated with a linear conditional McKean–Vlasov dynamic, where the control process is allowed to be adapted to the filtration generated by both common and idiosyncratic noises under random coefficients. By applying the stochastic maximum principle, we derive the optimal feedback control and characterize the corresponding value function in terms of backward stochastic Riccati differential equations. Furthermore, an application to conditional mean–variance portfolio selection in an incomplete market setting is provided.
{"title":"A Hilbert space method to LQ optimal control of conditional McKean–Vlasov dynamics","authors":"Liangquan Zhang , Xun Li","doi":"10.1016/j.sysconle.2026.106356","DOIUrl":"10.1016/j.sysconle.2026.106356","url":null,"abstract":"<div><div>In this paper, we employ a Hilbert space approach based on orthogonal decomposition to investigate an optimal control problem associated with a linear conditional McKean–Vlasov dynamic, where the control process is allowed to be adapted to the filtration generated by both common and idiosyncratic noises under random coefficients. By applying the stochastic maximum principle, we derive the optimal feedback control and characterize the corresponding value function in terms of backward stochastic Riccati differential equations. Furthermore, an application to conditional mean–variance portfolio selection in an incomplete market setting is provided.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106356"},"PeriodicalIF":2.5,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979539","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 : 2026-01-14DOI: 10.1016/j.sysconle.2025.106329
Feng Xiao , Xiaoyu Wang , Bo Wei , Qian Feng
In networked systems with limited communication capacities, model-based control can reduce the frequency of data transmission and control updates by estimating the system dynamics during each sampling interval. In this paper, synchronization problems in asynchronous networked systems with model uncertainties are investigated under model-based hybrid edge-event-triggered control. A novel model-based hybrid edge-event-triggering scheme is proposed, where the term hybrid refers to the combination of an edge-event-triggering condition and a sampling scheduling mechanism. Sampling tasks are rescheduled via a timer when the event detection logic returns TRUE, ensuring a positive lower bound for inter-sampling time intervals. Prediction models based on relative states are developed without requiring exact prior knowledge of system matrices. A robust model-based controller is proposed accounting for communication delays in the transmission links. The control gain parameter is designed using the available model information. Sufficient conditions for systems to achieve synchronization and conditions for the design of prediction models are derived using an integral approach. Our stability results contribute to the robustness analysis of asynchronous networked systems with parameter uncertainties. Simulation results are provided to illustrate the effectiveness of this novel approach.
{"title":"Synchronization of asynchronous networked systems via hybrid edge-event-triggered control with model uncertainties","authors":"Feng Xiao , Xiaoyu Wang , Bo Wei , Qian Feng","doi":"10.1016/j.sysconle.2025.106329","DOIUrl":"10.1016/j.sysconle.2025.106329","url":null,"abstract":"<div><div>In networked systems with limited communication capacities, model-based control can reduce the frequency of data transmission and control updates by estimating the system dynamics during each sampling interval. In this paper, synchronization problems in asynchronous networked systems with model uncertainties are investigated under model-based hybrid edge-event-triggered control. A novel model-based hybrid edge-event-triggering scheme is proposed, where the term hybrid refers to the combination of an edge-event-triggering condition and a sampling scheduling mechanism. Sampling tasks are rescheduled via a timer when the event detection logic returns TRUE, ensuring a positive lower bound for inter-sampling time intervals. Prediction models based on relative states are developed without requiring exact prior knowledge of system matrices. A robust model-based controller is proposed accounting for communication delays in the transmission links. The control gain parameter is designed using the available model information. Sufficient conditions for systems to achieve synchronization and conditions for the design of prediction models are derived using an integral approach. Our stability results contribute to the robustness analysis of asynchronous networked systems with parameter uncertainties. Simulation results are provided to illustrate the effectiveness of this novel approach.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106329"},"PeriodicalIF":2.5,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979605","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 : 2026-01-09DOI: 10.1016/j.sysconle.2026.106352
Mohsen Amiri , Ilya Kolmanovsky , Mehdi Hosseinzadeh
This paper presents a method for solving time-varying constrained convex optimization problems in real time. The key idea is to embed the optimal solution within the internal state of a virtual dynamical system that evolves in parallel with the underlying optimization problem. This system is designed such that its trajectory tracks the optimal solution with a tunable, analytically-computable bound and remains feasible with respect to the problem constraints at all times, without requiring prior knowledge of the dynamics of either the cost function or the constraints. Moreover, when the cost function and constraints are time-invariant, the proposed method guarantees exponential convergence to the optimal solution. The effectiveness of the proposed approach is demonstrated through two numerical examples: (i) a multi-agent tracking scenario; and (ii) a collision-free robot navigation task.
{"title":"A dynamic embedding method for the real-time solution of time-varying constrained convex optimization problems","authors":"Mohsen Amiri , Ilya Kolmanovsky , Mehdi Hosseinzadeh","doi":"10.1016/j.sysconle.2026.106352","DOIUrl":"10.1016/j.sysconle.2026.106352","url":null,"abstract":"<div><div>This paper presents a method for solving time-varying constrained convex optimization problems in real time. The key idea is to embed the optimal solution within the internal state of a virtual dynamical system that evolves in parallel with the underlying optimization problem. This system is designed such that its trajectory tracks the optimal solution with a tunable, analytically-computable bound and remains feasible with respect to the problem constraints at all times, without requiring prior knowledge of the dynamics of either the cost function or the constraints. Moreover, when the cost function and constraints are time-invariant, the proposed method guarantees exponential convergence to the optimal solution. The effectiveness of the proposed approach is demonstrated through two numerical examples: (i) a multi-agent tracking scenario; and (ii) a collision-free robot navigation task.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106352"},"PeriodicalIF":2.5,"publicationDate":"2026-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941052","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 : 2026-01-08DOI: 10.1016/j.sysconle.2026.106342
Siteng Ma , Jun Hu , Zhihui Wu , Weilu Chen
This paper addresses the fault detection (FD) issue of T–S fuzzy systems under limited network bandwidth. To alleviate the communication burden between sensors and the remote filter, a dynamic quantizer pre-processes transmitted data. Moreover, a new FlexRay protocol (FRP) is proposed to schedule communication sequences, where an event-based redundant channel access mechanism is embedded, balancing resource conservation against filtering performance. Based on available measurements, a fuzzy FD filter with mismatched membership functions (MFs) is constructed. By employing the Lyapunov stability theory, sufficient criteria are developed to guarantee that the filtering error system (FES) is finite-time stable with specified performance. Furthermore, the expected filter gains are determined by solving the recursive linear matrix inequalities. Finally, the efficiency of the FD algorithm is demonstrated by the mass–spring–damper mechanical system and the single-link robotic manipulator model.
{"title":"Finite-time fault detection for T–S fuzzy systems with dynamic quantization under a new improved FlexRay protocol via event-based redundant channel access mechanism","authors":"Siteng Ma , Jun Hu , Zhihui Wu , Weilu Chen","doi":"10.1016/j.sysconle.2026.106342","DOIUrl":"10.1016/j.sysconle.2026.106342","url":null,"abstract":"<div><div>This paper addresses the fault detection (FD) issue of T–S fuzzy systems under limited network bandwidth. To alleviate the communication burden between sensors and the remote filter, a dynamic quantizer pre-processes transmitted data. Moreover, a new FlexRay protocol (FRP) is proposed to schedule communication sequences, where an event-based redundant channel access mechanism is embedded, balancing resource conservation against filtering performance. Based on available measurements, a fuzzy FD filter with mismatched membership functions (MFs) is constructed. By employing the Lyapunov stability theory, sufficient criteria are developed to guarantee that the filtering error system (FES) is finite-time stable with specified <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance. Furthermore, the expected filter gains are determined by solving the recursive linear matrix inequalities. Finally, the efficiency of the FD algorithm is demonstrated by the mass–spring–damper mechanical system and the single-link robotic manipulator model.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106342"},"PeriodicalIF":2.5,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941050","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}
In this work we consider the problem of controlling a dynamical system affected by bounded disturbances and subject to constraints through a wireless network. Existing works guarantee constraint satisfaction despite packet losses and delays by enforcing the past input sequence used in the estimation at the remote unit and the past input sequence applied at the plant to be the same. This condition, typically referred to as prediction consistency, requires strong assumptions on the network, such as a TCP-like protocol or a known delay bound, and conservative control design. In this work, we propose a novel approach to enforce constraints without requiring prediction consistency by handling unmatched input sequences as an additive disturbance. We define a theoretically sound Tube MPC to be implemented at the remote side and we introduce a novel acceptance rule at the plant side that allows to use control packets even if the past input sequences used in the estimation and applied at the plant are different. Simulations with real Wi-Fi channel realizations show that the proposed strategy has a more reactive response and better performance compared to existing solutions.
{"title":"Remote tube MPC over lossy networks for constrained control without prediction consistency","authors":"Matthias Pezzutto , Marcello Farina , Ruggero Carli , Luca Schenato","doi":"10.1016/j.sysconle.2025.106334","DOIUrl":"10.1016/j.sysconle.2025.106334","url":null,"abstract":"<div><div>In this work we consider the problem of controlling a dynamical system affected by bounded disturbances and subject to constraints through a wireless network. Existing works guarantee constraint satisfaction despite packet losses and delays by enforcing the past input sequence used in the estimation at the remote unit and the past input sequence applied at the plant to be the same. This condition, typically referred to as prediction consistency, requires strong assumptions on the network, such as a TCP-like protocol or a known delay bound, and conservative control design. In this work, we propose a novel approach to enforce constraints without requiring prediction consistency by handling unmatched input sequences as an additive disturbance. We define a theoretically sound Tube MPC to be implemented at the remote side and we introduce a novel acceptance rule at the plant side that allows to use control packets even if the past input sequences used in the estimation and applied at the plant are different. Simulations with real Wi-Fi channel realizations show that the proposed strategy has a more reactive response and better performance compared to existing solutions.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106334"},"PeriodicalIF":2.5,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941051","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 : 2026-01-06DOI: 10.1016/j.sysconle.2025.106289
Tomonori Sadamoto , Takashi Tanaka
We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an input–output-history (IOH) representation of the closed-loop system. First, we show that any dynamic output-feedback controller is equivalent to a static partial-state feedback gain for a new system representation characterized by a finite-length IOH. Leveraging this equivalence, we reformulate the search for an optimal dynamic output feedback controller as an optimization problem over the corresponding partial-state feedback gain. Next, we introduce a relaxed version of the IOH-based LQG problem by incorporating a small process noise with covariance into the new system to ensure coerciveness, a key condition for establishing gradient-based convergence guarantees. Consequently, we show that a vanilla PGM for the relaxed problem converges to an -stationary point, i.e., satisfying , where denotes the original LQG cost. Numerical experiments empirically indicate convergence to the vicinity of the globally optimal LQG controller.
{"title":"Policy gradient method for LQG control via input–output-history representation: Convergence to O(ϵ)-stationary points","authors":"Tomonori Sadamoto , Takashi Tanaka","doi":"10.1016/j.sysconle.2025.106289","DOIUrl":"10.1016/j.sysconle.2025.106289","url":null,"abstract":"<div><div>We study the policy gradient method (PGM) for the linear quadratic Gaussian (LQG) dynamic output-feedback control problem using an <em>input–output-history</em> (IOH) representation of the closed-loop system. First, we show that any dynamic output-feedback controller is equivalent to a static partial-state feedback gain for a new system representation characterized by a finite-length IOH. Leveraging this equivalence, we reformulate the search for an optimal dynamic output feedback controller as an optimization problem over the corresponding partial-state feedback gain. Next, we introduce a relaxed version of the IOH-based LQG problem by incorporating a small process noise with covariance <span><math><mrow><mi>ϵ</mi><mi>I</mi></mrow></math></span> into the new system to ensure coerciveness, a key condition for establishing gradient-based convergence guarantees. Consequently, we show that a vanilla PGM for the relaxed problem converges to an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></math></span>-<em>stationary</em> point, i.e., <span><math><mover><mrow><mi>K</mi></mrow><mo>¯</mo></mover></math></span> satisfying <span><math><mrow><msub><mrow><mo>‖</mo><mo>∇</mo><mi>J</mi><mrow><mo>(</mo><mover><mrow><mi>K</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mo>‖</mo></mrow><mrow><mi>F</mi></mrow></msub><mo>≤</mo><mi>O</mi><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>J</mi></math></span> denotes the original LQG cost. Numerical experiments empirically indicate convergence to the vicinity of the globally optimal LQG controller.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"209 ","pages":"Article 106289"},"PeriodicalIF":2.5,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145898077","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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