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This paper focuses on secure consensus for leader-following multiagent systems (MASs) modeled by partial differential equations (PDEs) under denial of service (DoS) attacks. To mitigate the negative effects of DoS attacks, which can paralyze communication and cause agents to fail to receive valid control inputs, a buffer region is established in the communication channels among agents to temporarily store messages from neighbors. Additionally, since the states of the leader and followers are not always measurable, observers are used to estimate these states. To address these challenges, this paper proposes two boundary controllers to ensure leader-following consensus in both measurable and unmeasurable states. One controller is based on original boundary information, while the other utilizes observation information from both the leader and followers. To the best of our knowledge, this is the first attempt to use buffers to solve a class of PDEs-based MASs under DoS attacks. Furthermore, the boundary control approach has the potential to significantly reduce the number of actuators required, thereby lowering control costs. Finally, we present two numerical examples to validate the feasibility of the proposed methods.

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The main objective of this paper is to address the issue of vibration control for a class of Euler-Bernoulli beam systems that are subject to external disturbances and input saturation. The proposed controller differs from other backstepping methods in that it employs a radial basis function (RBF) neural network to accurately estimate boundary disturbances and incorporates the hyperbolic tangent function to ensure input constraints. The nonlinear partial differential equation (PDE) model is initially derived based on Hamilton's principle to capture the dominant dynamic characteristics of the flexible beam. In the framework of the Lyapunov direct approach, an adaptive RBF neural network-based law is subsequently designed to estimate the state-related boundary disturbances. The backstepping approach is then developed to propose sufficient conditions for ensuring the stability and convergence of closed-loop systems subject to input saturation. Finally, the effectiveness and superiority of the proposed methodology are further demonstrated by comparing the simulation results of constrained backstepping controllers.

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This paper tries to study the problem of finite-time synchronization for delayed semi-Markov reaction-diffusion systems. Based on the spatial and parametric characteristics of the considered systems, a new asynchronous boundary control scheme is proposed to ensure the finite-time synchronization of the drive and response systems. In the asynchronous boundary control scheme, only an actuator should be placed at the spatial boundary, which is more easier to implement and economical than the other non-boundary control strategies. Besides, the system parameters and controller follow two asynchronous semi-Markov chains for jumping, which is more practical than obeying one semi-Markov chain. Moreover, for the considered systems, we proposes a new lemma of finite-time stability, and by employing the inequality methods and variable substitution, we derive the criterion of finite-time synchronization and a correlative corollary. Finally, a numerical example and an application example on secure communication are carried out to support the developed approach.

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We present the dynamical equation model of the axially moving system, which is expressed through one partial differential equation (PDE) and two ordinary differential equations (ODEs) obtained using the extended Hamilton's principle. In the case of large acceleration/deceleration axially moving system with system parameters uncertainty and input saturation limitation, the combination of Lyapunov theory, S-curve acceleration and deceleration (Sc A/D) and adaptive control techniques adopts auxiliary systems to overcome the saturation limitations of the actuator, thus achieving the purpose of vibration suppression and improving the quality of vibration control. Sc A/D has better flexibility than that of constant speed to ensure the operator performance and diminish the force of impact by tempering the initial acceleration. The designed adaptive control law can avoid the control spillover effect and compensate the system parameters uncertainty. In practice, time-varying boundary interference and distributed disturbance exist in the system. The interference observer is used to track and eliminate the unknown disturbance of the system. The control strategy guarantees the stability of the closed-loop system and the uniform boundedness of all closed-loop states. The numerical simulation results test the effectiveness of the proposed control strategy.

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With the rapid development of smart campus, this paper studies the attitude tracking control of flexible manipulator (FM) in colleges and universities under elastic vibration and external disturbances. First, different from the traditional modeling based on ordinary differential equations (ODEs), the partial differential equations (PDEs) dynamic model of a manipulator system is established based on the Hamilton principle (HP). Second, the boundary control condition of the end system of the manipulator is introduced to adjust the vibration of the manipulator. Furthermore, a Proportional-Derivative (PD) boundary control (PDBC) strategy is proposed by the Lyapunov function to suppress the vibration of the manipulator. Finally, a numerical comparison simulation based on MATLAB/SIMULINK further verifies the robustness and anti-disturbance performance of the control method proposed in this paper.

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In this paper, the exponential bipartite consensus issue is investigated for multi-agent networks, whose dynamic is characterized by fractional diffusion partial differential equations (PDEs). The main contribution is that a novel exponential convergence principle is proposed for networks of fractional PDEs via aperiodically intermittent control scheme. First, under the aperiodically intermittent control strategy, an exponential convergence principle is developed for continuously differentiable function. Second, on the basis of the proposed convergence principle and the designed intermittent boundary control protocol, the exponential bipartite consensus condition is addressed in the form of linear matrix inequalities (LMIs). Compared with the existing works, the result of the exponential intermittent consensus presented in this paper is applied to the networks of PDEs. Finally, the high-speed aerospace vehicle model is applied to verify the effectiveness of the control protocol.

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In engineering applications, flexible beam vibration control is an important issue. Although several researchers have discussed controlling beam vibration, there are few strategies for implementing it in actual applications. The passivity-based boundary control for suppressing flexible beam vibration was investigated in this paper. The controller was implemented using a moving base, and the beam model was an undamped shear beam. The control law was established using the storage function in the design technique. The finite-gain L2 - stability of the feedback control system was then proven. This method dealt directly with the PDE of the beam model with no model reduction. Because of the non-collocated measurement and actuation in many applications, the backstepping observer was required for state estimation. Since the controller was implemented at the end of the beam via a moving base, the beam domain remained intact. Therefore, the method is simple to apply in applications. With the use of the finite-difference approach, the PDEs were numerically solved. The controller's performance of the proposed control scheme was demonstrated using computer simulation.

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Difficulty in balancing the demands of work and nonwork has been shown to be associated with lower physical and psychological health. Grounded on the self-regulation theory, we examined the effect of work-nonwork conflict on general health among employees who transitioned to remote work (remote workers), and we tested whether this association was mediated by impaired self-control capacity. The study further examined the perceived boundary control as a moderator of these associations. We collected two waves of questionnaire data with a one-month interval from 461 remote workers, and the results of regression-based analyses revealed that work-nonwork conflict was negatively related to remote workers' general health through increased self-control capacity impairment. In addition, this indirect effect was weaker for remote workers with higher perceived boundary control than those with lower perceived boundary control. These findings expand our understanding of remote workers' work-nonwork conflict and have practical implications for promoting the general health of remote workers who are experiencing work-nonwork conflict.

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This paper mainly addresses the practical consensus problem of nonlinear multi-agent systems modeled by reaction-diffusion equations subject to the bounded external disturbances. Different from the existing consensus control methods associated with spatiotemporal dynamics, the proposed H∞ Neumann boundary controller based on distributed measurement data can guarantee the optimal disturbance attenuation performance under the actuator saturation. Initially, a consensus spatiotemporal error model is constructed by introducing the Kronecker product and equivalent directed graph. Subsequently, a linear matrix inequalities (LMIs)-based sufficient condition is derived by combining the improved Lyapunov-based approach and H∞ norm. Then, an optimization problem is proposed by applying invariant set, such that the consensus errors can converge to a minimized bounded region in the presence of actuator saturation. Finally, comparison simulations on the synchronization of FitzHugh-Nagumo (FHN) model are given to demonstrate the effectiveness of proposed methodology.

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The imposition of telework due to the COVID-19 pandemic brought with it the need for individuals to readjust their work-non-work boundaries. In this crisis situation, individuals' needs to manage these boundaries may have been influenced by contextual factors, such as family-supportive supervisor behaviors (FSSB) and macro-structural aspects, such as the country to which the teleworkers belong. This study tests the mediating effect of boundary control on the relationship between FSSB and satisfaction with life and examines the moderating effect of the country (Pakistan vs. Portugal) in the relationship between FSSB and boundary control. With a sample of 108 Portuguese and 118 Pakistani individuals, the results were analyzed using Process tool. FSSB was found to be important for teleworkers to control their boundaries and for their satisfaction with life and this control was also seen to contribute to higher levels of life satisfaction. Differences between the two countries were observed: boundary control mediates the relationship between FSSB and satisfaction with life for Pakistani teleworkers and these workers are more dependent on FSSB to exercise boundary control than Portuguese teleworkers. This study highlights the importance of considering contextual factors when implementing telework. Practical implications are discussed.

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BACKGROUND: Job crafting is associated with positive work-related outcomes, but its effects on nonwork-related outcomes are unclear. The conservation of resources theory informed the hypotheses that work-nonwork facilitation mediates the relationship between job crafting and general health, and this mediation process is moderated by perceived boundary control. METHODS: Using a two-wave design, 383 employees from a range of work settings completed questionnaires in which they rated job crafting, work-nonwork facilitation, general health and perceived boundary control. RESULTS: Moderated mediation analysis showed that work-nonwork facilitation mediated the relationship between job crafting and employee general health. Further, perceived boundary control moderated this indirect effect, such that the indirect effect was stronger for employees with high perceived boundary control than those with low perceived boundary control. CONCLUSIONS: This study is an important step forward in understanding the effect of job crafting on nonwork domains, and in clarifying "how" and "when" job crafting might affect employees' general health. Further, the results have practical implications for fostering employee general health.

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BACKGROUND: Burnout for doctors-in-training is increasingly cause for concern. Our objectives were to assess the feasibility, acceptability and impact of a novel intervention to reduce burnout and improve wellbeing. This is the first wellbeing intervention for medical doctors to include strategies for work-life boundary management and digital wellbeing. METHODS: Twenty-two doctors participated in face-to-face workshops which included group discussion of challenges experienced and strategies to enhance self-care and wellbeing. A pre-post-test mixed-methods evaluation was undertaken. Questionnaire measures were the Oldenburg Burnout Inventory, Warwick-Edinburgh Mental Wellbeing Scale and the boundary control subscale of the Work-Life Indicator (i.e., the degree of perception of control of the boundaries between work and personal life). Paired t-tests examined whether there were statistically significant differences. Eleven doctors also participated in post-intervention semi-structured interviews. Transcripts were analysed using thematic analysis. RESULTS: The intervention was well-received, with all trainees finding the workshop useful and saying they would recommend it to others. At baseline most participants had scores indicative of burnout on both the disengagement (82%) and exhaustion (82%) subscales of the Oldenburg Burnout Inventory. One month post-intervention, participants had a statistically significant reduction in burnout (both disengagement and exhaustion) and improvement in boundary control. Wellbeing scores also improved, but differences were not statistically significant. Qualitative analysis indicated participants had welcomed a safe space to discuss stressors and many had implemented digital wellbeing strategies to manage their smartphone technology, and increased self-care such as mindfulness practice and walking in green space. CONCLUSIONS: The intervention reduced burnout and improved boundary control. We suggest that having protected time for doctors to share personal experiences, adopt digital wellbeing and self-care strategies are effective tools to support doctors' wellbeing and should be investigated further.

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Mittag-Leffler stabilization is studied for fractional reaction-diffusion cellular neural networks (FRDCNNs) in this paper. Different from previous literature, the FRDCNNs in this paper are high-dimensional systems, and boundary control and observed-based boundary control are both used to make FRDCNNs achieve Mittag-Leffler stability. First, a state-dependent boundary controller is designed when system states are available. By employing the spatial integral functional method and some inequalities, a criterion ensuring Mittag-Leffler stability of FRDCNNs is presented. Then, when the information of system states is not fully accessible, an observer is presented to estimate the system states based on boundary output and an observer-based boundary controller is provided aiming to stabilize the considered FRDCNNs. Furthermore, a robust observer-based boundary controller is proposed to ensure the Mittag-Leffler stability for FRDCNNs with uncertainties. Examples are given to illustrate the effectiveness of obtained theoretical results.

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Cohen-Grossberg neural networks (CGNNs) play an important role in many applications and the stabilization of this system has been well studied. This study considers the exponential stabilization for stochastic reaction-diffusion Cohen-Grossberg neural networks (SRDCGNNs) by means of an aperiodically intermittent boundary control. Both SRDCGNNs without and with time-delays are discussed. By employing the spatial integral functional method and Poincare's inequality, criteria are derived to ensure the controlled systems achieve mean square exponential stabilization. Based on these criteria, the effects of diffusion item, control gains, the minimum control proportion and time-delays on exponential stability are analyzed. Examples are given to illustrate the effectiveness of the obtained theoretical results.

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Growing concerns about intensive information and communication technology (ICT) use led to abundant research on its debilitating effects on employees' abilities to meet family demands. Drawing on the stressor-strain model, we conducted a daily diary study to investigate how different types of daily ICT demands experienced during work hours and after work influence work-family conflict (WFC) in the evening. We collected data from 98 full-time employees (793 day-level observations) for 10 consecutive workdays to understand employees' work-nonwork interface experiences, namely, negative spillover and role conflict. First, we examined a multilevel mediation model to test the negative spillover effect of on-the-job ICT demands on WFC in the evening via negative affect (NA) at the end of the workday. Second, we investigated the effects of off-the-job ICT demands on WFC to provide evidence of role conflict in the nonwork domain. Further, we tested the protective role of boundary control in these phenomena. The multilevel analysis results revealed that different types of ICT demands experienced at work have idiosyncratic impacts on WFC. Also, while extended availability after work hours yields greater WFC, this link was weaker for the employees who perceive high boundary control.

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In this article, a weighted multiple model adaptive boundary control scheme is proposed for a flexible manipulator with unknown large parameter uncertainties. First, the uncertainties are approximatively covered by a finite number of constant models. Second, based on Euler-Bernoulli beam theory and Hamilton principle, the distributed parameter model of the flexible manipulator is constructed in terms of partial differential equation for each local constant model. Correspondingly, local boundary controllers are designed to control the manipulator movement and suppress its vibration for each partial differential equation model, which are based on Lyapunov stability theory. Then, a novel weighted multiple model adaptive control strategy is developed based on an improved weighting algorithm. The stability of the overall closed-loop system is ensured by virtual equivalent system theory. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed control strategy.

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In this paper, the active disturbance rejection control (ADRC) is utilized to stabilize the vibration of perturbed Timoshenko beam model with tip mass. The boundary control design is based on a hybrid PDE-ODE model, and is accompanied with designing a high-gain extended state observer (ESO) that is used to estimate the boundary disturbances. By transforming the model into the appropriate state space, the semigroup theory is employed to prove the well-posedness of the closed-loop system. To this end, it is proved by a frequency domain method that the semigroup generated by the system operator is exponentially stable, which allows to conclude the boundedness of perturbed closed-loop system response. The stability of the closed-loop system is further analyzed using the Lyapunov approach. Simulation results are presented to illustrate the efficacy of the suggested method.

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The aim of this paper is to develop a boundary control for the vibration reduction of a flexible marine riser system in the presence of parametric uncertainties and system states obtained inaccurately. To this end, an adaptive output feedback boundary control is proposed to suppress the riser's vibration fusing with observer-based backstepping, high-gain observers and robust adaptive control theory. In addition, the parameter adaptive laws are designed to compensate for the system parametric uncertainties, and the disturbance observer is introduced to mitigate the effects of external environmental disturbance. The uniformly bounded stability of the closed-loop system is achieved through rigorous Lyapunov analysis without any discretisation or simplification of the dynamics in the time and space, and the state observer error is ensured to exponentially converge to zero as time grows to infinity. In the end, the simulation and comparison studies are carried out to illustrate the performance of the proposed control under the proper choice of the design parameters.

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This paper is concerned with boundary control for an axially moving belt system with high acceleration/deceleration subject to the input saturation constraint. The dynamics of belt system is expressed by a nonhomogeneous hyperbolic partial differential equation coupled with an ordinary differential equation. First, state feedback boundary control is designed for the case that the boundary states of the belt system can be measured. Subsequently, output feedback boundary control is developed when some of the system states can not be accurately obtained. The well-posedness and the uniformly bounded stability of the closed-loop system are achieved through rigorous mathematical analysis. In addition, high-gain observers are utilized to estimate those unmeasurable states, the auxiliary system is introduced to eliminate the constraint effects of the input saturation, and the disturbance observer is adopted to cope with unknown boundary disturbance. Finally, the control performance of the belt system is illustrated by carrying out numerical simulations.

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Several advances have been made in data assimilation techniques applied to blood flow modeling. Typically, idealized boundary conditions, only verified in straight parts of the vessel, are assumed. We present a general approach, on the basis of a Dirichlet boundary control problem, that may potentially be used in different parts of the arterial system. The relevance of this method appears when computational reconstructions of the 3D domains, prone to be considered sufficiently extended, are either not possible, or desirable, because of computational costs. On the basis of taking a fully unknown velocity profile as the control, the approach uses a discretize then optimize methodology to solve the control problem numerically. The methodology is applied to a realistic 3D geometry representing a brain aneurysm. The results show that this data assimilation approach may be preferable to a pressure control strategy and that it can significantly improve the accuracy associated to typical solutions obtained using idealized velocity profiles.

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