Pub Date : 2026-06-01Epub Date: 2026-01-16DOI: 10.1016/j.cnsns.2026.109748
Yonghui Lv , Hui Wang , Jian Ding , Quanxin Zhu
In this paper, we consider the effects of intraguild predation, predator-switching, and stochastic factors on the dynamics of a stochastic three species predator-prey model. It is assumed that the interactions between the two predators and the prey follow the Holling type II functional response. Meanwhile, the predation between the top predator and the intermediate predator is governed by a preference mechanism modulated by prey density. The existence of positive solutions and the boundedness are established. The analysis of the Lyapunov exponents reveals that intraguild predation and predator-switching can maintain species coexistence under certain conditions. Furthermore, we provide a comprehensive classification of persistence and extinction for all populations. Finally, we conduct numerical simulations to verify the theoretical results by employing the Monte Carlo method to calculate the Lyapunov exponents of the two-dimensional boundary measures.
{"title":"Dynamic analysis of a stochastic three species predator-prey model with intraguild predation and predator-switching","authors":"Yonghui Lv , Hui Wang , Jian Ding , Quanxin Zhu","doi":"10.1016/j.cnsns.2026.109748","DOIUrl":"10.1016/j.cnsns.2026.109748","url":null,"abstract":"<div><div>In this paper, we consider the effects of intraguild predation, predator-switching, and stochastic factors on the dynamics of a stochastic three species predator-prey model. It is assumed that the interactions between the two predators and the prey follow the Holling type II functional response. Meanwhile, the predation between the top predator and the intermediate predator is governed by a preference mechanism modulated by prey density. The existence of positive solutions and the boundedness are established. The analysis of the Lyapunov exponents reveals that intraguild predation and predator-switching can maintain species coexistence under certain conditions. Furthermore, we provide a comprehensive classification of persistence and extinction for all populations. Finally, we conduct numerical simulations to verify the theoretical results by employing the Monte Carlo method to calculate the Lyapunov exponents of the two-dimensional boundary measures.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109748"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995140","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 : 2026-06-01Epub Date: 2026-01-20DOI: 10.1016/j.cnsns.2026.109766
Fei Yan , Hao Wang , Yingmin Yi
This paper proposes a novel model-free adaptive control with independent time-varying parameters (MFAC-ITVP) framework for containment control in nonlinear multi-agent systems (MASs). Unlike conventional MFAC schemes that require globally homogeneous controller parameters, the proposed framework allows each agent to autonomously adjust its controller gains through independently evolving time-varying parameters. This independence significantly enhances adaptability and robustness, especially under dynamic communication topologies and varying agent participation. By transforming nonlinear agent dynamics into local data-driven linear models through dynamic linearization, a fully distributed control law is developed that depends solely on local input–output data without any prior model knowledge. Rigorous theoretical analysis establishes convergence and stability in the maximum-norm sense under generalized Lipschitz conditions. Extensive simulations under both fixed and switching topologies verify that the proposed MFAC-ITVP method achieves faster convergence and stronger disturbance rejection compared with traditional MFAC approaches.
{"title":"Model-free adaptive control with independent time-varying parameters for containment control in multi-agent systems","authors":"Fei Yan , Hao Wang , Yingmin Yi","doi":"10.1016/j.cnsns.2026.109766","DOIUrl":"10.1016/j.cnsns.2026.109766","url":null,"abstract":"<div><div>This paper proposes a novel model-free adaptive control with independent time-varying parameters (MFAC-ITVP) framework for containment control in nonlinear multi-agent systems (MASs). Unlike conventional MFAC schemes that require globally homogeneous controller parameters, the proposed framework allows each agent to autonomously adjust its controller gains through independently evolving time-varying parameters. This independence significantly enhances adaptability and robustness, especially under dynamic communication topologies and varying agent participation. By transforming nonlinear agent dynamics into local data-driven linear models through dynamic linearization, a fully distributed control law is developed that depends solely on local input–output data without any prior model knowledge. Rigorous theoretical analysis establishes convergence and stability in the maximum-norm sense under generalized Lipschitz conditions. Extensive simulations under both fixed and switching topologies verify that the proposed MFAC-ITVP method achieves faster convergence and stronger disturbance rejection compared with traditional MFAC approaches.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109766"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014494","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 : 2026-06-01Epub Date: 2026-01-10DOI: 10.1016/j.cnsns.2026.109727
Yiwei Liu , Ning Pang , Ziming Wang , Xin Wang
This paper proposes a unified preset-time formation control framework for multi-input multi-output (MIMO) uncertain nonlinear systems. The framework is built upon a newly developed family of performance functions that ensure all error signals remain within prescribed boundaries and converge to arbitrarily designated sets within a preset time, independent of their initial conditions. In contrast to existing MIMO control schemes that rely on adaptive parameter estimation or disturbance observers, the proposed strategy achieves an approximation-free design, thereby simplifying the overall control architecture. To realize prescribed performance control (PPC) for agents with arbitrarily bounded initial states, a novel transformation mechanism is incorporated, which further avoids dependence on the homogeneity of agents’ dynamics. An event-triggered mechanism is also integrated to reduce communication burden between controllers and actuators, while rigorous analysis guarantees boundedness of all closed-loop signals and strictly excludes Zeno behavior. The effectiveness and advantages of the proposed approach are validated through numerical simulations of spacecraft formation control.
{"title":"Approximation-free full-state error constrained distributed formation control with unified preset-time performance","authors":"Yiwei Liu , Ning Pang , Ziming Wang , Xin Wang","doi":"10.1016/j.cnsns.2026.109727","DOIUrl":"10.1016/j.cnsns.2026.109727","url":null,"abstract":"<div><div>This paper proposes a unified preset-time formation control framework for multi-input multi-output (MIMO) uncertain nonlinear systems. The framework is built upon a newly developed family of performance functions that ensure all error signals remain within prescribed boundaries and converge to arbitrarily designated sets within a preset time, independent of their initial conditions. In contrast to existing MIMO control schemes that rely on adaptive parameter estimation or disturbance observers, the proposed strategy achieves an approximation-free design, thereby simplifying the overall control architecture. To realize prescribed performance control (PPC) for agents with arbitrarily bounded initial states, a novel transformation mechanism is incorporated, which further avoids dependence on the homogeneity of agents’ dynamics. An event-triggered mechanism is also integrated to reduce communication burden between controllers and actuators, while rigorous analysis guarantees boundedness of all closed-loop signals and strictly excludes Zeno behavior. The effectiveness and advantages of the proposed approach are validated through numerical simulations of spacecraft formation control.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109727"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957223","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 : 2026-06-01Epub Date: 2026-01-10DOI: 10.1016/j.cnsns.2026.109742
Robert Nebeluk
The purpose of this paper is to provide a detailed implementation procedure for a Model Predictive Control (MPC) algorithm with a L1 cost-function based on a deep state-space neural model with any number of hidden layers, number of nodes in each layer, and differentiable activation function. The formulation includes an Extended Kalman Filter (EKF) to handle the problem of unmeasurable state variables. The effectiveness of shallow and deep neural state-space models in modeling is also discussed. The presented control scheme provides less computational load thanks to the use of a neural approximator of the L1 norm and an advanced on-line trajectory linearization technique. The algorithm is tested for a given nonlinear polymerization process. The advantages of deep neural state-space models in control are assessed in detail for three simulation scenarios. It is shown that the control performance obtained for the presented algorithm is similar to that of an MPC algorithm requiring nonlinear optimization.
{"title":"Development of state-space model predictive control with L1 cost-function and deep state-space neural models","authors":"Robert Nebeluk","doi":"10.1016/j.cnsns.2026.109742","DOIUrl":"10.1016/j.cnsns.2026.109742","url":null,"abstract":"<div><div>The purpose of this paper is to provide a detailed implementation procedure for a Model Predictive Control (MPC) algorithm with a L<sub>1</sub> cost-function based on a deep state-space neural model with any number of hidden layers, number of nodes in each layer, and differentiable activation function. The formulation includes an Extended Kalman Filter (EKF) to handle the problem of unmeasurable state variables. The effectiveness of shallow and deep neural state-space models in modeling is also discussed. The presented control scheme provides less computational load thanks to the use of a neural approximator of the L<sub>1</sub> norm and an advanced on-line trajectory linearization technique. The algorithm is tested for a given nonlinear polymerization process. The advantages of deep neural state-space models in control are assessed in detail for three simulation scenarios. It is shown that the control performance obtained for the presented algorithm is similar to that of an MPC algorithm requiring nonlinear optimization.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109742"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957219","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 : 2026-06-01Epub Date: 2026-01-11DOI: 10.1016/j.cnsns.2026.109665
Haoyu Li , Leimin Wang , Weilong Zhang , Xiongbo Wan , Shiping Wen
In this paper, an improvement path for preassigned-time synchronization of T-S fuzzy neural networks is presented to optimize the energy consumption during the synchronization process. The “primary realization” method starts based on fixed-time estimation results and directly achieves the preassigned-time synchronization without the introduction of infinite gains and redesign of controller. More importantly, this paper combines energy estimation with conservatism for the first time, emphasizing the potential relationship between energy consumption and conservatism with the same control objective, i.e., continuously improving the estimated time can effectively improve the results of preassigned time synchronization (lower energy consumption as well as less conservatism). Numerical simulations validate the effectiveness of the methodology in this paper, highlighting the potential for refining the synchronization process by optimizing energy consumption and reducing conservatism.
{"title":"Novel results for preassigned-time synchronization of fuzzy neural networks with energy consumption: Primary realization approach","authors":"Haoyu Li , Leimin Wang , Weilong Zhang , Xiongbo Wan , Shiping Wen","doi":"10.1016/j.cnsns.2026.109665","DOIUrl":"10.1016/j.cnsns.2026.109665","url":null,"abstract":"<div><div>In this paper, an improvement path for preassigned-time synchronization of T-S fuzzy neural networks is presented to optimize the energy consumption during the synchronization process. The “primary realization” method starts based on fixed-time estimation results and directly achieves the preassigned-time synchronization without the introduction of infinite gains and redesign of controller. More importantly, this paper combines energy estimation with conservatism for the first time, emphasizing the potential relationship between energy consumption and conservatism with the same control objective, i.e., continuously improving the estimated time can effectively improve the results of preassigned time synchronization (lower energy consumption as well as less conservatism). Numerical simulations validate the effectiveness of the methodology in this paper, highlighting the potential for refining the synchronization process by optimizing energy consumption and reducing conservatism.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109665"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957217","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 : 2026-06-01Epub Date: 2026-01-10DOI: 10.1016/j.cnsns.2026.109690
Mohamed Kharrat
This paper investigates the problem of adaptive fixed-time output feedback control for a class of nonstrict-feedback stochastic nonlinear systems subject to unmodeled dynamics and actuator faults. To handle the issue of partial state availability, a state observer is designed to estimate the unmeasurable system states. Additionally, a dynamic compensation mechanism is developed to mitigate the effects of unmodeled dynamics. By combining the approximation capabilities of fuzzy logic systems with a backstepping-based control framework, a fixed-time adaptive controller is constructed. The proposed method guarantees that all closed-loop system signals remain bounded and that the tracking error converges to a small residual set within a predefined fixed-time, independent of initial conditions. The robustness and effectiveness of the control strategy are validated through a numerical example and a real-world example on a single-link robot system.
{"title":"Fixed-time adaptive output feedback control of stochastic nonlinear systems with actuator faults and unmodeled dynamics","authors":"Mohamed Kharrat","doi":"10.1016/j.cnsns.2026.109690","DOIUrl":"10.1016/j.cnsns.2026.109690","url":null,"abstract":"<div><div>This paper investigates the problem of adaptive fixed-time output feedback control for a class of nonstrict-feedback stochastic nonlinear systems subject to unmodeled dynamics and actuator faults. To handle the issue of partial state availability, a state observer is designed to estimate the unmeasurable system states. Additionally, a dynamic compensation mechanism is developed to mitigate the effects of unmodeled dynamics. By combining the approximation capabilities of fuzzy logic systems with a backstepping-based control framework, a fixed-time adaptive controller is constructed. The proposed method guarantees that all closed-loop system signals remain bounded and that the tracking error converges to a small residual set within a predefined fixed-time, independent of initial conditions. The robustness and effectiveness of the control strategy are validated through a numerical example and a real-world example on a single-link robot system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109690"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145957276","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 : 2026-06-01Epub Date: 2026-01-21DOI: 10.1016/j.cnsns.2026.109776
Zirui Du, Tianliang Hou
In this paper, we present first- and second-order stabilized exponential-SAV (sESAV) schemes preserving energy stability and maximum bound principle (MBP) for ternary Allen-Cahn equations. We prove that the first-order sESAV (sESAV1) scheme unconditionally preserves the discrete MBP and energy stability, the second-order sESAV (sESAV2) scheme preserves energy stability unconditionally and the discrete MBP under a constraint on temporal step size τ. Optimal L∞ error estimates for sESAV1 and sESAV2 are rigorously analyzed. To the best of our knowledge, it is the first time to discuss L∞ error estimates for SAV-type schemes. Several numerical experiments are performed to verify the validity of our schemes.
{"title":"Stabilized exponential-SAV schemes preserving energy stability and maximum bound principle for ternary Allen-Cahn equations","authors":"Zirui Du, Tianliang Hou","doi":"10.1016/j.cnsns.2026.109776","DOIUrl":"10.1016/j.cnsns.2026.109776","url":null,"abstract":"<div><div>In this paper, we present first- and second-order stabilized exponential-SAV (sESAV) schemes preserving energy stability and maximum bound principle (MBP) for ternary Allen-Cahn equations. We prove that the first-order sESAV (sESAV1) scheme unconditionally preserves the discrete MBP and energy stability, the second-order sESAV (sESAV2) scheme preserves energy stability unconditionally and the discrete MBP under a constraint on temporal step size <em>τ</em>. Optimal <em>L</em><sup>∞</sup> error estimates for sESAV1 and sESAV2 are rigorously analyzed. To the best of our knowledge, it is the first time to discuss <em>L</em><sup>∞</sup> error estimates for SAV-type schemes. Several numerical experiments are performed to verify the validity of our schemes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109776"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033545","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 : 2026-06-01Epub Date: 2026-01-22DOI: 10.1016/j.cnsns.2026.109767
Yaojia Zhang , Tao Chen , Stanislaw Migórski
This paper investigates a system of two nonlinear elliptic equations coupled with a variational-hemivariational inequality (VHVI) under constraints. The system provides a critical mathematical model for the flowback problem of viscoelastic surfactant fluids in shale gas extraction. The model features strong couplings among the chloride ion concentration, rod-like micelle density, and flowback velocity, governed by nonsmooth multivalued frictional boundary laws and nonlinear diffusion mechanisms. Under minimal regularity assumptions on the data, we prove the existence of at least one weak solution to the system. The proof combines techniques from nonsmooth analysis, the theory of pseudomonotone operators, elliptic hemivariational inequalities, monotonicity and compactness methods, and exploits the Kakutani–Ky Fan fixed point theorem for set-valued maps.
{"title":"Viscoelastic surfactant flowback model with rod-like micelle leading to differential variational-hemivariational inequality","authors":"Yaojia Zhang , Tao Chen , Stanislaw Migórski","doi":"10.1016/j.cnsns.2026.109767","DOIUrl":"10.1016/j.cnsns.2026.109767","url":null,"abstract":"<div><div>This paper investigates a system of two nonlinear elliptic equations coupled with a variational-hemivariational inequality (VHVI) under constraints. The system provides a critical mathematical model for the flowback problem of viscoelastic surfactant fluids in shale gas extraction. The model features strong couplings among the chloride ion concentration, rod-like micelle density, and flowback velocity, governed by nonsmooth multivalued frictional boundary laws and nonlinear diffusion mechanisms. Under minimal regularity assumptions on the data, we prove the existence of at least one weak solution to the system. The proof combines techniques from nonsmooth analysis, the theory of pseudomonotone operators, elliptic hemivariational inequalities, monotonicity and compactness methods, and exploits the Kakutani–Ky Fan fixed point theorem for set-valued maps.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109767"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033540","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 : 2026-06-01Epub Date: 2026-01-22DOI: 10.1016/j.cnsns.2026.109775
Yudong Zhou, Qinghui Zhang
Deep neural network (DNN) methods generally achieve about 1E-4 accuracy (for L2 relative errors) when solving partial differential equations (PDEs). Extreme learning machines (ELMs), a sort of shallow neural networks, can realize spectral accuracy for certain PDEs. Studies on ELM are mostly focused on the linear PDEs, where training process can be equivalent to linear least square problems and Pseudo inverse operations. The training of ELM with Gauss-Newton method for the nonlinear PDEs poses big challenges, including sensitivity to initial guess, a great number of iterations, and robustness. These issues are largely caused by ill-posed nature of the problem in a sense that the condition number of discrete matrix is extremely large. We propose a novel Gauss-Newton method of ELM for the nonlinear PDEs, which is composed of three major strategies. (a) The conventional loss function based on ELM is penalized to establish a penalized nonlinear least square problem (PNLS). (b) The PNLS problem is approximated using a first-order Taylor expansion of the residual vector to avoid the explicit Hessian calculation, as executed in the conventional Gauss-Newton method. (c) Most importantly, the penalty decays to zero as the iteration progresses. The new method is referred to as DPELM (the ELM with decaying penalties). The motivation of DPELM is both to improve the conditioning of the discrete matrix by adding the penalty and to avoid the loss of accuracy (caused by the penalty) by making the penalty decay to zero. The effectiveness of the proposed method is validated by numerous numerical experiments of the nonlinear PDEs, including minimal surface equations, Navier-Stokes equations, nonlinear reaction-diffusion equations, etc. The comparisons with the existing neural network methods, the DNN and conventional ELM, are also made.
{"title":"Extreme learning machines with decaying penalties for nonlinear partial differential equations","authors":"Yudong Zhou, Qinghui Zhang","doi":"10.1016/j.cnsns.2026.109775","DOIUrl":"10.1016/j.cnsns.2026.109775","url":null,"abstract":"<div><div>Deep neural network (DNN) methods generally achieve about 1E-4 accuracy (for <em>L</em><sup>2</sup> relative errors) when solving partial differential equations (PDEs). Extreme learning machines (ELMs), a sort of shallow neural networks, can realize spectral accuracy for certain PDEs. Studies on ELM are mostly focused on the linear PDEs, where training process can be equivalent to linear least square problems and Pseudo inverse operations. The training of ELM with Gauss-Newton method for the nonlinear PDEs poses big challenges, including sensitivity to initial guess, a great number of iterations, and robustness. These issues are largely caused by ill-posed nature of the problem in a sense that the condition number of discrete matrix is extremely large. We propose a novel Gauss-Newton method of ELM for the nonlinear PDEs, which is composed of three major strategies. (a) The conventional loss function based on ELM is penalized to establish a penalized nonlinear least square problem (PNLS). (b) The PNLS problem is approximated using a first-order Taylor expansion of the residual vector to avoid the explicit Hessian calculation, as executed in the conventional Gauss-Newton method. (c) Most importantly, the penalty decays to zero as the iteration progresses. The new method is referred to as DPELM (the ELM with decaying penalties). The motivation of DPELM is both to improve the conditioning of the discrete matrix by adding the penalty and to avoid the loss of accuracy (caused by the penalty) by making the penalty decay to zero. The effectiveness of the proposed method is validated by numerous numerical experiments of the nonlinear PDEs, including minimal surface equations, Navier-Stokes equations, nonlinear reaction-diffusion equations, etc. The comparisons with the existing neural network methods, the DNN and conventional ELM, are also made.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109775"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033905","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 : 2026-06-01Epub Date: 2026-01-17DOI: 10.1016/j.cnsns.2026.109687
Heting Zhang , Wenqiang Ji , Zepeng Ning
The observer-based output feedback dissipative control problem for neural networks is addressed through piecewise affine (PWA) models. To estimate the unmeasurable neuron states, a PWA observer is designed firstly and the information of the affine terms can be fully exploited. By sufficiently making utilization of the Young’s matrix inequality with its variant, two enhanced methods are proposed for the observer-based output feedback dissipative controller design. Under a unified convex optimization framework, improved output feedback dissipative controller design results are given, and the strict dissipative performance can be obtained simultaneously, which also achieves further conservativeness reduction. Simulation studies are provided to verify the validity of the theoretical results.
{"title":"New results on observer-based output feedback dissipative control of neural networks by piecewise affine models","authors":"Heting Zhang , Wenqiang Ji , Zepeng Ning","doi":"10.1016/j.cnsns.2026.109687","DOIUrl":"10.1016/j.cnsns.2026.109687","url":null,"abstract":"<div><div>The observer-based output feedback dissipative control problem for neural networks is addressed through piecewise affine (PWA) models. To estimate the unmeasurable neuron states, a PWA observer is designed firstly and the information of the affine terms can be fully exploited. By sufficiently making utilization of the Young’s matrix inequality with its variant, two enhanced methods are proposed for the observer-based output feedback dissipative controller design. Under a unified convex optimization framework, improved output feedback dissipative controller design results are given, and the strict <span><math><mrow><mo>(</mo><msub><mi>S</mi><mn>1</mn></msub><mo>,</mo><msub><mi>S</mi><mn>2</mn></msub><mo>,</mo><msub><mi>S</mi><mn>3</mn></msub><mo>,</mo><mi>γ</mi><mo>)</mo><mo>−</mo></mrow></math></span>dissipative performance can be obtained simultaneously, which also achieves further conservativeness reduction. Simulation studies are provided to verify the validity of the theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109687"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995130","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}
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