This paper addresses the fault estimation (FE) problem in stochastic linear discrete-time varying systems with data dropouts and variable pass lengths. To comprehensively characterize the randomness of pass lengths and data dropouts, we utilize recursive Gaussian and Bernoulli distributions. We design a novel switch-type modified weighted iterative learning observer to achieve accurate FE. The fault estimation strategy of this observer integrates a modified weighted averaging operator with an intermittent update strategy (IUS) to address information loss and redundancy caused by variable pass lengths and data dropouts. Convergence conditions are established using the -norm method and recursive analysis. Additionally, the proposed iterative learning (IL) method effectively ensures the boundedness of FE errors. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed FE method.
{"title":"Iterative learning based fault estimation for stochastic systems with variable pass lengths and data dropouts","authors":"Jiantao Shi, Shaodong Gu, Jiawen Tang, Wenli Zhang, Chuang Chen, Dongdong Yue","doi":"10.1016/j.jfranklin.2025.107550","DOIUrl":"10.1016/j.jfranklin.2025.107550","url":null,"abstract":"<div><div>This paper addresses the fault estimation (FE) problem in stochastic linear discrete-time varying systems with data dropouts and variable pass lengths. To comprehensively characterize the randomness of pass lengths and data dropouts, we utilize recursive Gaussian and Bernoulli distributions. We design a novel switch-type modified weighted iterative learning observer to achieve accurate FE. The fault estimation strategy of this observer integrates a modified weighted averaging operator with an intermittent update strategy (IUS) to address information loss and redundancy caused by variable pass lengths and data dropouts. Convergence conditions are established using the <span><math><mi>λ</mi></math></span>-norm method and recursive analysis. Additionally, the proposed iterative learning (IL) method effectively ensures the boundedness of FE errors. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed FE method.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107550"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107547
Xiang Chen, Xiaogang Wang, Fei Liu
The robust identification of linear parameter-varying (LPV) finite impulse response (FIR) system with unknown missing output is considered. This paper provides a comprehensive discussion of common outliers and unknown missing measurement problems in practical processes. A Student’s t distribution is utilized to data with outliers, and also to automatically identify missing measurements, an indicator variable is introduced for each measurement that follows a Bernoulli distribution. After that, determining whether measurements are missing or not and estimating the unknown parameters by the variational Bayesian (VB) algorithm. A numerical example and the cascaded tank system are provided to exemplify this algorithm and demonstrate its robustness and innovation.
{"title":"Identification of linear parameter-varying system with missing measurement data and outliers","authors":"Xiang Chen, Xiaogang Wang, Fei Liu","doi":"10.1016/j.jfranklin.2025.107547","DOIUrl":"10.1016/j.jfranklin.2025.107547","url":null,"abstract":"<div><div>The robust identification of linear parameter-varying (LPV) finite impulse response (FIR) system with unknown missing output is considered. This paper provides a comprehensive discussion of common outliers and unknown missing measurement problems in practical processes. A Student’s <em>t</em> distribution is utilized to data with outliers, and also to automatically identify missing measurements, an indicator variable is introduced for each measurement that follows a Bernoulli distribution. After that, determining whether measurements are missing or not and estimating the unknown parameters by the variational Bayesian (VB) algorithm. A numerical example and the cascaded tank system are provided to exemplify this algorithm and demonstrate its robustness and innovation.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107547"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145982","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}
This paper proposes particle filtering for state estimation considering Round-Robin protocol for discrete-time nonlinear cyber–physical systems with non-Gaussian noise affecting the channels and multiple complex sensor phenomena, including missing measurements (MMs) and randomly occurring sensor saturations (ROSSs). A novel energy harvesting sensor is applied to ensure uninterrupted measurement transmission, and a simplified energy-transfer recursive algorithm is proposed to further calculate the measurement transmission probability of energy harvesting sensors. In addition, considering actual engineering scenarios, two sequences of Bernoulli-distributed random variables with known probability distributions are employed to describe the characteristics of MMs and ROSSs. During the design process of the filtering scheme, we construct a modified likelihood function to compensate for the impact of MMs, ROSSs, and energy harvesting sensors in cyber–physical systems. Subsequently, based on the mathematical characterisation of the likelihood function, we propose a particle filtering algorithm that can address the difficulty in obtaining the likelihood function when MMs and ROSSs occur simultaneously. Finally, the usefulness of the proposed particle filtering method is validated using two tracking examples.
{"title":"Particle filtering for nonlinear cyber–physical systems under Round-Robin protocol: Handling complex sensor issues and non-Gaussian noise","authors":"Beiyuan Li, Juan Li, Peng Lou, Lihong Rong, Ziyang Wang, Haitao Xiong","doi":"10.1016/j.jfranklin.2025.107507","DOIUrl":"10.1016/j.jfranklin.2025.107507","url":null,"abstract":"<div><div>This paper proposes particle filtering for state estimation considering Round-Robin protocol for discrete-time nonlinear cyber–physical systems with non-Gaussian noise affecting the channels and multiple complex sensor phenomena, including missing measurements (MMs) and randomly occurring sensor saturations (ROSSs). A novel energy harvesting sensor is applied to ensure uninterrupted measurement transmission, and a simplified energy-transfer recursive algorithm is proposed to further calculate the measurement transmission probability of energy harvesting sensors. In addition, considering actual engineering scenarios, two sequences of Bernoulli-distributed random variables with known probability distributions are employed to describe the characteristics of MMs and ROSSs. During the design process of the filtering scheme, we construct a modified likelihood function to compensate for the impact of MMs, ROSSs, and energy harvesting sensors in cyber–physical systems. Subsequently, based on the mathematical characterisation of the likelihood function, we propose a particle filtering algorithm that can address the difficulty in obtaining the likelihood function when MMs and ROSSs occur simultaneously. Finally, the usefulness of the proposed particle filtering method is validated using two tracking examples.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107507"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107529
Fang Zhao , Bo Wu , Xisheng Zhan , Lingli Cheng , Huaicheng Yan
The distributed secure filtering issue is concerned for discrete time-varying systems with state-saturation constraints subjected to both deception attacks and Round-Robin (RR) protocol over sensor networks in this paper. Firstly, the phenomenon of state-saturation, a prevalent issue encountered in real-world projects, is considered in this paper. In order to reduce the burden on the network, the RR protocol is introduced to determine which sensor node is connected to the network at each transmission moment. Subsequently, the randomness of the occurrence of deception attacks is modeled in this paper, with each event being assigned a specific probability through the utilization of a series of Bernoulli-distributed white sequences. Next, a sufficient condition for the expectation filter to satisfy the prediction error variance requirement is obtained based on the recursive linear matrix inequality (RLMI) method. Based on this, an optimization problem is created to find the filtering parameters that guarantee locally optimal filtering performance at every moment. Ultimately, the efficacy of the proposed algorithm is substantiated through a series of illustrative simulation scenarios.
{"title":"Distributed state-saturation secure filtering under Round-Robin protocol and deception attacks","authors":"Fang Zhao , Bo Wu , Xisheng Zhan , Lingli Cheng , Huaicheng Yan","doi":"10.1016/j.jfranklin.2025.107529","DOIUrl":"10.1016/j.jfranklin.2025.107529","url":null,"abstract":"<div><div>The distributed secure filtering issue is concerned for discrete time-varying systems with state-saturation constraints subjected to both deception attacks and Round-Robin (RR) protocol over sensor networks in this paper. Firstly, the phenomenon of state-saturation, a prevalent issue encountered in real-world projects, is considered in this paper. In order to reduce the burden on the network, the RR protocol is introduced to determine which sensor node is connected to the network at each transmission moment. Subsequently, the randomness of the occurrence of deception attacks is modeled in this paper, with each event being assigned a specific probability through the utilization of a series of Bernoulli-distributed white sequences. Next, a sufficient condition for the expectation filter to satisfy the prediction error variance requirement is obtained based on the recursive linear matrix inequality (RLMI) method. Based on this, an optimization problem is created to find the filtering parameters that guarantee locally optimal filtering performance at every moment. Ultimately, the efficacy of the proposed algorithm is substantiated through a series of illustrative simulation scenarios.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107529"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2024.107505
Changhui Wang, Yihao Wang, Mei Liang, Yibao Chen
In this article, a distributed event-triggered finite-time adaptive fuzzy attitude and altitude control is developed for the multiple quadrotor unmanned aerial vehicles (QUAVs) with asymmetric time-varying state constraints and unknown external disturbances. By constructing the asymmetric time-varying barrier Lyapunov functions, all the state constraints of the QUAVs are not exceeded. The finite-time command filters are adopted to deal with the explosion of complexity problem from backstepping. Based on the relative threshold algorithm, the distributed event-triggered adaptive attitude and altitude controller is developed by establishing the communication mechanism between the QUAVs and the virtual leader to reduce the communication burden, in which a disturbance observer is designed to compensate the complex disturbance composed of fuzzy approximation error and external disturbance. Finally, simulation results verify the effectiveness of the distributed scheme for the QUAVs.
{"title":"Distributed event-triggered adaptive fuzzy finite-time control for multiple QUAVs with time-varying state constraints","authors":"Changhui Wang, Yihao Wang, Mei Liang, Yibao Chen","doi":"10.1016/j.jfranklin.2024.107505","DOIUrl":"10.1016/j.jfranklin.2024.107505","url":null,"abstract":"<div><div>In this article, a distributed event-triggered finite-time adaptive fuzzy attitude and altitude control is developed for the multiple quadrotor unmanned aerial vehicles (QUAVs) with asymmetric time-varying state constraints and unknown external disturbances. By constructing the asymmetric time-varying barrier Lyapunov functions, all the state constraints of the QUAVs are not exceeded. The finite-time command filters are adopted to deal with the explosion of complexity problem from backstepping. Based on the relative threshold algorithm, the distributed event-triggered adaptive attitude and altitude controller is developed by establishing the communication mechanism between the QUAVs and the virtual leader to reduce the communication burden, in which a disturbance observer is designed to compensate the complex disturbance composed of fuzzy approximation error and external disturbance. Finally, simulation results verify the effectiveness of the distributed scheme for the QUAVs.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107505"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107508
Gang Wang , Tongsong Jiang , Dong Zhang , V.I. Vasil’ev
As digital media increasingly faces copyright threats, robust protection schemes are crucial. While gray-scale watermarking techniques are well-developed, color watermarking problems require more advanced solutions due to the complex spectral relationships among RGB channels. This paper introduces a novel color watermarking scheme based on the split quaternion matrix model, a 4D algebraic structure that preserves the linear spectral relationships among RGB channels, enhances computational efficiency, and improves color image processing. Watermark embedding employs a double split quaternion singular value decomposition (SVDSQ) process. The host image is divided into patches, and dominant singular values are extracted from each patch using SVDSQ. These values are assembled into a matrix, which undergoes a second SVDSQ to embed the watermark. This dual-layered method enhances the adaptability of the watermark embedding payload. Experimental results show that, under the same experimental conditions, our watermarking scheme demonstrates strong robustness against noise and geometric attacks, while maintaining a high peak signal-to-noise ratio (PSNR 35), compared to recent watermarking schemes. Despite introducing real part redundancy and requiring prior information for the watermark extraction, this approach advances color image processing using split quaternion matrices. Future work will focus on addressing these limitations and exploring new applications.
{"title":"Color image watermarking scheme based on singular value decomposition of split quaternion matrices","authors":"Gang Wang , Tongsong Jiang , Dong Zhang , V.I. Vasil’ev","doi":"10.1016/j.jfranklin.2025.107508","DOIUrl":"10.1016/j.jfranklin.2025.107508","url":null,"abstract":"<div><div>As digital media increasingly faces copyright threats, robust protection schemes are crucial. While gray-scale watermarking techniques are well-developed, color watermarking problems require more advanced solutions due to the complex spectral relationships among RGB channels. This paper introduces a novel color watermarking scheme based on the split quaternion matrix model, a 4D algebraic structure that preserves the linear spectral relationships among RGB channels, enhances computational efficiency, and improves color image processing. Watermark embedding employs a double split quaternion singular value decomposition (SVDSQ) process. The host image is divided into patches, and dominant singular values are extracted from each patch using SVDSQ. These values are assembled into a matrix, which undergoes a second SVDSQ to embed the watermark. This dual-layered method enhances the adaptability of the watermark embedding payload. Experimental results show that, under the same experimental conditions, our watermarking scheme demonstrates strong robustness against noise and geometric attacks, while maintaining a high peak signal-to-noise ratio (PSNR <span><math><mo>≥</mo></math></span> 35), compared to recent watermarking schemes. Despite introducing real part redundancy and requiring prior information for the watermark extraction, this approach advances color image processing using split quaternion matrices. Future work will focus on addressing these limitations and exploring new applications.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107508"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107514
Xiaoke Tang , Yunliang Wang , Jun Cheng , Dan Zhang , Wenhai Qi
This study briefly explores fuzzy control for Markov singularly perturbed systems with a dynamic-probabilistic event-triggered mechanism and a dynamic mismatch mechanism. To optimize resource consumption, the proposed event-triggered mechanism leverages the stochastic nature of communication delays. Additionally, a general dynamic mismatch mechanism is introduced to address scenarios where the system and controller modes do not align. Sufficient conditions for ensuring system stability are derived using Lyapunov theory. Finally, the effectiveness of the proposed methodology is validated through both numerical simulations and practical examples.
{"title":"Fuzzy control for Markov singularly perturbed systems with dynamic-probabilistic event-triggered mechanism","authors":"Xiaoke Tang , Yunliang Wang , Jun Cheng , Dan Zhang , Wenhai Qi","doi":"10.1016/j.jfranklin.2025.107514","DOIUrl":"10.1016/j.jfranklin.2025.107514","url":null,"abstract":"<div><div>This study briefly explores fuzzy control for Markov singularly perturbed systems with a dynamic-probabilistic event-triggered mechanism and a dynamic mismatch mechanism. To optimize resource consumption, the proposed event-triggered mechanism leverages the stochastic nature of communication delays. Additionally, a general dynamic mismatch mechanism is introduced to address scenarios where the system and controller modes do not align. Sufficient conditions for ensuring system stability are derived using Lyapunov theory. Finally, the effectiveness of the proposed methodology is validated through both numerical simulations and practical examples.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107514"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107530
Honglei Liu, Baoyong Zhang, Deming Yuan
In this paper, we focus on a decentralized online convex optimization problem over a multi-agent system, where each agent is equipped with a time-varying objective function. To handle the communication bottleneck and reduce the communication costs, we consider the method of local steps, where the agents communicate with their neighbors after performing local gradient descent steps. Under bandit feedback, we develop the Local-Decentralized Online Bandit Gradient Descent (Local-DOBGD) algorithm, which combines local steps and gradient descent. The performance of the developed algorithm is analyzed and the dynamic regret bound is obtained, which is concerned with time horizon and path-length . Finally, we provide a numerical example to verify the effectiveness of the Local-DOBGD algorithm.
{"title":"Dynamic regret for decentralized online bandit gradient descent with local steps","authors":"Honglei Liu, Baoyong Zhang, Deming Yuan","doi":"10.1016/j.jfranklin.2025.107530","DOIUrl":"10.1016/j.jfranklin.2025.107530","url":null,"abstract":"<div><div>In this paper, we focus on a decentralized online convex optimization problem over a multi-agent system, where each agent is equipped with a time-varying objective function. To handle the communication bottleneck and reduce the communication costs, we consider the method of local steps, where the agents communicate with their neighbors after performing local gradient descent steps. Under bandit feedback, we develop the Local-Decentralized Online Bandit Gradient Descent (Local-DOBGD) algorithm, which combines local steps and gradient descent. The performance of the developed algorithm is analyzed and the dynamic regret bound <span><math><mrow><mi>O</mi><mfenced><mrow><msqrt><mrow><mi>T</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>)</mo></mrow></mrow></msqrt></mrow></mfenced></mrow></math></span> is obtained, which is concerned with time horizon <span><math><mi>T</mi></math></span> and path-length <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span>. Finally, we provide a numerical example to verify the effectiveness of the Local-DOBGD algorithm.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107530"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107519
Yuhui Fu, Yuan Fan
This paper develops a dynamic event-triggered optimal control method based on a critic neural network (CNN) for nonlinear continuous-time (CT) systems with a state observer. Firstly, a discounted cost function is introduced to solve the optimal problem of the nonlinear systems, and the related optimal performance index function and a Hamilton–Jacobi–Bellman (HJB) equation are established to obtain the optimal control law. Then, to reduce communication burdens, a dynamic event-triggered control (DETC) method is defined by adding an additional dynamic variable on the basis of the traditional event-triggered control (ETC) method to keep the aperiodic update of the systems, and the stability of the systems based on these two methods are proved, respectively. Moreover, to approximate the optimal solution of the HJB equation, a CNN is utilized to approximate the optimal performance index function and tune its weight by the gradient descent approach. By the Lyapunov method, the uniform ultimate boundedness (UUB) of the closed-loop systems is proved, while also excluding Zeno behavior. Finally, the effectiveness of the proposed optimal control strategy is verified by two simulations.
{"title":"Dynamic event-triggered optimal critic-only control strategy for nonlinear systems based on state observer","authors":"Yuhui Fu, Yuan Fan","doi":"10.1016/j.jfranklin.2025.107519","DOIUrl":"10.1016/j.jfranklin.2025.107519","url":null,"abstract":"<div><div>This paper develops a dynamic event-triggered optimal control method based on a critic neural network (CNN) for nonlinear continuous-time (CT) systems with a state observer. Firstly, a discounted cost function is introduced to solve the optimal problem of the nonlinear systems, and the related optimal performance index function and a Hamilton–Jacobi–Bellman (HJB) equation are established to obtain the optimal control law. Then, to reduce communication burdens, a dynamic event-triggered control (DETC) method is defined by adding an additional dynamic variable on the basis of the traditional event-triggered control (ETC) method to keep the aperiodic update of the systems, and the stability of the systems based on these two methods are proved, respectively. Moreover, to approximate the optimal solution of the HJB equation, a CNN is utilized to approximate the optimal performance index function and tune its weight by the gradient descent approach. By the Lyapunov method, the uniform ultimate boundedness (UUB) of the closed-loop systems is proved, while also excluding Zeno behavior. Finally, the effectiveness of the proposed optimal control strategy is verified by two simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 4","pages":"Article 107519"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-01DOI: 10.1016/j.jfranklin.2025.107511
Hong Zhang , Mohamed Meyer Kana Kone , Xiao-Qian Ma , Nan-Run Zhou
Deep learning-based watermarking models usually take on shortcomings in visual fidelity and robustness. To address these limitations, a novel frequency-domain attention-guided adaptive robust watermarking model is explored. Frequency-domain transform and channel attention mechanism are integrated by the model, it dynamically adapts the watermark embedding process based on content features to ensure adaptability and robustness to different media types. To enhance the representation of image features, an information fusion module is designed to comprehensively capture both deep and shallow features of cover images for fusion with watermark. Additionally, the multi-scale frequency-domain attention module is deployed to generate an attention mask to guide the embedding of watermark, and the weight allocation for different frequencies are optimized during the watermark embedding. The robust feature learning is enhanced during the training by a noise layer. Furthermore, an information extraction module is devised to recover watermarks from the attacked encoded images. The experimental results indicate that the PSNR and the SSIM of the encoded image are above 44.65 dB and 0.9934 respectively. Meanwhile, the proposed model has strong robustness against JPEG attack, which achieves a bit accuracy >98.43 % for extracted messages with compression quality factor of 50. Besides, the proposed model shows strong robustness to many other distortions such as Gaussian noise, resizing, cropping, dropout and Salt & Pepper noise.
{"title":"Frequency-domain attention-guided adaptive robust watermarking model","authors":"Hong Zhang , Mohamed Meyer Kana Kone , Xiao-Qian Ma , Nan-Run Zhou","doi":"10.1016/j.jfranklin.2025.107511","DOIUrl":"10.1016/j.jfranklin.2025.107511","url":null,"abstract":"<div><div>Deep learning-based watermarking models usually take on shortcomings in visual fidelity and robustness. To address these limitations, a novel frequency-domain attention-guided adaptive robust watermarking model is explored. Frequency-domain transform and channel attention mechanism are integrated by the model, it dynamically adapts the watermark embedding process based on content features to ensure adaptability and robustness to different media types. To enhance the representation of image features, an information fusion module is designed to comprehensively capture both deep and shallow features of cover images for fusion with watermark. Additionally, the multi-scale frequency-domain attention module is deployed to generate an attention mask to guide the embedding of watermark, and the weight allocation for different frequencies are optimized during the watermark embedding. The robust feature learning is enhanced during the training by a noise layer. Furthermore, an information extraction module is devised to recover watermarks from the attacked encoded images. The experimental results indicate that the PSNR and the SSIM of the encoded image are above 44.65 dB and 0.9934 respectively. Meanwhile, the proposed model has strong robustness against JPEG attack, which achieves a bit accuracy >98.43 % for extracted messages with compression quality factor of 50. Besides, the proposed model shows strong robustness to many other distortions such as Gaussian noise, resizing, cropping, dropout and Salt & Pepper noise.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 3","pages":"Article 107511"},"PeriodicalIF":3.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136968","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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