Pub Date : 2025-01-03DOI: 10.1016/j.cnsns.2024.108584
P. Karthika, P. Sozhaeswari, A. Mohammadzadeh, R. Sakthivel
The focus of this study is on investigating the design of dynamic hybrid-triggered resilient control for partial differential equation (PDE) systems even in the presence of Neumann boundary conditions. To be specific, the PDE under consideration is of the parabolic type involving cyber–physical switched systems and is subject to randomly occurring uncertainties, external disturbances and false data injection (FDI) attacks. Moreover, in an attempt to minimize the volume of data transfers, a broader dynamic hybrid-triggered (DHT) approach is executed, amalgamating both time-triggered and dynamic event-triggered techniques. Concurrently, resilient control is being considered to guarantee the required stabilization of the system, even in the presence of gain fluctuations. Within the specified context, stochastic variables that conform to the Bernoulli distribution are incorporated in the DHT resilient scheme and FDI attacks. Furthermore, the construction of a pertinent Lyapunov–Krasovskii functional leads to the establishment of required conditions for ensuring both asymptotic stability and extended dissipative performance for the closed-loop structure. Moreover, the required controller gain matrices are derived through the utilization of linear matrix inequalities. Ultimately, the suggested control design technique’s effectiveness is showcased through the presentation of two numerical examples.
{"title":"Design of dynamic hybrid-triggered dissipative resilient control for parabolic PDE cyber–physical switched systems with attacks","authors":"P. Karthika, P. Sozhaeswari, A. Mohammadzadeh, R. Sakthivel","doi":"10.1016/j.cnsns.2024.108584","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108584","url":null,"abstract":"The focus of this study is on investigating the design of dynamic hybrid-triggered resilient control for partial differential equation (PDE) systems even in the presence of Neumann boundary conditions. To be specific, the PDE under consideration is of the parabolic type involving cyber–physical switched systems and is subject to randomly occurring uncertainties, external disturbances and false data injection (FDI) attacks. Moreover, in an attempt to minimize the volume of data transfers, a broader dynamic hybrid-triggered (DHT) approach is executed, amalgamating both time-triggered and dynamic event-triggered techniques. Concurrently, resilient control is being considered to guarantee the required stabilization of the system, even in the presence of gain fluctuations. Within the specified context, stochastic variables that conform to the Bernoulli distribution are incorporated in the DHT resilient scheme and FDI attacks. Furthermore, the construction of a pertinent Lyapunov–Krasovskii functional leads to the establishment of required conditions for ensuring both asymptotic stability and extended dissipative performance for the closed-loop structure. Moreover, the required controller gain matrices are derived through the utilization of linear matrix inequalities. Ultimately, the suggested control design technique’s effectiveness is showcased through the presentation of two numerical examples.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"20 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cnsns.2024.108589
Oleg Kuzenkov, Andrew Yu. Morozov, Ivan Bataev
Evolutionary fitness is a fundamental concept, widely utilised in modelling natural selection in self-replicating systems. This concept describes selective advantages of inherited elements in the underlying system. Maximisation of evolutionary fitness is traditionally used to predict the outcome of long-term evolution, in particular, to provide the best behavioural strategy or life-history trait. Deriving evolutionary fitness in theoretical models and in empirical systems has always been a challenge. Here we propose a novel computational approach to reconstructing fitness functions in biological systems, using empirical data under the scenario in which the result of competition and selection may depend on initial conditions. Such situations occur, for example, in systems with cyclic competition (e.g., rock–paper–scissors games), and modelling such scenarios has long been considered as a particularly complicated task. Our computational method combines the usage of empirical data with the implementation of a theoretical model of population dynamics in which each subpopulation uses a particular strategy. Firstly, we apply machine learning to empirical data to determine the relative ranking of competing strategies. Then we reconstruct fitness from data and estimate unknown model parameters by comparing the empirically determined fitness with its theoretical expression from the model. Unlike classical regression-based fitting, we quantify the goodness of fit based on the percentage of correctly reconstructed ranking orders of pairs of strategies. Finally, using the derived theoretical expression for fitness with the estimated parameters, we predict the evolutionarily optimal (winning) strategy. As an insightful biological case study, we derive evolutionarily stable diel vertical migration of zooplankton, when the predator (fish) density is a dynamic variable. Our methodology is generic, and can be applied to estimate fitness-like functions in non-biological systems, such as the optimisation of sales, Internet searches, or scientometrics.
{"title":"A novel computational approach to reconstructing evolutionary fitness in self-replicating systems","authors":"Oleg Kuzenkov, Andrew Yu. Morozov, Ivan Bataev","doi":"10.1016/j.cnsns.2024.108589","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108589","url":null,"abstract":"Evolutionary fitness is a fundamental concept, widely utilised in modelling natural selection in self-replicating systems. This concept describes selective advantages of inherited elements in the underlying system. Maximisation of evolutionary fitness is traditionally used to predict the outcome of long-term evolution, in particular, to provide the best behavioural strategy or life-history trait. Deriving evolutionary fitness in theoretical models and in empirical systems has always been a challenge. Here we propose a novel computational approach to reconstructing fitness functions in biological systems, using empirical data under the scenario in which the result of competition and selection may depend on initial conditions. Such situations occur, for example, in systems with cyclic competition (e.g., rock–paper–scissors games), and modelling such scenarios has long been considered as a particularly complicated task. Our computational method combines the usage of empirical data with the implementation of a theoretical model of population dynamics in which each subpopulation uses a particular strategy. Firstly, we apply machine learning to empirical data to determine the relative ranking of competing strategies. Then we reconstruct fitness from data and estimate unknown model parameters by comparing the empirically determined fitness with its theoretical expression from the model. Unlike classical regression-based fitting, we quantify the goodness of fit based on the percentage of correctly reconstructed ranking orders of pairs of strategies. Finally, using the derived theoretical expression for fitness with the estimated parameters, we predict the evolutionarily optimal (winning) strategy. As an insightful biological case study, we derive evolutionarily stable diel vertical migration of zooplankton, when the predator (fish) density is a dynamic variable. Our methodology is generic, and can be applied to estimate fitness-like functions in non-biological systems, such as the optimisation of sales, Internet searches, or scientometrics.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"85 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cnsns.2024.108586
Yang Cao, Zhijun Tan
This paper develops a localized meshless collocation technique for solving the two-dimensional (2D) fourth-order diffusion equation with the Caputo time-fractional derivative of order α∈(0,1). An auxiliary variable is introduced to transform the original fourth-order problem into an equivalent second-order system, preserving the weak singularity of the exact solution at the initial time. Two time semi-discrete schemes are constructed: the first utilizes the standard Alikhanov formula on general time meshes, including both uniform and nonuniform meshes, to approximate the Caputo fractional derivative; the second employs the fast Alikhanov formula, derived from the sum-of-exponentials (SOEs) technique, to reduce computational costs and storage requirements. The local radial basis function partition of unity (LRBF-PU) collocation method is then used for spatial discretization, resulting in two distinct fully discrete schemes. The unconditional stability and convergence of both time semi-discrete schemes are proved by L2 and H1 energy methods. Convergence analysis reveals that the algorithms achieve optimal second-order accuracy in time by selecting an appropriate time mesh parameter γ, which influences the temporal convergence rate. Numerical results on regular and irregular spatial domains with uniform and scattered nodes demonstrate the accuracy, efficiency, and robustness of the proposed algorithms, confirming the theoretical analysis.
{"title":"A fast and high-order localized meshless method for fourth-order time-fractional diffusion equations","authors":"Yang Cao, Zhijun Tan","doi":"10.1016/j.cnsns.2024.108586","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108586","url":null,"abstract":"This paper develops a localized meshless collocation technique for solving the two-dimensional (2D) fourth-order diffusion equation with the Caputo time-fractional derivative of order <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:mrow><mml:mi>α</mml:mi><mml:mo linebreak=\"goodbreak\" linebreakstyle=\"after\">∈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>. An auxiliary variable is introduced to transform the original fourth-order problem into an equivalent second-order system, preserving the weak singularity of the exact solution at the initial time. Two time semi-discrete schemes are constructed: the first utilizes the standard Alikhanov formula on general time meshes, including both uniform and nonuniform meshes, to approximate the Caputo fractional derivative; the second employs the fast Alikhanov formula, derived from the sum-of-exponentials (SOEs) technique, to reduce computational costs and storage requirements. The local radial basis function partition of unity (LRBF-PU) collocation method is then used for spatial discretization, resulting in two distinct fully discrete schemes. The unconditional stability and convergence of both time semi-discrete schemes are proved by <mml:math altimg=\"si1356.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> and <mml:math altimg=\"si1677.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi mathvariant=\"script\">H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> energy methods. Convergence analysis reveals that the algorithms achieve optimal second-order accuracy in time by selecting an appropriate time mesh parameter <mml:math altimg=\"si1334.svg\" display=\"inline\"><mml:mi>γ</mml:mi></mml:math>, which influences the temporal convergence rate. Numerical results on regular and irregular spatial domains with uniform and scattered nodes demonstrate the accuracy, efficiency, and robustness of the proposed algorithms, confirming the theoretical analysis.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"30 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cnsns.2024.108585
Bo Zheng, Yueqiang Shang
Motivated by reducing the computational time and computer storage requirements in the numerical simulations, we present a parallel full domain partition method based on finite element approximations for Stokes and Navier–Stokes type variational inequalities with damping in this paper. Within this parallel method, each subproblem used to calculate an approximate solution is actually a global problem defined in the whole domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for, making the present method easily implementable on the basis of existing black-box sequential solver without massive effort in recoding on the top of existing serial software. Errors of the approximate velocity in L2 norm and pressure in H−1 norm for the serial method are estimated. Based on these error estimate results and the theoretical tool of local a priori estimate for finite element solution, error estimates of the approximate solutions from the proposed method are derived. Correctness of the theoretical predictions and promise of the present method are illustrated by some results of numerics. It is numerically shown that by choosing suitable algorithmic parameters, our proposed parallel method can yield an approximate solution with an accuracy comparable to that of the one calculated by the serial method, and the computational time is reduced.
{"title":"A parallel full domain partition method for Stokes and Navier–Stokes type variational inequalities with damping","authors":"Bo Zheng, Yueqiang Shang","doi":"10.1016/j.cnsns.2024.108585","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108585","url":null,"abstract":"Motivated by reducing the computational time and computer storage requirements in the numerical simulations, we present a parallel full domain partition method based on finite element approximations for Stokes and Navier–Stokes type variational inequalities with damping in this paper. Within this parallel method, each subproblem used to calculate an approximate solution is actually a global problem defined in the whole domain with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for, making the present method easily implementable on the basis of existing black-box sequential solver without massive effort in recoding on the top of existing serial software. Errors of the approximate velocity in <mml:math altimg=\"si1.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> norm and pressure in <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math> norm for the serial method are estimated. Based on these error estimate results and the theoretical tool of local a priori estimate for finite element solution, error estimates of the approximate solutions from the proposed method are derived. Correctness of the theoretical predictions and promise of the present method are illustrated by some results of numerics. It is numerically shown that by choosing suitable algorithmic parameters, our proposed parallel method can yield an approximate solution with an accuracy comparable to that of the one calculated by the serial method, and the computational time is reduced.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"49 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.cnsns.2024.108580
Ho Sub Lee, Chan-eun Park, PooGyeon Park
This study proposes a heterogeneous consensus controller design for multi-agent saturated-input systems under switching topologies with partly unknown transition rates. This study makes three major contributions. First, multi-agent systems that consider both input saturation and switching topologies are addressed. Although both constraints can occur simultaneously, to the best of knowledge, there are no studies on consensus control for multi-agent saturated-input systems under switching topologies. Second, switching topologies with partly unknown transition rates are considered. This factor can be considered as a more realistic situation. Finally, rather than using a homogeneous consensus controller for all agents, a heterogeneous consensus controller is designed to reflect the topology information fully. The effectiveness of the proposed consensus controller is demonstrated using two numerical examples. The first example demonstrates that a heterogeneous controller derives a considerably wider region of attraction than a homogeneous controller. The second example shows that the proposed controller can stochastically reach a consensus of multi-agent systems.
{"title":"Heterogeneous consensus controller design for multi-agent saturated-input systems under switching topologies with partly unknown transition rates","authors":"Ho Sub Lee, Chan-eun Park, PooGyeon Park","doi":"10.1016/j.cnsns.2024.108580","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108580","url":null,"abstract":"This study proposes a heterogeneous consensus controller design for multi-agent saturated-input systems under switching topologies with partly unknown transition rates. This study makes three major contributions. First, multi-agent systems that consider both input saturation and switching topologies are addressed. Although both constraints can occur simultaneously, to the best of knowledge, there are no studies on consensus control for multi-agent saturated-input systems under switching topologies. Second, switching topologies with partly unknown transition rates are considered. This factor can be considered as a more realistic situation. Finally, rather than using a homogeneous consensus controller for all agents, a heterogeneous consensus controller is designed to reflect the topology information fully. The effectiveness of the proposed consensus controller is demonstrated using two numerical examples. The first example demonstrates that a heterogeneous controller derives a considerably wider region of attraction than a homogeneous controller. The second example shows that the proposed controller can stochastically reach a consensus of multi-agent systems.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"1 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.cnsns.2024.108570
Yaqi Wang, Huaiqin Wu, Jinde Cao
This paper is concerned with the finite-time synchronization (FNS) for a class of multi-weighted complex networks (MCNs) with time-varying delay couplings under hybrid delayed impulse effects. Firstly, a new finite-time stability (FTS) criterion is established for nonlinear time-varying delayed systems under hybrid delayed impulse effects, and the settling-time (ST), which is relevant to impulse gain and initial value of system, is estimated accurately. Secondly, a dynamical event-triggered controller is designed by introducing a novel internal dynamical variable. Under the designed event-triggering mechanism (ETM), by applying Lyapunov functional method, inequality analysis technique and the proposed the FTS criterion, the synchronization conditions are addressed in the form of linear matrix inequalities (LMIs). In addition, the exclusion of Zeno phenomenon is verified. At last, two practical simulation examples are provided to substantiate the reliability of the proposed control scheme and the validity of the obtained theoretical results.
{"title":"Finite-time synchronization for multi-weighted complex networks with time-varying delay couplings under hybrid delayed impulse effects via dynamic event-triggered control","authors":"Yaqi Wang, Huaiqin Wu, Jinde Cao","doi":"10.1016/j.cnsns.2024.108570","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108570","url":null,"abstract":"This paper is concerned with the finite-time synchronization (FNS) for a class of multi-weighted complex networks (MCNs) with time-varying delay couplings under hybrid delayed impulse effects. Firstly, a new finite-time stability (FTS) criterion is established for nonlinear time-varying delayed systems under hybrid delayed impulse effects, and the settling-time (ST), which is relevant to impulse gain and initial value of system, is estimated accurately. Secondly, a dynamical event-triggered controller is designed by introducing a novel internal dynamical variable. Under the designed event-triggering mechanism (ETM), by applying Lyapunov functional method, inequality analysis technique and the proposed the FTS criterion, the synchronization conditions are addressed in the form of linear matrix inequalities (LMIs). In addition, the exclusion of Zeno phenomenon is verified. At last, two practical simulation examples are provided to substantiate the reliability of the proposed control scheme and the validity of the obtained theoretical results.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"85 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-02DOI: 10.1016/j.cnsns.2024.108582
Yong-Gwon Lee, B. Kaviarasan, Myeong-Jin Park, Oh-Min Kwon
This paper introduces a new consensus pinning control strategy for second-order dynamic multi-agent systems with time-delayed input. A novel pinning controller is developed by utilizing betweenness centrality analysis and polynomial inequality to ensure efficient consensus of the addressed system. The Lyapunov-Krasovskii functionals are used to improve the maximum time-delay bound that occurs in the control input. Moreover, the ideal second-order system and the linearized ball and beam system are given to verify the superiority of the proposed method.
{"title":"Polynomial inequality-based consensus pinning control approach to time-delayed second-order multi-agent systems via betweenness centrality","authors":"Yong-Gwon Lee, B. Kaviarasan, Myeong-Jin Park, Oh-Min Kwon","doi":"10.1016/j.cnsns.2024.108582","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108582","url":null,"abstract":"This paper introduces a new consensus pinning control strategy for second-order dynamic multi-agent systems with time-delayed input. A novel pinning controller is developed by utilizing betweenness centrality analysis and polynomial inequality to ensure efficient consensus of the addressed system. The Lyapunov-Krasovskii functionals are used to improve the maximum time-delay bound that occurs in the control input. Moreover, the ideal second-order system and the linearized ball and beam system are given to verify the superiority of the proposed method.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"15 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01DOI: 10.1016/j.cnsns.2024.108573
Yanran Fu, Guangming Zhuang, Jun-e Feng, Yanqian Wang
This work investigates neural network (NN)-based compensation control for uncertain delayed discrete singular piecewise homogeneous Markov jump systems (PHMJSs) under deception attacks. Considering the unmeasurable system states and limited network bandwidth, the states of the discrete singular PHMJS are estimated via utilizing a state observer and communication resources are saved through an improved event-triggered mechanism (ETM). For Markov chains, time-varying transition probabilities (TPs) resulting from environmental changes and external disturbances are considered to be piecewise homogeneous, whose stochastic variations are regulated by a higher-level transition probability (HTP) matrix. Moreover, in order to alleviate the adverse impact arising from deception attacks over the controller-actuator transmission channel, the NN technique is employed to approximate malicious attacks. Then, an event-triggered compensation feedback controller based on the reconstructed deception attacks is devised to compensate for the negative effect of deception attacks on systems. By taking advantage of singular value decomposition technique and double-mode-dependent Lyapunov–Krasovskii (L-K) functional, fresh conditions of the regularity, causality and boundedness in probability for discrete singular PHMJSs are obtained under the framework of linear matrix inequalities (LMIs). Finally, DC motor is provided to verify the feasibility of the proposed NN and ETM-based compensation control approach.
{"title":"NN-based compensation control for uncertain delayed singular piecewise homogeneous jump systems with deception attacks and time-varying transition probabilities","authors":"Yanran Fu, Guangming Zhuang, Jun-e Feng, Yanqian Wang","doi":"10.1016/j.cnsns.2024.108573","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108573","url":null,"abstract":"This work investigates neural network (NN)-based compensation control for uncertain delayed discrete singular piecewise homogeneous Markov jump systems (PHMJSs) under deception attacks. Considering the unmeasurable system states and limited network bandwidth, the states of the discrete singular PHMJS are estimated via utilizing a state observer and communication resources are saved through an improved event-triggered mechanism (ETM). For Markov chains, time-varying transition probabilities (TPs) resulting from environmental changes and external disturbances are considered to be piecewise homogeneous, whose stochastic variations are regulated by a higher-level transition probability (HTP) matrix. Moreover, in order to alleviate the adverse impact arising from deception attacks over the controller-actuator transmission channel, the NN technique is employed to approximate malicious attacks. Then, an event-triggered compensation feedback controller based on the reconstructed deception attacks is devised to compensate for the negative effect of deception attacks on systems. By taking advantage of singular value decomposition technique and double-mode-dependent Lyapunov–Krasovskii (L-K) functional, fresh conditions of the regularity, causality and boundedness in probability for discrete singular PHMJSs are obtained under the framework of linear matrix inequalities (LMIs). Finally, DC motor is provided to verify the feasibility of the proposed NN and ETM-based compensation control approach.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"5 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142911854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01DOI: 10.1016/j.cnsns.2024.108579
Qiao-Li Li, Xiao-Heng Chang
The paper is mainly discusses the interval type-2 (IT2) fuzzy security control problem of improved event-triggered networked control systems (NCSs) under network attacks under dual communication channels. Firstly, under the premise of limited network bandwidth and unobservable system, an improved event-triggered (ET) mechanism is proposed to judge the data transmission conditions according to the average value of the current sampling time and the last triggering time. In addition, considering that the transmission of the networked system is carried out under multiple communication channels, this paper considers the role of event-triggered and deception attacks (DAs) at both ends of the system, and establishes a fuzzy system model under disturbance. The Lyapunov function method is used to analyze the stability of the system. The controller, observer and triggered matrix are designed by linear matrix inequalities (LMIs) approach, and the conditions satisfying the system stability and the expected performance index are obtained. Compared with common adaptive event triggered mechanism (AETM), the proposed improved adaptive ET scheme significantly saves network resources. Finally, The scheme’s effectiveness and superiority are validated through simulation examples.
{"title":"Observer-based improved event-triggered interval type-2 fuzzy networked control systems subject to deception attacks in dual communication channels","authors":"Qiao-Li Li, Xiao-Heng Chang","doi":"10.1016/j.cnsns.2024.108579","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108579","url":null,"abstract":"The paper is mainly discusses the interval type-2 (IT2) fuzzy security control problem of improved event-triggered networked control systems (NCSs) under network attacks under dual communication channels. Firstly, under the premise of limited network bandwidth and unobservable system, an improved event-triggered (ET) mechanism is proposed to judge the data transmission conditions according to the average value of the current sampling time and the last triggering time. In addition, considering that the transmission of the networked system is carried out under multiple communication channels, this paper considers the role of event-triggered and deception attacks (DAs) at both ends of the system, and establishes a fuzzy system model under disturbance. The Lyapunov function method is used to analyze the stability of the system. The controller, observer and triggered matrix are designed by linear matrix inequalities (LMIs) approach, and the conditions satisfying the system stability and the expected performance index are obtained. Compared with common adaptive event triggered mechanism (AETM), the proposed improved adaptive ET scheme significantly saves network resources. Finally, The scheme’s effectiveness and superiority are validated through simulation examples.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"24 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142937625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01DOI: 10.1016/j.cnsns.2024.108577
Jesús Dueñas, Carmen Núñez, Rafael Obaya
Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This paper describes the generalized simple or double saddle–node bifurcation diagrams for one-parametric families of equations of these types, from which the dynamical possibilities for each of the equations follow. This new framework allows the analysis of “almost stochastic” equations, whose coefficients vary in very large chaotic sets. The results also apply to the analysis of the occurrence of critical transitions for a range of models much larger than in previous approaches.
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