Pub Date : 2024-09-25DOI: 10.1016/j.jfranklin.2024.107294
This paper addresses the challenge of reachable set estimation in singular multi-agent systems with time-delay and semi-Markov switching topologies. The primary goal is to construct an ellipsoid that encompasses all states originating from the origin. Furthermore, criteria for reachable sets with reduced conservatism are developed. The singular multi-agent systems are reduced by the Laplace matrix, then the Lyapunov–Krasovskii functional is constructed by using decomposed state vector. In addition, the sufficient conditions for the reachable set of singular multi-agent systems bounded by ellipsoids are given by matrix theory and linear matrix inequality. Numerical examples show that our results is effective.
{"title":"Reachable set control of singular semi-Markov jump multi-agent systems with input delay via state decomposition method","authors":"","doi":"10.1016/j.jfranklin.2024.107294","DOIUrl":"10.1016/j.jfranklin.2024.107294","url":null,"abstract":"<div><div>This paper addresses the challenge of reachable set estimation in singular multi-agent systems with time-delay and semi-Markov switching topologies. The primary goal is to construct an ellipsoid that encompasses all states originating from the origin. Furthermore, criteria for reachable sets with reduced conservatism are developed. The singular multi-agent systems are reduced by the Laplace matrix, then the Lyapunov–Krasovskii functional is constructed by using decomposed state vector. In addition, the sufficient conditions for the reachable set of singular multi-agent systems bounded by ellipsoids are given by matrix theory and linear matrix inequality. Numerical examples show that our results is effective.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420679","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 : 2024-09-24DOI: 10.1016/j.jfranklin.2024.107284
In this paper, to achieve the synchronization control for a class of complex dynamic networks with completely unknown system dynamics, a reinforcement learning output feedback algorithm based on state reconstruction is proposed. Given the high cost and complexity associated with obtaining the full state information, an output-based node state reconstruction method is employed for the first time in complex dynamic networks. The proposed method utilizes a sequence composed of a finite number of output data to reconstruct the current state. At the same time, the overall error system is constructed to handle the coupling relationship between nodes, to facilitate the controller design. Thereafter, considering the system dynamics are unknown, an algorithm based on reinforcement learning is proposed to ensure rapid synchronization of node outputs, and the convergence of proposed method is proven. Finally, the feasibility of proposed algorithm is corroborated through a simulation example and a multi-vehicle system.
{"title":"Output synchronization of a class of complex dynamic networks: A reinforcement learning method","authors":"","doi":"10.1016/j.jfranklin.2024.107284","DOIUrl":"10.1016/j.jfranklin.2024.107284","url":null,"abstract":"<div><div>In this paper, to achieve the synchronization control for a class of complex dynamic networks with completely unknown system dynamics, a reinforcement learning output feedback algorithm based on state reconstruction is proposed. Given the high cost and complexity associated with obtaining the full state information, an output-based node state reconstruction method is employed for the first time in complex dynamic networks. The proposed method utilizes a sequence composed of a finite number of output data to reconstruct the current state. At the same time, the overall error system is constructed to handle the coupling relationship between nodes, to facilitate the controller design. Thereafter, considering the system dynamics are unknown, an algorithm based on reinforcement learning is proposed to ensure rapid synchronization of node outputs, and the convergence of proposed method is proven. Finally, the feasibility of proposed algorithm is corroborated through a simulation example and a multi-vehicle system.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420680","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 : 2024-09-24DOI: 10.1016/j.jfranklin.2024.107292
This paper employs an event-triggered control approach to investigate the simultaneous finite-time fault-tolerant control and disturbance rejection problem for stochastic Markovian jump systems with general transition probabilities. Firstly, in conjunction with the event-triggered mechanism, a novel composite observer is designed, which can not only simultaneously estimate states and faults as well as disturbances of the system, but also guarantee that the error system is stochastically finite-time bounded. Subsequently, leveraging the obtained estimations, an active fault-tolerant controller with anti-disturbance performance is constructed to guarantee the finite-time boundedness of closed-loop system. Finally, the effectiveness of the proposed scheme is verified by distinct examples.
{"title":"Event-triggered finite-time fault-tolerance control and simultaneous disturbance rejection for Markov jump systems with general transition probabilities","authors":"","doi":"10.1016/j.jfranklin.2024.107292","DOIUrl":"10.1016/j.jfranklin.2024.107292","url":null,"abstract":"<div><div>This paper employs an event-triggered control approach to investigate the simultaneous finite-time fault-tolerant control and disturbance rejection problem for stochastic Markovian jump systems with general transition probabilities. Firstly, in conjunction with the event-triggered mechanism, a novel composite observer is designed, which can not only simultaneously estimate states and faults as well as disturbances of the system, but also guarantee that the error system is stochastically finite-time bounded. Subsequently, leveraging the obtained estimations, an active fault-tolerant controller with anti-disturbance performance is constructed to guarantee the finite-time boundedness of closed-loop system. Finally, the effectiveness of the proposed scheme is verified by distinct examples.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420678","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 : 2024-09-24DOI: 10.1016/j.jfranklin.2024.107281
In this paper, the fusion estimation problem is studied for a class of multi-rate systems (MRS) subject to state saturation. The state update rate of the system and the sampling rate of sensors are different in MRS. In addition, to incorporate the requirements of actual engineering practice, the sensor resolution and the phenomenon of integral measurements are considered in the measurement output of sensors. The aim of this paper is to design an appropriate set of local estimators for each sensor node by taking into account the effects of integral measurement, sensor resolution and multi-rate sampling mechanism. Then, the upper bound on the error covariance of the estimator can be obtained by calculating solution of the matrix difference equation and the relevant filter parameter is determined by minimizing the upper bound. Based on the covariance intersection (CI) method, the fusion estimation is obtained by fusing local estimates. The consistency is demonstrated for this fusion estimating approach. Finally, the effectiveness and appropriateness of the multi-rate fusion estimation approach are confirmed by comprehensive simulations.
{"title":"Fusion estimation for state-saturated multi-rate systems with integral measurement and sensor resolution","authors":"","doi":"10.1016/j.jfranklin.2024.107281","DOIUrl":"10.1016/j.jfranklin.2024.107281","url":null,"abstract":"<div><div>In this paper, the fusion estimation problem is studied for a class of multi-rate systems (MRS) subject to state saturation. The state update rate of the system and the sampling rate of sensors are different in MRS. In addition, to incorporate the requirements of actual engineering practice, the sensor resolution and the phenomenon of integral measurements are considered in the measurement output of sensors. The aim of this paper is to design an appropriate set of local estimators for each sensor node by taking into account the effects of integral measurement, sensor resolution and multi-rate sampling mechanism. Then, the upper bound on the error covariance of the estimator can be obtained by calculating solution of the matrix difference equation and the relevant filter parameter is determined by minimizing the upper bound. Based on the covariance intersection (CI) method, the fusion estimation is obtained by fusing local estimates. The consistency is demonstrated for this fusion estimating approach. Finally, the effectiveness and appropriateness of the multi-rate fusion estimation approach are confirmed by comprehensive simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420763","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 : 2024-09-24DOI: 10.1016/j.jfranklin.2024.107297
This paper delves into the projective lag synchronization of Riemann–Liouville type fractional-order memristive neural networks accounting for jump mismatch. Recognizing the inherent inconsistencies in synchronizing traditional fractional-order memristive neural networks, we introduce a novel mathematical model that accommodates the jump mismatch phenomenon. A groundbreaking event-based hybrid pinning impulsive controller is then introduced, equipped with tailored event-triggering conditions, to elucidate the global asymptotic projective lag synchronization. Leveraging inequality principles and impulse analysis, a new Lyapunov functional is proposed, formulating sufficient conditions for synchronization while theoretically eliminating Zeno behavior in the controller. Notably, our approach substantially optimizes control overhead while fulfilling practical synchronization requisites. In addition, the obtained sufficient conditions can theoretically guide practical engineering applications of the network. Finally, a simulation example, emphasizing varied projective and lag factors, demonstrates our findings.
{"title":"Projective lag synchronization of fractional delayed memristive neural networks via event-based hybrid pinning impulsive controller","authors":"","doi":"10.1016/j.jfranklin.2024.107297","DOIUrl":"10.1016/j.jfranklin.2024.107297","url":null,"abstract":"<div><div>This paper delves into the projective lag synchronization of Riemann–Liouville type fractional-order memristive neural networks accounting for jump mismatch. Recognizing the inherent inconsistencies in synchronizing traditional fractional-order memristive neural networks, we introduce a novel mathematical model that accommodates the jump mismatch phenomenon. A groundbreaking event-based hybrid pinning impulsive controller is then introduced, equipped with tailored event-triggering conditions, to elucidate the global asymptotic projective lag synchronization. Leveraging inequality principles and impulse analysis, a new Lyapunov functional is proposed, formulating sufficient conditions for synchronization while theoretically eliminating Zeno behavior in the controller. Notably, our approach substantially optimizes control overhead while fulfilling practical synchronization requisites. In addition, the obtained sufficient conditions can theoretically guide practical engineering applications of the network. Finally, a simulation example, emphasizing varied projective and lag factors, demonstrates our findings.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322459","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 : 2024-09-23DOI: 10.1016/j.jfranklin.2024.107287
In the paper by Meng et al. (2023), an observer is proposed for nonlinear singular systems. The authors claim that their method effectively handles nonlinearity and disturbances affecting both the dynamic and algebraic parts of the system. They compare the performance of their observer with that proposed by Darouach et al. (2011), focusing on observer design for nonlinear singular systems with disturbances affecting the dynamic and algebraic parts as well as the output of the system. Furthermore, this approach has been extended to several other classes of systems, as discussed in Zerrougui et al. (2014) [1], Darouach et al. (2013) [2], and Darouach et al. (2010) [3]. Meng et al. apply their observer to estimate the state of charge of a lithium battery in comparison with the results in Snoussi et al. (2020). In this note, we aim to highlight the discrepancies between our respective findings. Specifically, we explain that the observer proposed by Meng et al. (2023), is more restrictive and may not be suitable for singular systems with nonlinear algebraic components or disturbances affecting this part or affecting outputs. Additionally, Meng et al. (2023) revisit the framework introduced in Darouach et al. (2011), adding a particular form for the matrix that renders it more restrictive, without any contribution in the stability synthesis part.
{"title":"Comment on: A robust observer based on the nonlinear descriptor systems application to estimate the state of charge of lithium-ion batteries","authors":"","doi":"10.1016/j.jfranklin.2024.107287","DOIUrl":"10.1016/j.jfranklin.2024.107287","url":null,"abstract":"<div><div>In the paper by Meng et al. (2023), an observer is proposed for nonlinear singular systems. The authors claim that their method effectively handles nonlinearity and disturbances affecting both the dynamic and algebraic parts of the system. They compare the performance of their observer with that proposed by Darouach et al. (2011), focusing on observer design for nonlinear singular systems with disturbances affecting the dynamic and algebraic parts as well as the output of the system. Furthermore, this approach has been extended to several other classes of systems, as discussed in Zerrougui et al. (2014) <span><span>[1]</span></span>, Darouach et al. (2013) <span><span>[2]</span></span>, and Darouach et al. (2010) <span><span>[3]</span></span>. Meng et al. apply their observer to estimate the state of charge of a lithium battery in comparison with the results in Snoussi et al. (2020). In this note, we aim to highlight the discrepancies between our respective findings. Specifically, we explain that the observer proposed by Meng et al. (2023), is more restrictive and may not be suitable for singular systems with nonlinear algebraic components or disturbances affecting this part or affecting outputs. Additionally, Meng et al. (2023) revisit the framework introduced in Darouach et al. (2011), adding a particular form for the matrix <span><math><mi>Φ</mi></math></span> that renders it more restrictive, without any contribution in the stability synthesis part.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420822","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 : 2024-09-23DOI: 10.1016/j.jfranklin.2024.107269
Medical hyperspectral imaging present a promising avenue for non-invasive diagnostic methods for diseases. Nonetheless, the sparsity of medical hyperspectral data within high-dimensional spaces introduces the “curse of dimensionality”, which diminishes the efficiency and accuracy of data processing efforts. Therefore, spectral dimensionality reduction emerges as an essential process in the analysis and utilization of MHSIs data. To retain the intrinsic properties of the spectral bands, an effective unsupervised band selection algorithm is proposed leveraging the gravitational search algorithm (GSA-UBS) to identify the optimal band subset. Taking into account the informational content and redundancy among candidate bands, a comprehensive evaluation criterion is established that incorporates a band distance matrix and an information entropy vector. Additionally, a straightforward discrete search strategy is developed that enables gravitational search algorithm to directly retrieve the original sequence numbers of the selected bands, bypassing the conventional 0–1 band weighting approach. The extensive evaluation of GSA-UBS on three publicly available brain cancer MHSIs datasets and a remote sensing hyperspectral image demonstrates its superior performance compared to various state-of-the-art methods. The source code for GSA-UBS can be accessed at https://github.com/zhangchenglong1116/GSA_UBS.
{"title":"Novel discretized gravitational search algorithm for effective medical hyperspectral band selection","authors":"","doi":"10.1016/j.jfranklin.2024.107269","DOIUrl":"10.1016/j.jfranklin.2024.107269","url":null,"abstract":"<div><div>Medical hyperspectral imaging present a promising avenue for non-invasive diagnostic methods for diseases. Nonetheless, the sparsity of medical hyperspectral data within high-dimensional spaces introduces the “curse of dimensionality”, which diminishes the efficiency and accuracy of data processing efforts. Therefore, spectral dimensionality reduction emerges as an essential process in the analysis and utilization of MHSIs data. To retain the intrinsic properties of the spectral bands, an effective unsupervised band selection algorithm is proposed leveraging the gravitational search algorithm (GSA-UBS) to identify the optimal band subset. Taking into account the informational content and redundancy among candidate bands, a comprehensive evaluation criterion is established that incorporates a band distance matrix and an information entropy vector. Additionally, a straightforward discrete search strategy is developed that enables gravitational search algorithm to directly retrieve the original sequence numbers of the selected bands, bypassing the conventional 0–1 band weighting approach. The extensive evaluation of GSA-UBS on three publicly available <span><math><mrow><mi>i</mi><mi>n</mi><mi>v</mi><mi>i</mi><mi>v</mi><mi>o</mi></mrow></math></span> brain cancer MHSIs datasets and a remote sensing hyperspectral image demonstrates its superior performance compared to various state-of-the-art methods. The source code for GSA-UBS can be accessed at <span><span>https://github.com/zhangchenglong1116/GSA_UBS</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420653","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 : 2024-09-23DOI: 10.1016/j.jfranklin.2024.107278
In this paper, a novel data-driven integral sliding mode predictive control algorithm based on an optimal disturbance observer (DDISMPC-ODO) is proposed for a class of nonlinear discrete-time systems (NDTS) subject to external disturbances. The designed optimal disturbance observer realizes the precise observation of the lumped disturbance, thus ameliorating the accuracy of the controller and weakening problems with chattering. In this work, a robust pseudo-partial derivative (PPD) estimation algorithm is introduced, which not only improves the system performance, but also facilitates theoretical proof of parameter estimation and tracking accuracy. The convergence of the PPD estimation error and disturbance observation error is proved. It is also proved that the accuracy of the disturbance observation error can converge to and then the magnitude of the sliding variable and the tracking error are also reduced to respectively. Finally, the effectiveness of the proposed method is demonstrated by a simulation example and an experiment.
{"title":"Data-driven integral sliding mode predictive control with optimal disturbance observer","authors":"","doi":"10.1016/j.jfranklin.2024.107278","DOIUrl":"10.1016/j.jfranklin.2024.107278","url":null,"abstract":"<div><div>In this paper, a novel data-driven integral sliding mode predictive control algorithm based on an optimal disturbance observer (DDISMPC-ODO) is proposed for a class of nonlinear discrete-time systems (NDTS) subject to external disturbances. The designed optimal disturbance observer realizes the precise observation of the lumped disturbance, thus ameliorating the accuracy of the controller and weakening problems with chattering. In this work, a robust pseudo-partial derivative (PPD) estimation algorithm is introduced, which not only improves the system performance, but also facilitates theoretical proof of parameter estimation and tracking accuracy. The convergence of the PPD estimation error and disturbance observation error is proved. It is also proved that the accuracy of the disturbance observation error can converge to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and then the magnitude of the sliding variable and the tracking error are also reduced to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> respectively. Finally, the effectiveness of the proposed method is demonstrated by a simulation example and an experiment.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420824","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 : 2024-09-22DOI: 10.1016/j.jfranklin.2024.107283
In this paper, a coupling cholera epidemic model is proposed, in which the pathogens could both spread within-host and between-host, meanwhile, there exist age-dependent infection between the asymptomatic and symptomatic infected people. For the fast-time subsystem, the infection-free and endemic equilibria are both globally asymptotically stable. For the slow-time subsystem, the basic reproduction number is determined, by which we observe that the disease-free equilibrium is globally asymptotically stable (the absence of pathogens in environment) if , while the endemic equilibrium is globally asymptotically stable (the presence of pathogens in environment) when . The theoretical results are illustrated by numerical simulations, by which we find that age-dependent and asymptomatic infections may further promote cholera spread. Besides, the linking of pathogen transmission at the individual level with infection at the population level could result in forward or backward bifurcation.
{"title":"A cholera model coupling within-host and between-host with age-dependent and asymptomatic infections","authors":"","doi":"10.1016/j.jfranklin.2024.107283","DOIUrl":"10.1016/j.jfranklin.2024.107283","url":null,"abstract":"<div><div>In this paper, a coupling cholera epidemic model is proposed, in which the pathogens could both spread within-host and between-host, meanwhile, there exist age-dependent infection between the asymptomatic and symptomatic infected people. For the fast-time subsystem, the infection-free and endemic equilibria are both globally asymptotically stable. For the slow-time subsystem, the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is determined, by which we observe that the disease-free equilibrium is globally asymptotically stable (the absence of pathogens in environment) if <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span>, while the endemic equilibrium is globally asymptotically stable (the presence of pathogens in environment) when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>. The theoretical results are illustrated by numerical simulations, by which we find that age-dependent and asymptomatic infections may further promote cholera spread. Besides, the linking of pathogen transmission at the individual level with infection at the population level could result in forward or backward bifurcation.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420819","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 : 2024-09-21DOI: 10.1016/j.jfranklin.2024.107286
In this paper, a rational-quadratic kernel-based maximum correntropy Kalman filter (RKMCKF) algorithm is proposed to improve the estimation accuracy for non-Gaussian noise interference. Firstly, the RKMCKF algorithm is derived to eliminate the singular matrix produced by multi-dimensional non-Gaussian noise disturbance. Secondly, the upper limit is analyzed to provide a theoretical range for kernel bandwidth, which is beneficial for the selection of proper kernel bandwidths and boosting the precision of state estimation. Furthermore, the boundness of the state estimation error is verified to manifest the RKMCKF algorithm stability. Finally, under different types of non-Gaussian noise, the proposed RKMCKF algorithm is demonstrated to promote the accuracy of state estimation compared with the conventional Kalman filter, Gaussian sum filter, Huber filter, and maximum correntropy Kalman filter through the simulations.
{"title":"Rational-quadratic kernel-based maximum correntropy Kalman filter for the non-Gaussian noises","authors":"","doi":"10.1016/j.jfranklin.2024.107286","DOIUrl":"10.1016/j.jfranklin.2024.107286","url":null,"abstract":"<div><div>In this paper, a rational-quadratic kernel-based maximum correntropy Kalman filter (RKMCKF) algorithm is proposed to improve the estimation accuracy for non-Gaussian noise interference. Firstly, the RKMCKF algorithm is derived to eliminate the singular matrix produced by multi-dimensional non-Gaussian noise disturbance. Secondly, the upper limit is analyzed to provide a theoretical range for kernel bandwidth, which is beneficial for the selection of proper kernel bandwidths and boosting the precision of state estimation. Furthermore, the boundness of the state estimation error is verified to manifest the RKMCKF algorithm stability. Finally, under different types of non-Gaussian noise, the proposed RKMCKF algorithm is demonstrated to promote the accuracy of state estimation compared with the conventional Kalman filter, Gaussian sum filter, Huber filter, and maximum correntropy Kalman filter through the simulations.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420622","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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