Pub Date : 2024-08-28DOI: 10.1016/j.jfranklin.2024.107217
In this paper, two kinds of hierarchical time-limited control (HTLC) algorithms with the ability to avoid singularities and simple parameter setting rules are proposed to achieve the bipartite consensus of Networked Lagrange Agents (NLAs), where each agent refers to external disturbances, dynamics uncertainties and bounded inputs. Each HTCL algorithm includes time-limited estimator and prescribed-time local controller. Specially, the HTCL algorithm is developed by combining error transformation and prescribed-time sliding surface. We formally demonstrate that all the states approach the neighborhood of the origin within the prescribed-time, where the settling time can be set only by selecting one parameter. The numerical examples verify the theoretical result.
{"title":"Performance-guaranteed prescribed-time bipartite consensus of networked Lagrangian agents with bounded inputs and signed digraphs","authors":"","doi":"10.1016/j.jfranklin.2024.107217","DOIUrl":"10.1016/j.jfranklin.2024.107217","url":null,"abstract":"<div><p>In this paper, two kinds of hierarchical time-limited control (HTLC) algorithms with the ability to avoid singularities and simple parameter setting rules are proposed to achieve the bipartite consensus of Networked Lagrange Agents (NLAs), where each agent refers to external disturbances, dynamics uncertainties and bounded inputs. Each HTCL algorithm includes time-limited estimator and prescribed-time local controller. Specially, the HTCL algorithm is developed by combining error transformation and prescribed-time sliding surface. We formally demonstrate that all the states approach the neighborhood of the origin within the prescribed-time, where the settling time can be set only by selecting one parameter. The numerical examples verify the theoretical result.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099292","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 : 2024-08-28DOI: 10.1016/j.jfranklin.2024.107221
In this paper, an enhanced parametric detection method employing diversified scan and iteration is proposed for heterogeneous environment. A diversified scan, encompassing both rough scan and intensive scan, is first conducted in the normalized space–time frequency field to acquire the interference’s frequency components, which is conducive to obtaining the outline of interference in the normalized space–time two-dimensional (2-D) frequency field. The intensities of these components are subsequently determined through iteration to reduce the impact brought by the randomness of training samples. Meanwhile, the environment is commonly sparse in most cases, which is fully utilized in the proposed method. Then the cross-correlation matrix and autoregressive (AR) covariance matrix are reconstructed to form the corresponding detector. In the end, the availability and superiority of the proposed method are validated by numerical results. It is shown from numerical results that the proposed method performs well in detection performance compared to several existing typical methods in heterogeneous environment.
{"title":"Enhanced parametric detection employing diversified scan and iteration","authors":"","doi":"10.1016/j.jfranklin.2024.107221","DOIUrl":"10.1016/j.jfranklin.2024.107221","url":null,"abstract":"<div><p>In this paper, an enhanced parametric detection method employing diversified scan and iteration is proposed for heterogeneous environment. A diversified scan, encompassing both rough scan and intensive scan, is first conducted in the normalized space–time frequency field to acquire the interference’s frequency components, which is conducive to obtaining the outline of interference in the normalized space–time two-dimensional (2-D) frequency field. The intensities of these components are subsequently determined through iteration to reduce the impact brought by the randomness of training samples. Meanwhile, the environment is commonly sparse in most cases, which is fully utilized in the proposed method. Then the cross-correlation matrix and autoregressive (AR) covariance matrix are reconstructed to form the corresponding detector. In the end, the availability and superiority of the proposed method are validated by numerical results. It is shown from numerical results that the proposed method performs well in detection performance compared to several existing typical methods in heterogeneous environment.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142129079","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 : 2024-08-28DOI: 10.1016/j.jfranklin.2024.107194
This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.
{"title":"Stabilization of delayed Markovian jump systems with sampled controllers","authors":"","doi":"10.1016/j.jfranklin.2024.107194","DOIUrl":"10.1016/j.jfranklin.2024.107194","url":null,"abstract":"<div><p>This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088778","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 : 2024-08-28DOI: 10.1016/j.jfranklin.2024.107205
This paper investigates finite-time input-to-state stability (FT-ISS) of impulsive switched systems with multiple impulses. Some FT-ISS conditions, using Lyapunov method and dwell-time condition, are established for impulsive switched systems involving destabilizing and stabilizing impulses simultaneously. When constituent modes regulating continuous dynamics are FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the FT-ISS is retained if impulsive-switching signal satisfies some dwell-time condition. When some constituent modes regulating continuous dynamics are not FT-ISS and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the impulsive-switching signal which satisfies some dwell-time conditions can achieve the FT-ISS of system. In addition, the settling time can be derived conveniently for certain impulsive-switching signal that is formalized by dwell-time condition. The estimation of settling time presents a class of uniformity with respect to the impulsive-switching signals. Two examples are finally presented for the proposed FT-ISS results.
{"title":"Finite-time input-to-state stability and settling-time estimation of impulsive switched systems with multiple impulses","authors":"","doi":"10.1016/j.jfranklin.2024.107205","DOIUrl":"10.1016/j.jfranklin.2024.107205","url":null,"abstract":"<div><p>This paper investigates finite-time input-to-state stability (<em>FT-ISS</em>) of impulsive switched systems with multiple impulses. Some <em>FT-ISS</em> conditions, using Lyapunov method and dwell-time condition, are established for impulsive switched systems involving destabilizing and stabilizing impulses simultaneously. When constituent modes regulating continuous dynamics are <em>FT-ISS</em> and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the <em>FT-ISS</em> is retained if impulsive-switching signal satisfies some dwell-time condition. When some constituent modes regulating continuous dynamics are not <em>FT-ISS</em> and discrete dynamics involve destabilizing and stabilizing impulses, it is shown that, the impulsive-switching signal which satisfies some dwell-time conditions can achieve the <em>FT-ISS</em> of system. In addition, the settling time can be derived conveniently for certain impulsive-switching signal that is formalized by dwell-time condition. The estimation of settling time presents a class of uniformity with respect to the impulsive-switching signals. Two examples are finally presented for the proposed <em>FT-ISS</em> results.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088774","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 : 2024-08-28DOI: 10.1016/j.jfranklin.2024.107218
This paper investigates the automatic carrier landing control problem in the presence of model uncertainty, airwake disturbances, input saturation, and output constraints. Considering the performance requirements of the carrier-based aircraft, a composite adaptive neural controller is proposed based on the time-varying barrier Lyapunov function and backstepping control techniques. The radial basis function neural network is used to approximate the model uncertainty, where the neural network weight update law incorporating prediction and tracking errors further improves the convergence rate of the neural network and mitigates high-frequency oscillations. Furthermore, an adaptive disturbance compensation model is established to mitigate the adverse effects of airwake disturbances and estimation errors in the neural network. Based on the Lyapunov stability theory, it is proven that the proposed controller maintains the aircraft trajectory within the prescribed constraints and also ensures that all signals in the closed-loop control system are semiglobally uniformly ultimately bounded. Finally, comparative simulations are performed to demonstrate the effectiveness and superiority of the proposed composite adaptive neural control method.
{"title":"Composite adaptive neural control for automatic carrier landing system with input saturation and output constraints","authors":"","doi":"10.1016/j.jfranklin.2024.107218","DOIUrl":"10.1016/j.jfranklin.2024.107218","url":null,"abstract":"<div><p>This paper investigates the automatic carrier landing control problem in the presence of model uncertainty, airwake disturbances, input saturation, and output constraints. Considering the performance requirements of the carrier-based aircraft, a composite adaptive neural controller is proposed based on the time-varying barrier Lyapunov function and backstepping control techniques. The radial basis function neural network is used to approximate the model uncertainty, where the neural network weight update law incorporating prediction and tracking errors further improves the convergence rate of the neural network and mitigates high-frequency oscillations. Furthermore, an adaptive disturbance compensation model is established to mitigate the adverse effects of airwake disturbances and estimation errors in the neural network. Based on the Lyapunov stability theory, it is proven that the proposed controller maintains the aircraft trajectory within the prescribed constraints and also ensures that all signals in the closed-loop control system are semiglobally uniformly ultimately bounded. Finally, comparative simulations are performed to demonstrate the effectiveness and superiority of the proposed composite adaptive neural control method.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088777","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 : 2024-08-28DOI: 10.1016/j.jfranklin.2024.107204
Localization technology is crucial for indoor robot navigation. However, because of the intricacies inherent in the indoor setting, the signal transmission is vulnerable to the interference of obstacles, which leads to the decline of positioning accuracy. Ultra-Wideband (UWB) has the characteristics of channel insensitivity and high localization accuracy. Inertial navigation system (INS) functions independently as a navigation system, and its positioning results will not be affected due to non-line-of-sight (NLOS) interference. When using UWB to locate the mobile node, the Variational Bayesian Gaussian Mixture Model (VBGMM) clustering algorithm based on Gaussian Mixture Model (GMM) is applied to lessen the influence of NLOS propagation. This paper proposed a loose coupling of the INS and UWB, which combines the advantages of the two subsystems and improves the performance of the positioning system. On the basis of INS autonomous positioning, the maximum entropy fuzzy generalized probability data association filter (MEF-GPDAF) is used to modify the INS positioning results, and then the virtual inertia points are further built to compensate the error of the corrected coordinates. Finally, Unscented Kalman Filter is applied to the compensated coordinates for enhanced positioning. Simulation indicates that the proposed approach in this paper exhibits superior location accuracy. The real experimental results show that the proposed algorithm achieves an average improvement of 61.12% in positioning accuracy.
定位技术对于室内机器人导航至关重要。然而,由于室内环境错综复杂,信号传输容易受到障碍物的干扰,导致定位精度下降。超宽带(UWB)具有信道不敏感和定位精度高的特点。惯性导航系统(INS)作为导航系统独立运行,其定位结果不会受到非视距(NLOS)干扰的影响。在使用 UWB 定位移动节点时,为了减少非视距传播的影响,需要使用基于高斯混杂模型(GMM)的变异贝叶斯高斯混杂模型(VBGMM)聚类算法。本文提出了一种松耦合的 INS 和 UWB,它结合了两个子系统的优势,提高了定位系统的性能。在 INS 自主定位的基础上,利用最大熵模糊广义概率数据关联滤波器(MEF-GPDAF)对 INS 定位结果进行修正,然后进一步建立虚拟惯性点来补偿修正后的坐标误差。最后,对补偿后的坐标应用无痕卡尔曼滤波器进行增强定位。仿真表明,本文提出的方法具有更高的定位精度。实际实验结果表明,所提算法的定位精度平均提高了 61.12%。
{"title":"INS/UWB fusion localization algorithm in indoor environment based on variational Bayesian and error compensation","authors":"","doi":"10.1016/j.jfranklin.2024.107204","DOIUrl":"10.1016/j.jfranklin.2024.107204","url":null,"abstract":"<div><p>Localization technology is crucial for indoor robot navigation. However, because of the intricacies inherent in the indoor setting, the signal transmission is vulnerable to the interference of obstacles, which leads to the decline of positioning accuracy. Ultra-Wideband (UWB) has the characteristics of channel insensitivity and high localization accuracy. Inertial navigation system (INS) functions independently as a navigation system, and its positioning results will not be affected due to non-line-of-sight (NLOS) interference. When using UWB to locate the mobile node, the Variational Bayesian Gaussian Mixture Model (VBGMM) clustering algorithm based on Gaussian Mixture Model (GMM) is applied to lessen the influence of NLOS propagation. This paper proposed a loose coupling of the INS and UWB, which combines the advantages of the two subsystems and improves the performance of the positioning system. On the basis of INS autonomous positioning, the maximum entropy fuzzy generalized probability data association filter (MEF-GPDAF) is used to modify the INS positioning results, and then the virtual inertia points are further built to compensate the error of the corrected coordinates. Finally, Unscented Kalman Filter is applied to the compensated coordinates for enhanced positioning. Simulation indicates that the proposed approach in this paper exhibits superior location accuracy. The real experimental results show that the proposed algorithm achieves an average improvement of 61.12% in positioning accuracy.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121623","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 : 2024-08-26DOI: 10.1016/j.jfranklin.2024.107201
Physiological recordings contain a great deal of information about the underlying dynamics of Life. The practical statistical treatment of these single-trial measurements is often hampered by the inadequacy of overly strong assumptions. Heisenberg’s uncertainty principle allows for more parsimony, trading off statistical significance for localization. By decomposing signals into time–frequency atoms and recomposing them into local quadratic estimates, we propose a concise and expressive implementation of these fundamental concepts based on the choice of a geometric paradigm and two physical parameters. Starting from the spectrogram based on two fixed timescales and Gabor’s normal window, we then build its scale-invariant analogue, the scalogram based on two quality factors and Grossmann’s log-normal wavelet. These canonical estimators provide a minimal and flexible framework for single trial time–frequency statistics, which we apply to polysomnographic signals: EEG representations, HRV extraction from ECG, coherence and mutual information between heart rate and respiration.
{"title":"Uncertainty and information in physiological signals: Explicit physical trade-off with log-normal wavelets","authors":"","doi":"10.1016/j.jfranklin.2024.107201","DOIUrl":"10.1016/j.jfranklin.2024.107201","url":null,"abstract":"<div><p>Physiological recordings contain a great deal of information about the underlying dynamics of Life. The practical statistical treatment of these single-trial measurements is often hampered by the inadequacy of overly strong assumptions. Heisenberg’s uncertainty principle allows for more parsimony, trading off statistical significance for localization. By decomposing signals into time–frequency atoms and recomposing them into local quadratic estimates, we propose a concise and expressive implementation of these fundamental concepts based on the choice of a geometric paradigm and two physical parameters. Starting from the spectrogram based on two fixed timescales and Gabor’s normal window, we then build its scale-invariant analogue, the scalogram based on two quality factors and Grossmann’s log-normal wavelet. These canonical estimators provide a minimal and flexible framework for single trial time–frequency statistics, which we apply to polysomnographic signals: EEG representations, HRV extraction from ECG, coherence and mutual information between heart rate and respiration.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0016003224006227/pdfft?md5=6318ced97a3dde91ccd2ac8cc17997f4&pid=1-s2.0-S0016003224006227-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-24DOI: 10.1016/j.jfranklin.2024.107199
This paper aims to generalize the quickest change detection (QCD) framework via a data-driven approach. To this end, a generic neural network architecture is proposed for the QCD task, composed of feature transformation, recurrent, and dense layers. The neural network is trained end-to-end to learn the change detection rule directly from data without needing the knowledge of probabilistic data models. Specifically, the feature transformation layers can perform a broad range of operations including feature extraction, scaling, and normalization. The recurrent layers keep an internal state summarizing the time-series data seen so far and update the state as new information comes in. Finally, the dense layers map the internal state into a decision statistic, defined as the posterior probability that a change has taken place. Comparisons with the existing model-based QCD algorithms demonstrate the power of the proposed data-driven approach, called DeepQCD, under several scenarios including transient changes and temporally correlated data streams. Experiments with real-world data illustrate superior performance of DeepQCD compared to state-of-the-art algorithms in real-time anomaly detection over surveillance videos and real-time attack detection over Internet of Things (IoT) networks.
{"title":"DeepQCD: An end-to-end deep learning approach to quickest change detection","authors":"","doi":"10.1016/j.jfranklin.2024.107199","DOIUrl":"10.1016/j.jfranklin.2024.107199","url":null,"abstract":"<div><div>This paper aims to generalize the quickest change detection (QCD) framework via a data-driven approach. To this end, a generic neural network architecture is proposed for the QCD task, composed of feature transformation, recurrent, and dense layers. The neural network is trained end-to-end to learn the change detection rule directly from data without needing the knowledge of probabilistic data models. Specifically, the feature transformation layers can perform a broad range of operations including feature extraction, scaling, and normalization. The recurrent layers keep an internal state summarizing the time-series data seen so far and update the state as new information comes in. Finally, the dense layers map the internal state into a decision statistic, defined as the posterior probability that a change has taken place. Comparisons with the existing model-based QCD algorithms demonstrate the power of the proposed data-driven approach, called DeepQCD, under several scenarios including transient changes and temporally correlated data streams. Experiments with real-world data illustrate superior performance of DeepQCD compared to state-of-the-art algorithms in real-time anomaly detection over surveillance videos and real-time attack detection over Internet of Things (IoT) networks.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316208","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 : 2024-08-24DOI: 10.1016/j.jfranklin.2024.107208
This paper proposes an observer-based quantized controller for parabolic partial differential equation systems interconnected by a nonlinear coupling protocol. First, a Markov jump model is introduced to describe various randomly occurring actuator failures, and an observer-based pointwise controller is designed under the averaged measurement scheme. Furthermore, taking into account the limitation of network communication resources, a quantization method is adopted to relieve bandwidth pressure. In addition, stability conditions of the closed-loop system with disturbance attenuation performance are derived by utilizing appropriate Lyapunov functional and inequality techniques. Ultimately, the proposed method is applied to the Fisher equation to verify its feasibility and effectiveness.
{"title":"Observer-based quantized control for networked interconnected PDE systems with actuator failures","authors":"","doi":"10.1016/j.jfranklin.2024.107208","DOIUrl":"10.1016/j.jfranklin.2024.107208","url":null,"abstract":"<div><p>This paper proposes an observer-based quantized controller for parabolic partial differential equation systems interconnected by a nonlinear coupling protocol. First, a Markov jump model is introduced to describe various randomly occurring actuator failures, and an observer-based pointwise controller is designed under the averaged measurement scheme. Furthermore, taking into account the limitation of network communication resources, a quantization method is adopted to relieve bandwidth pressure. In addition, stability conditions of the closed-loop system with <span><math><msub><mrow><mi>ℋ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> disturbance attenuation performance are derived by utilizing appropriate Lyapunov functional and inequality techniques. Ultimately, the proposed method is applied to the Fisher equation to verify its feasibility and effectiveness.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142099291","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 : 2024-08-23DOI: 10.1016/j.jfranklin.2024.107192
This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.
{"title":"Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching","authors":"","doi":"10.1016/j.jfranklin.2024.107192","DOIUrl":"10.1016/j.jfranklin.2024.107192","url":null,"abstract":"<div><p>This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.</p></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088770","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}