Pub Date : 2026-01-05DOI: 10.1016/j.jfranklin.2025.108384
Sadek Belamfedel Alaoui , Adnane Saoud , Abdelaziz Hmamed , Alejandro J. Rojas , El Houssaine Tissir
In this work, we extend the previously established scaled small gain problem to the realm of two-dimensional systems and introduce a new method to assess the stability of two-dimensional systems with time-varying delay. The method approximates the delayed state, in the horizontal and vertical directions, to constant delay states plus an approximation error. Using this transformation, the resulting model is expressed as an interconnection of two subsystems. The analysis based on the scaled small gain theorem and the Lyapunov’s method leads us to express the robust stability conditions in terms of a linear matrix inequality. Additionally, we introduce a new Lyapunov-Krasovskii functional, constructed using Legendre polynomials in two-dimensional space. Finally, we provide examples to demonstrate the effectiveness of our proposed method.
{"title":"Small-gain theorem-based stability analysis of two-dimensional systems with time delays","authors":"Sadek Belamfedel Alaoui , Adnane Saoud , Abdelaziz Hmamed , Alejandro J. Rojas , El Houssaine Tissir","doi":"10.1016/j.jfranklin.2025.108384","DOIUrl":"10.1016/j.jfranklin.2025.108384","url":null,"abstract":"<div><div>In this work, we extend the previously established scaled small gain problem to the realm of two-dimensional systems and introduce a new method to assess the stability of two-dimensional systems with time-varying delay. The method approximates the delayed state, in the horizontal and vertical directions, to constant delay states plus an approximation error. Using this transformation, the resulting model is expressed as an interconnection of two subsystems. The analysis based on the scaled small gain theorem and the Lyapunov’s method leads us to express the robust stability conditions in terms of a linear matrix inequality. Additionally, we introduce a new Lyapunov-Krasovskii functional, constructed using Legendre polynomials in two-dimensional space. Finally, we provide examples to demonstrate the effectiveness of our proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108384"},"PeriodicalIF":4.2,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145981008","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 : 2026-01-04DOI: 10.1016/j.jfranklin.2025.108382
Tianze Xie , Hui Wang , Jian Ding , Quanxin Zhu
Existing literature on input-to-state stability (ISS) primarily focuses on transient responses and robustness to external disturbances, yet it often fails to capture the inherent modeling bias in systems like those exhibiting mechanical hysteresis. To address this limitation, we introduce the concept of practical ISS for switched stochastic nonlinear time-delay systems (SSNTDSs), which provides a comprehensive framework for analyzing robustness against both internal bias and external disturbances. Acknowledging potential mismatches between the controller and subsystems, we establish less conservative criteria for practical ISS using Lyapunov-Razumikhin functions (LRFs) with indefinite differential operators. Furthermore, to accommodate mode variability and relax stringent constraints on switching signals, we develop a novel condition based on the mode-dependent average dwell time (MDADT) technique. This condition is specifically tailored for asynchronous switching and notably maintains consistency with the synchronous case, reducing to the classical condition when the switching signal delay approaches zero. The practical relevance of our work is highlighted through the extension of an exponential stability criterion and its successful application to a mechanical system with backlash hysteresis.
{"title":"Practical input-to-state stability of switched stochastic delay nonlinear systems and its application to hysteretic mechanical systems","authors":"Tianze Xie , Hui Wang , Jian Ding , Quanxin Zhu","doi":"10.1016/j.jfranklin.2025.108382","DOIUrl":"10.1016/j.jfranklin.2025.108382","url":null,"abstract":"<div><div>Existing literature on input-to-state stability (ISS) primarily focuses on transient responses and robustness to external disturbances, yet it often fails to capture the inherent modeling bias in systems like those exhibiting mechanical hysteresis. To address this limitation, we introduce the concept of practical ISS for switched stochastic nonlinear time-delay systems (SSNTDSs), which provides a comprehensive framework for analyzing robustness against both internal bias and external disturbances. Acknowledging potential mismatches between the controller and subsystems, we establish less conservative criteria for practical ISS using Lyapunov-Razumikhin functions (LRFs) with indefinite differential operators. Furthermore, to accommodate mode variability and relax stringent constraints on switching signals, we develop a novel condition based on the mode-dependent average dwell time (MDADT) technique. This condition is specifically tailored for asynchronous switching and notably maintains consistency with the synchronous case, reducing to the classical condition when the switching signal delay approaches zero. The practical relevance of our work is highlighted through the extension of an exponential stability criterion and its successful application to a mechanical system with backlash hysteresis.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108382"},"PeriodicalIF":4.2,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145915210","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 : 2026-01-04DOI: 10.1016/j.jfranklin.2025.108396
Shu-Xin Miao , Tomohiro Sogabe , Shao-Liang Zhang
The Stein tensor equation with the Einstein product arises in multidimensional signal processing, control theory, and data reconstruction. However, its inherent nonlinearity and high dimensionality present computational challenges. In this work, we design a predefined-time zeroing neural network model equipped with a novel activation function to efficiently solve the time-varying Stein tensor equation. Theoretical analysis establishes the model’s convergence and robustness, demonstrating that it not only converges to the exact solution within a predefined time but also exhibits strong resilience to two types of noise. Numerical experiments further confirm the superior performance of the proposed model in terms of accuracy, convergence speed, and noise robustness.
{"title":"Design and analysis of a predefined-time zeroing neural network model for solving the Stein tensor equation","authors":"Shu-Xin Miao , Tomohiro Sogabe , Shao-Liang Zhang","doi":"10.1016/j.jfranklin.2025.108396","DOIUrl":"10.1016/j.jfranklin.2025.108396","url":null,"abstract":"<div><div>The Stein tensor equation with the Einstein product arises in multidimensional signal processing, control theory, and data reconstruction. However, its inherent nonlinearity and high dimensionality present computational challenges. In this work, we design a predefined-time zeroing neural network model equipped with a novel activation function to efficiently solve the time-varying Stein tensor equation. Theoretical analysis establishes the model’s convergence and robustness, demonstrating that it not only converges to the exact solution within a predefined time but also exhibits strong resilience to two types of noise. Numerical experiments further confirm the superior performance of the proposed model in terms of accuracy, convergence speed, and noise robustness.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108396"},"PeriodicalIF":4.2,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926863","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 : 2026-01-03DOI: 10.1016/j.jfranklin.2025.108394
Shuo Liu , Huaguang Zhang , Hongbo Pang
This paper concerns on adaptive predefined-time asymptotic tracking control issume for switched uncertain nonlinear systems with switching deception attacks, although the output tracking control problem for each subsystem is not solvable. Switching deception attacks mode is constructed in channel of sensor-to-controller channel (S-C) and controller-to-actuatorb (C-A) firstly. A more general predefined-time stability criterion is established, which is an useful tool for predefined-time asymptotic tracking control. To overcome the disadvantage of recursive design methods, a predefined-time command filter has been constructed. Moreover, a predefined-time controller and a adaptive state dependent switching law dependent on adaptive parameter estimation are given to ensure that all the signals of the resulting closed-loop system subject to switching deception attacks are bounded. The tracking error can enter into the interval near origin in predefined time, and asymptotically tend towards to zero finally. To prevent the Zeno behavior, a hysteresis switching law dependent on parameter estimation is derived. Finally, an example on RLC circuite system is given to verty the effectiveness of the novel method.
{"title":"Adaptive predefined-time asymptotic tracking control for uncertain switched nonlinear systems with switching deception attacks","authors":"Shuo Liu , Huaguang Zhang , Hongbo Pang","doi":"10.1016/j.jfranklin.2025.108394","DOIUrl":"10.1016/j.jfranklin.2025.108394","url":null,"abstract":"<div><div>This paper concerns on adaptive predefined-time asymptotic tracking control issume for switched uncertain nonlinear systems with switching deception attacks, although the output tracking control problem for each subsystem is not solvable. Switching deception attacks mode is constructed in channel of sensor-to-controller channel (S-C) and controller-to-actuatorb (C-A) firstly. A more general predefined-time stability criterion is established, which is an useful tool for predefined-time asymptotic tracking control. To overcome the disadvantage of recursive design methods, a predefined-time command filter has been constructed. Moreover, a predefined-time controller and a adaptive state dependent switching law dependent on adaptive parameter estimation are given to ensure that all the signals of the resulting closed-loop system subject to switching deception attacks are bounded. The tracking error can enter into the interval near origin in predefined time, and asymptotically tend towards to zero finally. To prevent the Zeno behavior, a hysteresis switching law dependent on parameter estimation is derived. Finally, an example on RLC circuite system is given to verty the effectiveness of the novel method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108394"},"PeriodicalIF":4.2,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145915209","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 : 2026-01-03DOI: 10.1016/j.jfranklin.2025.108395
Tianhao Fei , Yongliang Yang , Xiaowei Zhao
In this paper, we investigate a distributed protocol design to achieve bipartite synchronization for a group of heterogeneous switched multi-agent systems (MASs) with state delays and input nonlinearity in each agent’s dynamics. To achieve this aim, the neural network-based approximation method is combined with an adaptive control method to stabilize each agent with uncertain dynamics. A two-layered compensation mechanism is also developed to attenuate the effect of input nonlinearity, consisting of two filters: one to address the input dead-zone and one to reduce the dynamic surface errors. The distributed command filters are introduced for the cascaded structure of each agent’s dynamics to eradicate recursive virtual control differentiation while diminishing the filtered error for each agent. Since it is challenging to address multiple distinct state delays for a group of MASs with asynchronous switching, the Lyapunov-Krasovskii functional design is extended and combined with the average dwell time (ADT) method. Bipartite synchronization of a group of switched nonlinear agents is ensured with the presented design and the boundedness of closed-loop signals is discussed through theoretical analysis. Finally, a simulation example is conducted to validate the distributed protocol design for bipartite synchronization.
{"title":"Command filtered adaptive bipartite synchronization for heterogeneous switched multi-agent systems with state delays and input nonlinearity","authors":"Tianhao Fei , Yongliang Yang , Xiaowei Zhao","doi":"10.1016/j.jfranklin.2025.108395","DOIUrl":"10.1016/j.jfranklin.2025.108395","url":null,"abstract":"<div><div>In this paper, we investigate a distributed protocol design to achieve bipartite synchronization for a group of heterogeneous switched multi-agent systems (MASs) with state delays and input nonlinearity in each agent’s dynamics. To achieve this aim, the neural network-based approximation method is combined with an adaptive control method to stabilize each agent with uncertain dynamics. A two-layered compensation mechanism is also developed to attenuate the effect of input nonlinearity, consisting of two filters: one to address the input dead-zone and one to reduce the dynamic surface errors. The distributed command filters are introduced for the cascaded structure of each agent’s dynamics to eradicate recursive virtual control differentiation while diminishing the filtered error for each agent. Since it is challenging to address multiple distinct state delays for a group of MASs with asynchronous switching, the Lyapunov-Krasovskii functional design is extended and combined with the average dwell time (ADT) method. Bipartite synchronization of a group of switched nonlinear agents is ensured with the presented design and the boundedness of closed-loop signals is discussed through theoretical analysis. Finally, a simulation example is conducted to validate the distributed protocol design for bipartite synchronization.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108395"},"PeriodicalIF":4.2,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926856","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 : 2026-01-03DOI: 10.1016/j.jfranklin.2025.108398
Hongwei Chen , Shengmei Xiang , Hengyu Gu
This article deals with the state estimation problem for a class of time-varying systems subject to stochastic nonlinearities and channel noise over sensor networks. A binary encoding scheme (BES) is employed in the filter design to overcome distortions caused by the limited communication capacity. In addition, stochastic perturbations are introduced into the filter gain to characterize the resilience of the filter. Measurements are transmitted as bit strings over a binary symmetric channel, taking into account the stochastic bit flips. An upper bound of estimation error covariance is derived with the help of the inductive approach, and such an upper bound is subsequently minimized to design the filter parameters at each time instant. Finally, a numerical example is employed to confirm the effectiveness of the proposed approach.
{"title":"Resilient state estimation for nonlinear systems: A binary encoding scheme under stochastic bit flips","authors":"Hongwei Chen , Shengmei Xiang , Hengyu Gu","doi":"10.1016/j.jfranklin.2025.108398","DOIUrl":"10.1016/j.jfranklin.2025.108398","url":null,"abstract":"<div><div>This article deals with the state estimation problem for a class of time-varying systems subject to stochastic nonlinearities and channel noise over sensor networks. A binary encoding scheme (BES) is employed in the filter design to overcome distortions caused by the limited communication capacity. In addition, stochastic perturbations are introduced into the filter gain to characterize the resilience of the filter. Measurements are transmitted as bit strings over a binary symmetric channel, taking into account the stochastic bit flips. An upper bound of estimation error covariance is derived with the help of the inductive approach, and such an upper bound is subsequently minimized to design the filter parameters at each time instant. Finally, a numerical example is employed to confirm the effectiveness of the proposed approach.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 5","pages":"Article 108398"},"PeriodicalIF":4.2,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146172575","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 : 2026-01-03DOI: 10.1016/j.jfranklin.2025.108390
Rui-Guo Li , Long-Fei Feng , Huai-Ning Wu
In this paper, we explore the fully distributed source localization for double-integrator agents in both model-based and model-free scalar fields. In the absence of velocity information, a novel prescribed-time velocity observer is designed relying on double-integrator dynamics. In consideration of unavailable field gradients, gradient estimators with parameter adaptation strategy are developed for model-based and model-free scalar fields, respectively. Coupled by velocity observers, gradient estimators and auxiliary variables, we propose cooperative event-triggered formation control schemes for agents in a fully distributed way. Further, the formation center of agents is driven toward the field source. Based on the Lyapunov principle and nonsmooth theory, we analyze the stability of the closed-loop system and exclusion of the Zeno phenomenon in theory. Ultimately, the feasibility of the proposed control schemes is verified by numerical simulation under field model-based and model-free cases, separately.
{"title":"Fully distributed and velocity-free multi-agent source localization under model-based/model-free scalar fields","authors":"Rui-Guo Li , Long-Fei Feng , Huai-Ning Wu","doi":"10.1016/j.jfranklin.2025.108390","DOIUrl":"10.1016/j.jfranklin.2025.108390","url":null,"abstract":"<div><div>In this paper, we explore the fully distributed source localization for double-integrator agents in both model-based and model-free scalar fields. In the absence of velocity information, a novel prescribed-time velocity observer is designed relying on double-integrator dynamics. In consideration of unavailable field gradients, gradient estimators with parameter adaptation strategy are developed for model-based and model-free scalar fields, respectively. Coupled by velocity observers, gradient estimators and auxiliary variables, we propose cooperative event-triggered formation control schemes for agents in a fully distributed way. Further, the formation center of agents is driven toward the field source. Based on the Lyapunov principle and nonsmooth theory, we analyze the stability of the closed-loop system and exclusion of the Zeno phenomenon in theory. Ultimately, the feasibility of the proposed control schemes is verified by numerical simulation under field model-based and model-free cases, separately.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108390"},"PeriodicalIF":4.2,"publicationDate":"2026-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926858","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 paper, a fixed-time control strategy based on prescribed performance function (PPF) and tan-type Barrier Lyapunov Function (tan-type BLF) is proposed for full-state constrained Autonomous Underwater Vehicle (AUV) considering input time delay. A prescribed performance function and a tan-type BLF are designed for the errors to prevent states from violating constraints, which guarantee the transient and steady state performance of the errors. A virtual control scheme is introduced to solve the singularity problem. The complexity explosion problem is resolved by employing a fixed-time differentiator, which simplifies the computational process and reduces the number of control parameters required. In addition, a radial basis function neural network (RBFNN) is used to estimate external disturbances and model uncertainties. It is proved through the fixed-time stability theory that the proposed control strategy ensures that the errors converge to a small neighborhood near the origin in fixed time considering time delay. Finally, simulation results and comparisons are presented to demonstrate the effectiveness and superiority of the proposed strategy.
{"title":"Fixed-time full-state constrained control considering time delay of autonomous underwater vehicle based on prescribed performance and tan-type barrier Lyapunov function","authors":"Yuyang Wang, Yanchao Sun, Huanzhe Zhang, Yipeng Zhao, Shuao Cui, Hongde Qin","doi":"10.1016/j.jfranklin.2025.108385","DOIUrl":"10.1016/j.jfranklin.2025.108385","url":null,"abstract":"<div><div>In this paper, a fixed-time control strategy based on prescribed performance function (PPF) and tan-type Barrier Lyapunov Function (tan-type BLF) is proposed for full-state constrained Autonomous Underwater Vehicle (AUV) considering input time delay. A prescribed performance function and a tan-type BLF are designed for the errors to prevent states from violating constraints, which guarantee the transient and steady state performance of the errors. A virtual control scheme is introduced to solve the singularity problem. The complexity explosion problem is resolved by employing a fixed-time differentiator, which simplifies the computational process and reduces the number of control parameters required. In addition, a radial basis function neural network (RBFNN) is used to estimate external disturbances and model uncertainties. It is proved through the fixed-time stability theory that the proposed control strategy ensures that the errors converge to a small neighborhood near the origin in fixed time considering time delay. Finally, simulation results and comparisons are presented to demonstrate the effectiveness and superiority of the proposed strategy.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 3","pages":"Article 108385"},"PeriodicalIF":4.2,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145941328","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 : 2026-01-02DOI: 10.1016/j.jfranklin.2025.108381
Yu Wang, Huiliao Yang, Dawei Wu, Yuquan Chen
This article presents a control strategy for quadrotor unmanned aerial vehicle (UAV) to achieve autonomous landing on moving unmanned surface vehicle (USV). First, to address the challenge of safe landing due to USV deck oscillations induced by wind and waves, the Long Short-Term Memory (LSTM) network is employed to predict motion trajectories and identify optimal landing window. Next, a modified practically predefined time stable (PPTS) system is established as theoretical basis of subsequent control design. Subsequently, by incorporating neural networks into the adaptive command-filtered backstepping control framework, the system’s unknown dynamics terms (UDT) and differential explosion phenomena are effectively addressed. Stability analysis demonstrates that the closed-loop system is practically predefined-time stable (PPTS), with tracking errors converging to a small residual set within the predefined time. Finally, simulation results verify the effectiveness and superiority of the proposed method.
{"title":"Autonomous shipboard landing of quadrotor UAV: A neuroadaptive predefined-time approach with LSTM prediction","authors":"Yu Wang, Huiliao Yang, Dawei Wu, Yuquan Chen","doi":"10.1016/j.jfranklin.2025.108381","DOIUrl":"10.1016/j.jfranklin.2025.108381","url":null,"abstract":"<div><div>This article presents a control strategy for quadrotor unmanned aerial vehicle (UAV) to achieve autonomous landing on moving unmanned surface vehicle (USV). First, to address the challenge of safe landing due to USV deck oscillations induced by wind and waves, the Long Short-Term Memory (LSTM) network is employed to predict motion trajectories and identify optimal landing window. Next, a modified practically predefined time stable (PPTS) system is established as theoretical basis of subsequent control design. Subsequently, by incorporating neural networks into the adaptive command-filtered backstepping control framework, the system’s unknown dynamics terms (UDT) and differential explosion phenomena are effectively addressed. Stability analysis demonstrates that the closed-loop system is practically predefined-time stable (PPTS), with tracking errors converging to a small residual set within the predefined time. Finally, simulation results verify the effectiveness and superiority of the proposed method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108381"},"PeriodicalIF":4.2,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926861","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 : 2026-01-02DOI: 10.1016/j.jfranklin.2025.108388
Zhichao Jin, Yujie Wang
Modern manufacturing is undergoing a transformation driven by the pursuit of efficiency, precision, and reliability in mechanical systems. As critical equipment, computer numerical control (CNC) lathes play an indispensable role, with their stability being paramount to preventing economic losses and production delays. This paper proposes a novel framework for CNC lathe fault diagnosis based on fine-tuned large language models (LLMs). The Hierarchical Supervised Fine-Tuning (HSFT) algorithm balances sequence generation, hierarchical classification, and Chain of Thought (CoT) consistency regularization losses by optimizing a composite loss function. This enhances model adaptability to precisely address domain-specific diagnostic challenges. The CoT inference module constructs a structured stepwise reasoning process, improving diagnostic accuracy and interpretability through multi-stage methods including fault classification, self-verification, and reasoning. Experimental results on Qwen and LLaMA series models demonstrate significant performance improvements over baseline models, validating the approach’s effectiveness. This framework provides a robust solution for practical CNC lathe fault diagnosis and delivers actionable diagnostic insights for maintenance engineers.
{"title":"Fault diagnosis for Computer Numerical Control lathes based on the fine-tuned large language model","authors":"Zhichao Jin, Yujie Wang","doi":"10.1016/j.jfranklin.2025.108388","DOIUrl":"10.1016/j.jfranklin.2025.108388","url":null,"abstract":"<div><div>Modern manufacturing is undergoing a transformation driven by the pursuit of efficiency, precision, and reliability in mechanical systems. As critical equipment, computer numerical control (CNC) lathes play an indispensable role, with their stability being paramount to preventing economic losses and production delays. This paper proposes a novel framework for CNC lathe fault diagnosis based on fine-tuned large language models (LLMs). The Hierarchical Supervised Fine-Tuning (HSFT) algorithm balances sequence generation, hierarchical classification, and Chain of Thought (CoT) consistency regularization losses by optimizing a composite loss function. This enhances model adaptability to precisely address domain-specific diagnostic challenges. The CoT inference module constructs a structured stepwise reasoning process, improving diagnostic accuracy and interpretability through multi-stage methods including fault classification, self-verification, and reasoning. Experimental results on Qwen and LLaMA series models demonstrate significant performance improvements over baseline models, validating the approach’s effectiveness. This framework provides a robust solution for practical CNC lathe fault diagnosis and delivers actionable diagnostic insights for maintenance engineers.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"363 2","pages":"Article 108388"},"PeriodicalIF":4.2,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145926833","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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