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So G. DS based 2-DOF PID controller for various integrating processes with time delay. ISA TRANSACTIONS 2024; 153:276-294. [PMID: 39112128 DOI: 10.1016/j.isatra.2024.07.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2022] [Revised: 07/23/2024] [Accepted: 07/23/2024] [Indexed: 09/14/2024]
Abstract
This study proposes a direct synthesis-based two-degree-of-freedom (2-DOF) controller for various types of integrating processes with time delays. This 2-DOF controller includes a proportional-integral-derivative (PID) controller to enhance load disturbance rejection performance and a set-point filter to improve servo response performance. The main PID controller parameters are expressed as process model parameters and a single adjustment variable, while the set-point filter is composed of PID controller parameters with weighted factors. The adjustment variable is tuned to achieve an optimal balance between response performance and robustness, based on the maximum magnitude of the sensitivity function (Ms). Controller parameters for various Ms values and guidelines for setting these parameters are provided in a consistent formulaic form using a curve-fitting method. These parameter-setting formulas facilitate the accurate implementation of PID controllers with specified Ms values and allow the controller design to be extended to processes with larger dimensionless time delays for a given Ms value. Although a 2-DOF controller was proposed, the adjustment variable for setting the parameters of the main PID controller and the set-point filter was solely the desired time constant. The proposed method was applied to various integrating processes with time delays, and its performance was compared with existing methods reported in the literature, based on performance indices such as settling time, overshoot, integral of absolute error, total variation in input usage, and global performance index. Simulations were conducted using six examples of various integrating processes with time delays to verify the effectiveness and applicability of the proposed controller.
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Dong H, Ma B, Meng Y, Wu Y, Liu Y, Zeng T, Huang J. GRNMOPT: Inference of gene regulatory networks based on a multi-objective optimization approach. Comput Biol Chem 2024; 113:108223. [PMID: 39340962 DOI: 10.1016/j.compbiolchem.2024.108223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2024] [Revised: 08/21/2024] [Accepted: 09/20/2024] [Indexed: 09/30/2024]
Abstract
BACKGROUND AND OBJECTIVE The reconstruction of gene regulatory networks (GRNs) stands as a vital approach in deciphering complex biological processes. The application of nonlinear ordinary differential equations (ODEs) models has demonstrated considerable efficacy in predicting GRNs. Notably, the decay rate and time delay are pivotal in authentic gene regulation, yet their systematic determination in ODEs models remains underexplored. The development of a comprehensive optimization framework for the effective estimation of these key parameters is essential for accurate GRN inference. METHOD This study introduces GRNMOPT, an innovative methodology for inferring GRNs from time-series and steady-state data. GRNMOPT employs a combined use of decay rate and time delay in constructing ODEs models to authentically represent gene regulatory processes. It incorporates a multi-objective optimization approach, optimizing decay rate and time delay concurrently to derive Pareto optimal sets for these factors, thereby maximizing accuracy metrics such as AUROC (Area Under the Receiver Operating Characteristic curve) and AUPR (Area Under the Precision-Recall curve). Additionally, the use of XGBoost for calculating feature importance aids in identifying potential regulatory gene links. RESULTS Comprehensive experimental evaluations on two simulated datasets from DREAM4 and three real gene expression datasets (Yeast, In vivo Reverse-engineering and Modeling Assessment [IRMA], and Escherichia coli [E. coli]) reveal that GRNMOPT performs commendably across varying network scales. Furthermore, cross-validation experiments substantiate the robustness of GRNMOPT. CONCLUSION We propose a novel approach called GRNMOPT to infer GRNs based on a multi-objective optimization framework, which effectively improves inference accuracy and provides a powerful tool for GRNs inference.
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Huo Z, Huang J, Kuang Y, Ruan S, Zhang Y. Oscillations in a tumor-immune system interaction model with immune response delay. MATHEMATICAL MEDICINE AND BIOLOGY : A JOURNAL OF THE IMA 2024:dqae016. [PMID: 39287223 DOI: 10.1093/imammb/dqae016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Revised: 06/18/2024] [Accepted: 09/03/2024] [Indexed: 09/19/2024]
Abstract
In this paper we consider a tumor-immune system interaction model with immune response delay, in which a nonmonotonic function is used to describe immune response to the tumor burden and a time delay is used to represent the time for the immune system to respond and take effect. It is shown that the model may have one, two or three tumor equilibria, respectively, under different conditions. Time delay can only affect the stability of the low tumor equilibrium and local Hopf bifurcation occurs when the time delay passes through a critical value. The direction and stability of the bifurcating periodic solutions are also determined. Moreover, the global existence of periodic solutions is established by using a global Hopf bifurcation theorem. We also observe the existence of relaxation oscillations and complex oscillating patterns driven by the time delay. Numerical simulations are presented to illustrate the theoretical results.
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Liang Z, Liu X. Finite-time hybrid impulsive formation tracking control of multi-agent systems via aperiodic intermittent communication. ISA TRANSACTIONS 2024:1-14. [PMID: 39299846 DOI: 10.1016/j.isatra.2024.09.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 06/29/2024] [Accepted: 09/06/2024] [Indexed: 09/22/2024]
Abstract
This article studies the problem of formation tracking control in multi-agent systems, achieved in finite time, under challenging conditions such as strong nonlinearity, aperiodic intermittent communication, and time-delay effects, all within a hybrid impulsive framework. The impulses are categorized as either stabilizing control impulses or disruptive impulses. Furthermore, by integrating Lyapunov-based stability theory, graph theory, and the linear matrix inequality (LMI) method, new stability criteria are established. These criteria ensure finite-time intermittent formation tracking while considering weak Lyapunov inequality conditions, intermittent communication rates, and time-varying gain strengths. Additionally, the approach manages an indefinite number of impulsive moments and adjusts the control domain's width based on the average impulsive interval and state-dependent control width. Numerical simulations are provided to validate the applicability and effectiveness of the proposed formation tracking control protocols.
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Daba IT, Melesse WG, Gelu FW, Kebede GD. An efficient numerical approach for singularly perturbed time delayed parabolic problems with two-parameters. BMC Res Notes 2024; 17:158. [PMID: 38845043 PMCID: PMC11157779 DOI: 10.1186/s13104-024-06813-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Accepted: 05/28/2024] [Indexed: 06/09/2024] Open
Abstract
OBJECTIVES The main objective of this work is to design an efficient numerical scheme is proposed for solving singularly perturbed time delayed parabolic problems with two parameters. RESULTS The scheme is constructed via the implicit Euler and non-standard finite difference method to approximate the time and space derivatives, respectively. Besides, to enhance the accuracy and order of convergence of the method Richardson extrapolation technique is employed. Intensive numerical experimentation has been done on some model examples. Further, the layer behavior of the solutions is presented using graphs and observed to agree with the existing theories. Finally, error analysis of the scheme is done and observed that the proposed method is parameter uniform convergent with the order of convergence( Δ t ) 2 + h 2 .
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Yan J, Hu B, Guan ZH. Controllability on impulsive systems with delays in both input and impulse and its applications to multi-agent networks. ISA TRANSACTIONS 2024; 149:94-105. [PMID: 38614898 DOI: 10.1016/j.isatra.2024.03.035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 03/15/2024] [Accepted: 03/29/2024] [Indexed: 04/15/2024]
Abstract
This paper investigates the controllability of impulsive systems with input delay and impulse delay and its applications in multi-agent networks. We adopt the geometric and algebraic analytical tools to establish some easily verified controllability conditions for the considered system model. First, the analytic solution of the considered system is established on every impulsive interval by using ordinary differential equation theory. Then, according to the solution derived, some sufficient complete controllability criteria are developed to reveal the role of the Gramian matrices in different subintervals. By introducing a row matrix of different kinds of Gramian matrices, a complete controllability condition that is proved to be necessary and sufficient is further obtained. By using the relevant geometric matrix theory, the derived algebraic controllability condition is then converted to a geometric one. On other hand, we introduce a multi-agent network with delayed input and impulse and investigate its controllability. By resorting to graph theory and matrix theory, several factors affecting the controllability of the considered multi-agent networks are investigated, such as the topology structure, the inner coupling matrix, and the dynamics of each agent. Finally, two numerical examples are worked out to verify the derived controllability criteria.
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Borrelli M, Shokohyar S, Rampichini S, Bruseghini P, Doria C, Limonta EG, Ferretti G, Esposito F. Energetics of sinusoidal exercise below and across critical power and the effects of fatigue. Eur J Appl Physiol 2024; 124:1845-1859. [PMID: 38242972 PMCID: PMC11130025 DOI: 10.1007/s00421-023-05410-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 12/23/2023] [Indexed: 01/21/2024]
Abstract
PURPOSE Previous studies investigating sinusoidal exercise were not devoted to an analysis of its energetics and of the effects of fatigue. We aimed to determine the contribution of aerobic and anaerobic lactic metabolism to the energy balance and investigate the fatigue effects on the cardiorespiratory and metabolic responses to sinusoidal protocols, across and below critical power (CP). METHODS Eight males (26.6 ± 6.2 years; 75.6 ± 8.7 kg; maximum oxygen uptake 52.8 ± 7.9 ml·min-1·kg-1; CP 218 ± 13 W) underwent exhausting sinusoidal cycloergometric exercises, with sinusoid midpoint (MP) at CP (CPex) and 50 W below CP (CP-50ex). Sinusoid amplitude (AMP) and period were 50 W and 4 min, respectively. MP, AMP, and time-delay (tD) between mechanical and metabolic signals of expiratory ventilation (V ˙ E ), oxygen uptake (V ˙ O 2 ), and heart rate ( f H ) were assessed sinusoid-by-sinusoid. Blood lactate ([La-]) and rate of perceived exertion (RPE) were determined at each sinusoid. RESULTS V ˙ O 2 AMP was 304 ± 11 and 488 ± 36 ml·min-1 in CPex and CP-50ex, respectively. Asymmetries between rising and declining sinusoid phases occurred in CPex (36.1 ± 7.7 vs. 41.4 ± 9.7 s forV ˙ O 2 tD up and tD down, respectively; P < 0.01), with unchanged tDs.V ˙ O 2 MP and RPE increased progressively during CPex. [La-] increased by 2.1 mM in CPex but remained stable during CP-50ex. Anaerobic contribution was larger in CPex than CP-50ex. CONCLUSION The lower aerobic component during CPex than CP-50ex associated with lactate accumulation explained lowerV ˙ O 2 AMP in CPex. The asymmetries in CPex suggest progressive decline of muscle phosphocreatine concentration, leading to fatigue, as witnessed by RPE.
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Wang T, Xia M, Wang J, Zhilenkov A, Wang J, Xi X, Li L. Delay estimation for cortical-muscular interaction with wavelet coherence time lag. J Neurosci Methods 2024; 405:110098. [PMID: 38423364 DOI: 10.1016/j.jneumeth.2024.110098] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2023] [Revised: 02/09/2024] [Accepted: 02/23/2024] [Indexed: 03/02/2024]
Abstract
BACKGROUND Cortico-muscular coherence (CMC) between the cerebral cortex and muscle activity is an effective tool for studying neural communication in the motor control system. To accurately evaluate the coherence between electroencephalogram (EEG) and electromyogram (EMG) signals, it is necessary to accurately calculate the time delay between physiological signals to ensure signal synchronization. NEW METHOD We proposed a new delay estimation method, named wavelet coherence time lag (WCTL) and the significant increase areas (SIA) index as a measure of the specific region enhancement effect of the magnitude squared coherence (MSC) image. RESULTS The grip strength level had a small effect on the information transmission time from the cortex to the muscles, while the transmission time from the cortex to different muscle channels was different for the same task. A positive correlation was found between the grip strength level and the SIA index on the β band of C3-B and the α and β bands of C3-FDS. COMPARISON WITH EXISTING METHOD The WCTL method was found to accurately calculate the delay time even when the number of repeated segments was low in a simple motor control model, and the results were more accurate than the rate of voxels change (RVC) and CMC with time lag (CMCTL) methods. CONCLUSIONS The WCTL is an effective method for detecting the transmission time of information between the cortex and muscles, laying the foundation for future rehabilitation treatment for stroke patients.
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Sadeqian A, Ahmadi MT, Bodaghzadeh M, Abazari AM. Calculating and analyzing time delay in zigzag graphene nanoscrolls based complementary metal-oxide-semiconductors. Sci Rep 2024; 14:9009. [PMID: 38637607 DOI: 10.1038/s41598-024-58593-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Accepted: 04/01/2024] [Indexed: 04/20/2024] Open
Abstract
Graphene Nano Scrolls (GNSs) and Zigzag graphene nanoscrolls (ZGNSs) are semi-one-dimensional materials with exceptional electrical and optical properties, making them attractive to be used in nanoelectronics and complementary metal-oxide-semiconductor (CMOS) technology. With in CMOS device technology, time delay is a crucial issue in the design and implementation of CMOS based ZGNSs. Current paper focus is on ZGNSs application in the channel area of metal-oxide-semiconductor field-effect transistors (MOSFETs) in CMOS technology. We studied analytically, the importance of different parameters on time delay reduction, resulting in faster switching and higher frequency in integrated circuits (ICs). The results of this research demonstrates that, the ZGNS-based CMOS proves considerable variations in the current due to the geometrical parameters, such as chirality number, channel length, and nanoscroll length which can be engineered to produce faster ICs.
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Bowen D. Impact of coronavirus pandemic on stock index: A polynomial regression with time delay. Heliyon 2024; 10:e28850. [PMID: 38623212 PMCID: PMC11016598 DOI: 10.1016/j.heliyon.2024.e28850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2023] [Revised: 03/23/2024] [Accepted: 03/26/2024] [Indexed: 04/17/2024] Open
Abstract
Motivation Under contemporary market conditions in China, the stock index has been volatile and highly reflect trends in the coronavirus pandemic, but rare scientific research has been conducted to model the possible nonlinear relations between the two indicators. Added, on the advent that covid-related news in one time period impacts the stock market in another period, time delay can be an equally good predictor of the stock index but rarely investigated. Objectives To contribute to filling the gaps identified in existing research, this study models relationship between the stock market index and coronavirus pandemic by leveraging volatility in the stock market and covid data through time delay and best degree in a polynomial environment. The resultant optimal time delay and best degree model is used to derive a high-accuracy prediction of stock market index. Novelty In line with the possible relations, the novelty of this study is that it proposes, validates and implements polynomial regression with time delay to model nonlinear relationship between the stock index and covid. Methods This study utilizes high-frequency data from January 2020 to the first week of July 2022 to model the nonlinear relationship between the stock index, new covid cases and time delay under polynomial regression environment. Findings The empirical results show that time delay and new covid cases, when modelled in a polynomial environment with optimal degree and delay, do present better representation of the nonlinear relationship such predictors have with stock index for China. Relative to results from the polynomial regression without delay, the empirical evidence from the model with delay show that an optimal time delay of 17 weeks makes it possible to predict the stock index at high accuracy and record improvements of 16-fold or higher. The representative delay model is used to project for up to 17 weeks for future trends in the stock index. Implication The implication of the findings herein is that the prowess of the time delay polynomial regression is heavily dependent on instability in covid-related time trends and that researchers and decision-makers should consider modeling to cover for the unsteadiness in coronavirus cases to achieve better results.
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Gan H, Cao Z, Chen P, Luo Y, Luo X. Fractional-order electromagnetic modeling and identification for PMSM servo system. ISA TRANSACTIONS 2024; 147:527-539. [PMID: 38342652 DOI: 10.1016/j.isatra.2024.01.036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2023] [Revised: 01/30/2024] [Accepted: 01/30/2024] [Indexed: 02/13/2024]
Abstract
An accurate electromagnetic model is essential for an optimal controller tuning of the high-performance servo system. This paper proposes a fractional-order electromagnetic model of a permanent magnet synchronous motor (PMSM) servo system and an identification methodology of this model. The reason why the investigated electromagnetic model should be a fractional-order one is addressed with a detailed explanation. The influence of voltage source inverter nonlinearity, which may cause system identification error, is analyzed. An improved inverter nonlinearity model and compensation method are proposed to promote the accuracy of the model parameter identification. Compared with the existing typical electromagnetic models of the PMSM servo system, the current open-loop and closed-loop experiments prove that the proposed fractional-order electromagnetic model with time delay is more accurate for the actual physical system. The effectiveness of the proposed nonlinearity modeling and compensation scheme of the inverter is also verified on an experimental PMSM servo system.
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Li Z, Zhao XQ. Global dynamics of a time-delayed nonlocal reaction-diffusion model of within-host viral infections. J Math Biol 2024; 88:38. [PMID: 38436782 DOI: 10.1007/s00285-024-02052-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Revised: 01/08/2024] [Accepted: 01/21/2024] [Indexed: 03/05/2024]
Abstract
In this paper, we study a time-delayed nonlocal reaction-diffusion model of within-host viral infections. We introduce the basic reproduction number R 0 and show that the infection-free steady state is globally asymptotically stable whenR 0 ≤ 1 , while the disease is uniformly persistent whenR 0 > 1 . In the case where all coefficients and reaction terms are spatially homogeneous, we obtain an explicit formula of R 0 and the global attractivity of the positive constant steady state. Numerically, we illustrate the analytical results, conduct sensitivity analysis, and investigate the impact of drugs on curtailing the spread of the viruses.
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Essongo FE, Mvogo A, Ben-Bolie GH. Dynamics of a diffusive model for cancer stem cells with time delay in microRNA-differentiated cancer cell interactions and radiotherapy effects. Sci Rep 2024; 14:5295. [PMID: 38438408 PMCID: PMC10912232 DOI: 10.1038/s41598-024-55212-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 02/21/2024] [Indexed: 03/06/2024] Open
Abstract
Understand the dynamics of cancer stem cells (CSCs), prevent the non-recurrence of cancers and develop therapeutic strategies to destroy both cancer cells and CSCs remain a challenge topic. In this paper, we study both analytically and numerically the dynamics of CSCs under radiotherapy effects. The dynamical model takes into account the diffusion of cells, the de-differentiation (or plasticity) mechanism of differentiated cancer cells (DCs) and the time delay on the interaction between microRNAs molecules (microRNAs) with DCs. The stability of the model system is studied by using a Hopf bifurcation analysis. We mainly investigate on the critical time delay τ c , that represents the time for DCs to transform into CSCs after the interaction of microRNAs with DCs. Using the system parameters, we calculate the value of τ c for prostate, lung and breast cancers. To confirm the analytical predictions, the numerical simulations are performed and show the formation of spatiotemporal circular patterns. Such patterns have been found as promising diagnostic and therapeutic value in management of cancer and various diseases. The radiotherapy is applied in the particular case of prostate model. We calculate the optimum dose of radiation and determine the probability of avoiding local cancer recurrence after radiotherapy treatment. We find numerically a complete eradication of patterns when the radiotherapy is applied before a time t < τ c . This scenario induces microRNAs to act as suppressors as experimentally observed in prostate cancer. The results obtained in this paper will provide a better concept for the clinicians and oncologists to understand the complex dynamics of CSCs and to design more efficacious therapeutic strategies to prevent the non-recurrence of cancers.
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Zhang W, Xiao J, Gong B. Global μ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control. ISA TRANSACTIONS 2024; 145:124-131. [PMID: 38097468 DOI: 10.1016/j.isatra.2023.12.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Revised: 10/09/2023] [Accepted: 12/08/2023] [Indexed: 02/24/2024]
Abstract
This paper mainly focuses on solving the global μ-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize μ-synchronization for CDNs in this paper, which means that event-triggered control has been applied to μ-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov-Razumikhin, recursion, etc, some valid global μ-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.
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Piao X, Lin C, Zhang M, Chen B. Attack estimation and state reconstruction for cyber-physical systems with state delay via reduced-order observer. ISA TRANSACTIONS 2024; 144:11-17. [PMID: 37891071 DOI: 10.1016/j.isatra.2023.10.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Revised: 08/23/2023] [Accepted: 10/13/2023] [Indexed: 10/29/2023]
Abstract
This paper investigates the attack estimation and state reconstruction problem for linear cyber-physical systems with state delay and simultaneous sensor and actuator attacks. Reduced-order observer is designed for the augmented system to simultaneously estimate the actuator attack, sensor attack and the state of system. By adopting the double integral term into the Lyapunov-Krasovskii functional and decomposing the cross term, the delay-dependent results are obtained. The method proposed in this paper can accurately estimate the state, actuator and sensor attacks simultaneously without additional design. Compared with the previous method, the time delay information is fully utilized and the conservation is greatly reduced. Finally, the correctness of the results is verified by simulation.
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Mu T, Feng JE, Wang B, Jia Y. Identification of Boolean control networks with time delay. ISA TRANSACTIONS 2024; 144:113-123. [PMID: 37865590 DOI: 10.1016/j.isatra.2023.10.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Revised: 09/18/2023] [Accepted: 10/13/2023] [Indexed: 10/23/2023]
Abstract
This paper investigates the identification of time-delay Boolean networks (TBNs) and time-delay Boolean control networks (TBCNs) via Cheng product. According to all admissible (input-)output sequences, definition on identifiability of the (TBCN) TBN is given. Two algorithms are designed to select suitable delay parameters of the TBN and TBCN, respectively. Based on these, the original systems are divided into several subsystems. Then by virtue of observability, the criteria for identifiability of the TBN and TBCN are obtained. Moreover, the corresponding constructing processes are presented to establish the internal structures of the TBN and TBCN. Finally, two illustrative examples are given to show the feasibility of the proposed methods.
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Rao F, Zhang Z, Li J. Dynamical analysis of a glucose-insulin regulatory system with insulin-degrading enzyme and multiple delays. J Math Biol 2023; 87:73. [PMID: 37856001 DOI: 10.1007/s00285-023-02003-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2021] [Revised: 12/28/2022] [Accepted: 09/18/2023] [Indexed: 10/20/2023]
Abstract
This paper investigates the dynamics of a glucose-insulin regulatory system model that incorporates: (1) insulin-degrading enzyme in the insulin equation; and (2) discrete time delays respectively in the insulin production term, hepatic glucose production term, and the insulin-degrading enzyme. We provide rigorous results of our model including the asymptotic stability of the equilibrium solution and the existence of Hopf bifurcation. We show that analytically and numerically at a certain value the time delays driven stability or instability occurs when the corresponding model has an interior equilibrium. Moreover, we illustrate the oscillatory regulation and insulin secretion via numerical simulations, which show that the model dynamics exhibit physiological observations and more information by allowing parameters to vary. Our results may provide useful biological insights into diabetes for the glucose-insulin regulatory system model.
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Negero NT. Uniformly convergent extended cubic B-spline collocation method for two parameters singularly perturbed time-delayed convection-diffusion problems. BMC Res Notes 2023; 16:282. [PMID: 37858117 PMCID: PMC10588288 DOI: 10.1186/s13104-023-06457-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Accepted: 08/10/2023] [Indexed: 10/21/2023] Open
Abstract
This work proposes a uniformly convergent numerical scheme to solve singularly perturbed parabolic problems of large time delay with two small parameters. The approach uses implicit Euler and the exponentially fitted extended cubic B-spline for time and space derivatives respectively. Extended cubic B-splines have advantages over classical B-splines. This is because for a given value of the free parameter [Formula: see text] the solution obtained by the extended B-spline is better than the solution obtained by the classical B-spline. To confirm the correspondence of the numerical methods with the theoretical results, numerical examples are presented. The present numerical technique converges uniformly, leading to the current study of being more efficient.
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Qiu L, Chen R, Teng J, Pan J. Feedback control strategy of networked multi-LSRMs system with semi-Markov topology switching and time delay. ISA TRANSACTIONS 2023:S0019-0578(23)00460-3. [PMID: 37838478 DOI: 10.1016/j.isatra.2023.10.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Revised: 09/11/2023] [Accepted: 10/06/2023] [Indexed: 10/16/2023]
Abstract
This paper studies the networked control system (NCS) with semi-Markov topology switching and network delay. The time delays of the system are considered in the measurement and control channels. The control channel is between the controller and the actuator, the measurement channel is between the sensor and the controller. The topology switching and the transition process among modes are described by semi-Markov sojourn-time probability density function and Markov transition probability matrix respectively. The mean square stability conditions for the networked multi-LSRMs system are obtained by constructing a new Lyapunov function. To ensure the σ-error mean square stability of the closed loop system, a state feedback controller is designed by combining the variation technique of inequalities and Lyapunov stability theory. Finally, several experiments results verify the effectiveness and rationality of the proposed control strategy.
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Zhang JR, Lu JG, Jin XC, Yang XY. Novel results on asymptotic stability and synchronization of fractional-order memristive neural networks with time delays: The 0<δ≤1 case. Neural Netw 2023; 167:680-691. [PMID: 37722271 DOI: 10.1016/j.neunet.2023.09.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Revised: 07/14/2023] [Accepted: 09/04/2023] [Indexed: 09/20/2023]
Abstract
This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples.
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Salman M, Mohanty SK, Nayak C, Kumar S. The role of delay in vaccination rate on Covid-19. Heliyon 2023; 9:e20688. [PMID: 37867852 PMCID: PMC10587488 DOI: 10.1016/j.heliyon.2023.e20688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Revised: 09/26/2023] [Accepted: 10/04/2023] [Indexed: 10/24/2023] Open
Abstract
The role of vaccination in tackling Covid-19 and the potential consequences of a time delay in vaccination rate are discussed. This study presents a mathematical model that incorporates the rate of vaccination and parameters related to the presence and absence of time delay in the context of Covid-19. We conducted a study on the global dynamics of a Covid-19 outbreak model, which incorporates a vaccinated population and a time delay parameter. Our findings demonstrate the global stability of these models. Our observation indicates that lower vaccination rates are associated with an increase in the overall number of infected individuals. The stability of the corresponding time delay model is determined by the value of the time delay parameter. If the time delay parameter is less than the critical value at which the Hopf bifurcation occurs, the model is stable. The results are supported by numerical illustrations that have epidemiological relevance.
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Khan MMUR, Arefin MR, Tanimoto J. Time delay of the appearance of a new strain can affect vaccination behavior and disease dynamics: An evolutionary explanation. Infect Dis Model 2023; 8:656-671. [PMID: 37346475 PMCID: PMC10257886 DOI: 10.1016/j.idm.2023.06.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Revised: 03/26/2023] [Accepted: 06/05/2023] [Indexed: 06/23/2023] Open
Abstract
The emergence of a novel strain during a pandemic, like the current COVID-19, is a major concern to the healthcare system. The most effective strategy to control this type of pandemic is vaccination. Many previous studies suggest that the existing vaccine may not be fully effective against the new strain. Additionally, the new strain's late arrival has a significant impact on the disease dynamics and vaccine coverage. Focusing on these issues, this study presents a two-strain epidemic model in which the new strain appears with a time delay. We considered two vaccination provisions, namely preinfection and postinfection vaccinations, which are governed by human behavioral dynamics. In such a framework, individuals have the option to commit vaccination before being infected with the first strain. Additionally, people who forgo vaccination and become infected with the first train have the chance to be vaccinated (after recovery) in an attempt to avoid infection from the second strain. However, a second strain can infect vaccinated and unvaccinated individuals. People may have additional opportunities to be vaccinated and to protect themselves from the second strain due to the time delay. Considering the cost of the vaccine, the severity of the new strain, and the vaccine's effectiveness, our results indicated that delaying the second strain decreases the peak size of the infected individuals. Finally, by estimating the social efficiency deficit, we discovered that the social dilemma for receiving immunization decreases with the delay in the arrival of the second strain.
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Lv J, Ma W. Global asymptotic stability of a delay differential equation model for SARS-CoV-2 virus infection mediated by ACE2 receptor protein. APPLIED MATHEMATICS LETTERS 2023; 142:108631. [PMID: 36936728 PMCID: PMC10000301 DOI: 10.1016/j.aml.2023.108631] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Revised: 02/21/2023] [Accepted: 02/21/2023] [Indexed: 06/18/2023]
Abstract
The COVID-19 pandemic has brought a serious threat to human life safety worldwide. SARS-CoV-2 virus mainly binds to the target cell surface receptor ACE2 (Angiotensin-converting enzyme 2 ) through the S protein expressed on the surface of the virus, resulting in infection of target cells. During this infection process, the target cell ACE2 receptor plays a very important mediating role. In this paper, a delay differential equation model containing the mediated effect of target cell receptor is established according to the mechanism of SARS-CoV-2 virus invasion of target cells, and the global stability of the infection-free equilibrium and the infected equilibrium of the model is obtained by using the basic reproduction number ℛ 0 and constructing the appropriate Lyapunov functional. The expression of the basic reproduction number ℛ 0 intuitively gives the dependence on the expression ratio of the target cell surface ACE2 receptor, which is helpful for the understanding of the mechanism of SARS-CoV-2 virus infection.
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Messé A, Hollensteiner KJ, Delettre C, Dell-Brown LA, Pieper F, Nentwig LJ, Galindo-Leon EE, Larrat B, Mériaux S, Mangin JF, Reillo I, de Juan Romero C, Borrell V, Engler G, Toro R, Engel AK, Hilgetag CC. Structural basis of envelope and phase intrinsic coupling modes in the cerebral cortex. Neuroimage 2023; 276:120212. [PMID: 37269959 PMCID: PMC10300241 DOI: 10.1016/j.neuroimage.2023.120212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Revised: 05/09/2023] [Accepted: 05/30/2023] [Indexed: 06/05/2023] Open
Abstract
Intrinsic coupling modes (ICMs) can be observed in ongoing brain activity at multiple spatial and temporal scales. Two families of ICMs can be distinguished: phase and envelope ICMs. The principles that shape these ICMs remain partly elusive, in particular their relation to the underlying brain structure. Here we explored structure-function relationships in the ferret brain between ICMs quantified from ongoing brain activity recorded with chronically implanted micro-ECoG arrays and structural connectivity (SC) obtained from high-resolution diffusion MRI tractography. Large-scale computational models were used to explore the ability to predict both types of ICMs. Importantly, all investigations were conducted with ICM measures that are sensitive or insensitive to volume conduction effects. The results show that both types of ICMs are significantly related to SC, except for phase ICMs when using measures removing zero-lag coupling. The correlation between SC and ICMs increases with increasing frequency which is accompanied by reduced delays. Computational models produced results that were highly dependent on the specific parameter settings. The most consistent predictions were derived from measures solely based on SC. Overall, the results demonstrate that patterns of cortical functional coupling as reflected in both phase and envelope ICMs are both related, albeit to different degrees, to the underlying structural connectivity in the cerebral cortex.
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Ma XY, Huang CQ. Data-driven approach for time-delay estimation of industrial processes. ISA TRANSACTIONS 2023; 137:35-58. [PMID: 36813662 DOI: 10.1016/j.isatra.2023.01.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Revised: 01/22/2023] [Accepted: 01/22/2023] [Indexed: 06/04/2023]
Abstract
An accurate estimate of time delay is of crucial importance for control tasks such as performance assessment and controller design. In this paper, a novel data-driven approach to time-delay estimation is developed for a process subject to industrial background disturbances, in which the closed-loop output data under the routine operating conditions is only required. The practical solutions are proposed to estimate the time delay based on the estimated impulse response of the closed loop that is estimated online by utilizing the output data. Without relying on system identification and any prior knowledge of the process as well, the time delay is estimated directly for a large time delayed process; while for a small time delayed process, the time delay is estimated by means of the stationarilized filter, the pre-filter and the loop filter. The effectiveness of the proposed approach is validated by various numerical and industrial examples including a distillation column, a petroleum refinery heating furnace and a ceramic dryer.
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