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This article proposes a novel multidimensional Taylor network (MTN)‐based adaptive finite‐time control approach for stochastic nonlinear systems with input saturation constraints. First, by introducing the hyperbolic tangent function, a piecewise smooth function is proposed to approximate the input saturation constraints, which can solve the problem caused by input saturation. Then, with the aid of MTN approximation theorem, a novel adaptive finite‐time control approach is proposed, which can guarantee that all signals of the closed‐loop system are semi‐globally finite‐time stability in probability (SGFTSP), the system output follows the given reference signal, meanwhile, the tracking error converges to a small neighborhood of the origin in finite‐time. Compared with the existing results, the proposed approach has the characteristics of simple structure and low calculation, which can achieve the satisfactory control performance with a reduced computational burden. In the end, the effectiveness of the proposed approach is validated by Lyapunov stability theory and two simulation experiments. [ABSTRACT FROM AUTHOR]

This paper investigates an event‐triggered adaptive resilient control problem for nonlinear systems against unknown false data injection and actuator saturation. The sensors of the controlled system are subject to unknown false data injection attacks so that all original states can not be directly applied in the controller design process. To address the negative effects of the false data injection attacks, attack compensators are introduced in control design. Simultaneously, a dynamic event‐triggering mechanism is set up to reduce the communication burden of the network. Furthermore, an auxiliary system is constructed to cope with the actuator saturation that commonly exists in practical systems. Based on the Lyapunov stability theory, it is demonstrated that the designed adaptive controller can guarantee the stability of the controlled system and the boundedness of all signals. The validity of the proposed control scheme is evidenced by simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a predictor‐based continuous‐discrete nonlinear observer is proposed for a class of nonaffine Lipschitz nonlinear systems with aperiodic sampled delayed output measurements and external disturbance. Firstly, this study introduces a class of delayed sampling hybrid nonlinear systems. By employing Lyapunov techniques and trajectory‐based stability theory, sufficient conditions are established for ensuring input‐to‐state stability of the delayed sampling hybrid nonlinear system with respect to external disturbances. Then the predictor‐based continuous‐discrete nonlinear observer is designed which consists of a continuous‐time observer, a compensating injector and a predictor. The continuous‐time observer is utilized to obtain continuous and delay‐free state estimation. The compensating injector is designed to compensate for output errors that occur between sampling instants. Furthermore, the predictor is employed to obtain delay‐free output error information, which is then utilized by the continuous‐time observer for feedback correction. The proposed observer's exponential input‐to‐state property against the disturbance is proved via the proposed hybrid system stability theory. The effectiveness of the proposed observers has been demonstrated through numerical simulations and performance comparisons with the zero‐order holder‐based observer and the output predictor‐based observer designs in order to highlight the effectiveness and advantages of the proposed observer. [ABSTRACT FROM AUTHOR]

In this paper, an energy harvester consisting of a cantilever beam, magnets, and magnetic springs embedded on its structure is proposed to harvest electricity energy. In order to extract energy from the system permanently, an adaptive controller is proposed. With the help of the proposed controller, it is prevented from damping the oscillations of the beam or excessive increasing in the amplitude of these oscillations. Also, the use of the proposed controller provides the possibility that despite the presence of unknown external disturbances such as wind waves and sudden changes of sea waves, as well as the uncertainty of the parameters of the cantilever beam, a permanent energy is harvested from the proposed mechanism. The equations describing the electromechanical behavior of the proposed mechanism are derived from Lagrange equations. On the other hand, dynamic surface control technique is employed to design the adaptive and control laws. The stability of the closed-loop system is shown using Lyapunov stability theory, and the tracking error converges to a small neighborhood around the origin. Numerical simulation for cantilever beam is investigated to clarify the effectiveness of the proposed mechanism and controller. [ABSTRACT FROM AUTHOR]

Practical stability can describe qualitative behavior and quantitative properties of systems in comparison with traditional Lyapunov stability theory. In this paper, such stability problem is formulated for nonlinear delayed urban traffic systems described by uncertain differential equations which are a type of differential equations driven by Liu processes. First of all, we prove the existence and uniqueness of the solution. Then, we analyze the pth moment practically exponential stability and quasi surely globally practically uniformly exponential stability of the system by employing general It'o formula, Gronwall's inequality, Holder inequality and Borel-Cantelli lemma. Moreover, an example is presented to verify the validity of our theoretical methods. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates an observer‐based adaptive robust fuzzy formation tracking control method for nonlinear multi‐agent systems (MAS) with input delay. The considered nonlinear MAS contains the unknown nonlinear functions, that is, unmeasured states. The fuzzy logic systems (FLS) are used to approximate the unknown nonlinear functions, and then a fuzzy adaptive state observer is designed to estimate the unmeasured states. The Pade approximation approach is introduced to solve the input delay issue. By combining command filtering and backstepping recursive control techniques, a robust adaptive prescribed performance formation output feedback tracking controller is designed. Moreover, the proposed controller can avoid the "explosion of complexity" and "singularity" problems in the backstepping design framework. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (SGUUB), and the formation tracking errors do not exceed the prescribed performance bounds. Finally, the feasibility of the proposed control approach can be further verified through numerical and practical examples. [ABSTRACT FROM AUTHOR]

Summary: In this article, the cluster consensus problems of two classes of nonlinear multi‐agent systems (NMASs) are studied under the dynamic event‐triggered control (ETC) strategy, where cooperative‐competitive interactions among agents and high‐order dynamics are considered. First, two dynamic ETC protocols are developed to realize the cluster synchronization of NMASs. Different from the static ETC, a dynamic parameter regulated by an adaptive law is used in place of a constant which can improve the trigger time intervals and reduce the energy consumption. Subsequently, an adaptive control mechanism based on the proposed ETC strategy is designed to adjust the controller parameter for agents. Some sufficient conditions for achieving the cluster consensus of NMASs are derived by using the Lyapunov stability theory and algebraic graph theory. Moreover, it is proved in theory that Zeno phenomenon can be excluded with these control schemes. Finally, two simulation examples validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

An adaptive super-twisting sliding mode control (AST-SMC) is proposed for the power-line inspection (PLI) robot system with two degrees of freedom and single control input underactuated with multiple balances. Firstly, the nonlinear dynamic equation of PLI robot is established, and the model is linearized at the nominal equilibrium point. Secondly, a special transformation is introduced to transform the original input delay system into a delay-free model, and an equilibrium manifold linearization (EML) model is established by using scheduling variables to expand the operating range of the controlled system, as a result of which the disturbance observer control (DOC) is designed to estimate the external disturbance. Thirdly, in order to achieve fast convergence and continuous control, the super-twisting sliding mode control(ST-SMC) method is proposed to decrease chattering in the control law. Finally, it can be verified by Lyapunov stability theory that the system reaches the sliding mode surface in finite time and the trajectory tracking error converges to zero in finite time. The simulation results verify that the combination of DOC and AST-SMC has a optimal disturbance approximation and control convergence ability, clarifying the effectiveness and robustness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a new two-body self-synchronization vibration system characterized by two ideal vibration-exciting motors (asynchronous motors) installed on different vibrating bodies is investigated. Firstly, differential equations of the system are established via the Lagrange equation. Moreover, natural frequencies and stable solutions are obtained. Then, the conditions for the system to implement stable self-synchronization are derived using the equilibrium point theory of the dynamics system and Lyapunov's stability theory. The effects of spring stiffness on the natural frequencies and synchronous motion are numerically analyzed. The steady-state responses of the system are obtained for different structure parameters. The research results show that this system can implement two types of self-synchronization motion under different structure parameters. The first type fluctuates the phase differences in the proximity of zero rad, while the other one fluctuates the phase differences near π rad. Resonance significantly affects the synchronous motion of the system, rapidly changing in phase differences and amplitudes. An increase in the value of k y 2 is not conducive to implementing the stable synchronous motion. Finally, the correctness of the theory and electromechanical coupling simulation results is experimentally validated. The results of this paper can be directly used to determine the structural parameters for a new type of vibrating machine. [ABSTRACT FROM AUTHOR]

We explore the interaction between dark matter and curvature-driven dark energy within viable f (R) gravity models, employing the phase-space analysis approach of linear stability theory. By incorporating an interacting term, denoted as Q = α H ρ ~ m (κ 2 3 H 2 ρ curv + 1) , into the continuity equations of both sectors, we examine dynamics of two f (R) gravity models that adhere to local gravity constraints and fulfill cosmological viability criteria. In de Sitter phase, our investigation reveals modifications of critical points compared to the conventional form, attributed to the introduced interaction. Through a comprehensive phase-space analysis, we illustrate the trajectories near critical points and outline the constraints on the phase space based on cosmological and cosmographic parameters. Furthermore, we can also observe stable behavior of this interacting system during the de Sitter phase of the Universe. [ABSTRACT FROM AUTHOR]

Flexible vibration has a great impact on flexible spacecraft attitude control, which will reduce the pointing accuracy of the spacecraft platform and bring severe challenges to the design of a high-precision attitude control system for flexible spacecraft. Aiming at the problem of attitude and vibration coupling control of flexible spacecraft, an anti-unwinding attitude coupling controller using the positive position feedback (PPF) control is proposed in this paper. The model compensation control term is constructed based on the prior information to improve the tracking performance. The proposed attitude coupling control method can effectively suppress the flexible vibration while achieving more accurate attitude control. The obtained closed-loop system under the proposed control scheme is asymptotically stable, which is proved by the Lyapunov stability theory. The numerical simulation illustrates that the proposed method can effectively improve the attitude control accuracy of the flexible spacecraft and is capable of large-angle attitude maneuver control because of its prominent performance in attitude tracking and its unwinding-free performance. • Coupling control for flexible spacecraft. • Active vibration control using positive position feedback. • Model compensation control term is constructed to improve the dynamic performance. • The obtained closed-loop system achieves the asymptotic stability and anti-unwinding performance. [ABSTRACT FROM AUTHOR]

This paper suggests a new dynamic sliding mode controller incorporating a disturbance observer for controlling integrating processes with time delay. Here, a new reaching law has been introduced to expedite the system response without evoking chattering. The convergence of this law is also studied. Additionally, the whole system stability is proved using the Lyapunov stability theory. This paper also proposes a new disturbance observer to improve the disturbance rejection and to help suppress chattering further. The suggested observer has only one parameter to be designed. Therefore, this observer can easily be implemented. Several simulation examples and a real-time application are considered to prove the superiority of the suggested controller over the reported controllers in the literature. [ABSTRACT FROM AUTHOR]

A complex dynamical network (CDN) can be considered as the composition system with the nodes subsystem (NS) and the links subsystem (LS), and both subsystems are coupled with each other. In this paper, two vector differential equations (VDE) are used to describe the dynamical behaviours of NS and LS, respectively, in which the dynamical behaviour of NS is considered as the VDE with the second derivative term (SDT). This paper mainly focuses on the dynamics of LS, which is represented as VDE with the intuitive topologic feature of outgoing links, and investigates the design of the tracking controller for NS and the auxiliary tracking objectives (ATO) for LS. Firstly, the dynamical models of NS and LS in CDN are proposed, and the corresponding assumptions are given. Secondly, based on Lyapunov stability theory, the controller of NS and the ATO of LS are designed so that the state of NS can asymptotically track the given reference signal. Finally, the effectiveness of the proposed control strategy in this paper is verified by the numerical simulation example with N two-links robots. Abbreviations: ATO: auxiliary tracking objectives; CDN: complex dynamical network; LS: links subsystem; MDE: matrix differential equation; NS: nodes subsystem; SDT:second derivative term; VDE: vector differential equation; [ABSTRACT FROM AUTHOR]

The onset of thermal convection in an incompressible Oldroydian fluid‐saturating porous media is examined to study the combined impact of uniform rotation and temperature‐dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress‐free and slip‐free boundaries, the expressions for the Darcy–Rayleigh numbers for both non‐oscillatory as well as oscillatory convection with linear and exponential temperature‐dependent viscosity are derived, using the "weighted residual method." The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non‐oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman‐Darcy number stabilize the system for each set of boundary conditions. [ABSTRACT FROM AUTHOR]

This paper studies the distributed attitude tracking control problem for rigid spacecraft under a directed graph with external disturbances and full-state constraints. First, because only a subset of the follower spacecraft can acquire the states of the leader spacecraft, a distributed finite-time observer was used to estimate the leader spacecraft's attitude and angular velocity accurately. Then a nonhomogeneous disturbances observer (NDO) was employed to estimate and compensate for external disturbances. Next, based on the barrier Lyapunov functions (BLFs), a distributed finite-time command-filtered backstepping controller was designed to make the tracking error converge to a small neighborhood of the origin in finite time. The BLFs were used to ensure the full-state constraints and the compensating signals were designed to eliminate the influence of the command filter errors. Furthermore, stability of the closed-loop system was analyzed based on the finite-time Lyapunov stability theory. Numerical simulations were conducted to validate the effectiveness of the proposed control law. [ABSTRACT FROM AUTHOR]

A nonlinear elastic medium containing sharp inhomogeneities is considered. The properties of a modified model of such a medium are investigated. The modification consists in including in the asymptotic equation of state those terms that were discarded in the previously considered models. The main purpose of the ongoing research is to analyze the existence, stability, and dynamic properties of soliton-like solutions within the modified model, as well as to compare these solutions with analogous solutions obtained in the previously considered models. [ABSTRACT FROM AUTHOR]

In this paper, stability analysis and stabilization control of discrete-time impulsive switched time-delay systems with all unstable subsystems are discussed. By utilizing a switching time-varying Lyapunov-Krasovskii functional and the mode-dependent interval dwell-time switching rule, we derive some more general stability theorems for the considered time-delay system with all subsystems being unstable. Moreover, we design a time-varying state feedback controller to ensure the stabilization of the resulting closed-loop system. Eventually, the theoretical findings are demonstrated utilizing numerical examples. [ABSTRACT FROM AUTHOR]

The article investigated the stability of a two‐lane car‐following model with lateral friction on the basis of cluster synchronization theory of complex network. By using the Lyapunov stability theory and designing the appropriate controller, the two‐lane car‐following model with lateral friction is quickly stabilized and the stability condition of the model is obtained. Besides, based on the adaptive H∞$$ {H}_{\infty } $$ cluster synchronization theory for complex networks with external disturbances, the stability of two‐lane car‐following model with lateral friction is studied when the vehicles is subjected to random external disturbance. Finally, the numerical simulation is carried out by using Matlab simulation technology, the results show that the two‐lane car‐following model with lateral friction is rapidly stabilizing and congestion phenomenon is effectively alleviated under the controller designed. [ABSTRACT FROM AUTHOR]

This paper presents asymptotic stability criteria for fractional‐order gene regulatory networks (FOGRNs) with impulses, time delays, and two numerical cases to illustrate the applicability of the results. The established system's boundedness, existence, and uniqueness are discussed using the Mittag–Leffler function, homeomorphism theory, and Cauchy–Schwartz inequality. The delay‐independent asymptotic stability criteria for FOGRNs are derived using algebraic and LMI methods, famous inequality techniques, and Lyapunov stability theory. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of event‐triggered consensus for a class of singular multi‐agent systems with nonlinear dynamics. Firstly, in consideration of the impossibility to reach all agents in some case, an observer is designed to access these agents' states. Secondly, a novel adaptive event‐triggered scheme is proposed based on asynchronous data sampling. In this scheme, the trigger parameter can be adjusted dynamically in order to reduce information transmissions among agents. Thirdly, by employing Lyapunov stability theory, a sufficient condition on the consensus of singular multi‐agent systems is obtained. Then, the control protocol and event‐triggering scheme are designed by solving a linear matrix inequality condition. Finally, an example is given to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

To deal with the problems of low positioning accuracy and poor stability caused by model parameter uncertainty and external disturbances in the remotely operated vehicle (ROV) dynamic positioning control system, the adaptive fuzzy control is combined with a disturbance observer to estimate the lumped disturbances and the error compensation mechanism is introduced to design the ROV dynamic positioning controller based on the finite‐time command filter. The combination of finite‐time command filter control and the backstepping method ensures that the positioning error converges to a smaller neighborhood near zero in finite time. The stability of the closed‐loop system is demonstrated according to the Lyapunov stability theory. The simulation results show that a 13% performance improvement over traditional backstepping methods is achieved by the designed controller, effectively suppressing system lumped disturbances and achieving fast and accurate positioning of the desired positions. [ABSTRACT FROM AUTHOR]

It is well known that control effort is the key factor considered in formation control of a multi‐agent system (MAS). To reduce the controller effort, an economic event‐triggered super twisting control (STC) protocol for the formation tracking of a nonlinear MAS, which avoids the unnecessary computations and transmission of control inputs among agents. Specifically, a distributed leader‐follower control framework, combing the multi‐input STC with event‐triggered strategy, is proposed to ensure that the followers' states reach an agreement on the leaders state. Then, the sufficient conditions for the selection of controller parameters are formulated in terms of linear matrix inequalities (LMIs). On this basis, the event‐triggered conditions for implementing the STC protocol in the network environment are obtained using Lyapunov stability theory. Simulation study is carried out to demonstrate the effectiveness and merits of the STC in terms of formation construction, trajectory tracking, and robustness to system uncertainties. [ABSTRACT FROM AUTHOR]

Summary: This study investigates the ℋ∞$$ {\mathscr{H}}_{\infty } $$ secure consensus issue for Markov jump multi‐agent systems with denial‐of‐service attacks and disturbance. Considering that the mode of the system cannot be directly obtained in the actual situation, a detector is constructed to obtain the mode of the system indirectly with the help of the hidden Markov model. The network communications between agents are undirected, and denial‐of‐service attacks are encountered randomly and represented by a random variate obeying Bernoulli distribution. The reduced‐order decomposed system is obtained by the method of model reduction. On this basis, the Lyapunov stability theory is applied to derive some sufficient conditions to guarantee that the system achieves consensus with a stipulated ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance index. Finally, a numerical example is employed to verify the validity of the proposed protocol. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates group consensus tracking problems with time‐varying reference velocities. The multiple agents are described as second‐order nonlinear dynamics in directed information exchange settings. For the multi‐agent networks formed by finite agent groups, novel distributed protocols with/without time‐varying transmission delays are designed to solve the group consensus tracking problems. The problems are first transformed into the asymptotical stability of consensus error systems and the input‐to‐state stability of tracking error systems, and then sufficient conditions are derived to guarantee the agents realizing the group consensus tracking based on Lyapunov stability theories. Finally, several simulations are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The results of the swept wing boundary layer stability investigation are presented for the case, when the wing surface has a region of gas suction through the wall normal to the surface, while the wing is in Mach number 2 flow. In the flow regime considered the predominant boundary layer instability type is the crossflow instability. The gas suction effect on the development of unstable modes in the boundary layer is investigated using the linear stability theory and direct numerical modeling. The numerical modeling of laminar (undisturbed) flow fields with regions of gas suction and disturbed flow fields is carried out by integrating Navier–Stokes equations. An analysis within the framework of the linear stability theory is performed using the -method. The suction region location is varied with conservation of the integral intensity. It is shown that the mode instability growth can be considerably suppressed at the expense of an optimal disposition of the suction region. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive terminal sliding-mode control (ATSMC) method is proposed for the synchronization of uncertain fractional-order chaotic systems with disturbances. According to the sliding-mode control theory, a non-singular sliding surface is constructed. To overcome the chattering problem of ATSMC, a smooth term is used in the controller. In order to reduce the estimation error of an uncertain parameter, adaptive laws are designed to adjust the amplitude of the continuous function. Based on the Lyapunov stability theory, a stability analysis of the error system is performed to ensure that the tracking error eventually converges to the origin. The effectiveness and applicability of the proposed control strategy are verified using the simulation results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of clustering component synchronization of nonlinearly coupled complex networks with nonidentical nodes and asymmetric couplings is investigated. A pinning control strategy is designed to achieve the clustering component synchronization with respect to the specified components. Based on matrix analysis and stability theory, clustering component synchronization criteria are established. Two numerical simulations are also provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: In this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with H∞$$ {H}_{\infty } $$ performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique. [ABSTRACT FROM AUTHOR]

Summary: The underlying intention of this work is to devise a tracking control protocol for the nonlinear cyber‐physical systems that are prone to external disturbances, time‐varying input delays and deception attacks. To be more precise, the modified repetitive tracking controller is formulated for ensuring the asymptotic tracking outcomes of the assayed system with the aim of addressing the impacts caused by external disturbances as well as input time‐varying delays. First of all, the nonlinearities of the investigated cyber‐physical systems are efficaciously approximated by the interval type‐2 fuzzy model approach. Further, the predictor technique is utilized in this study to mitigate the influence of input delays and specifically, the extended Smith predictor approach is employed. That is, the transfer function is inserted into the conventional Smith predictor's main feedback channel. In parallel, the active disturbance rejection technique is executed to reject and estimate the external disturbance impacts on the assayed system. Notably, the improved equivalent‐input‐disturbance estimator approach is tied up and more precisely, the estimated disturbances obtained from the afore‐said estimator are incorporated into the proposed controller. Whilst the deception attacks are characterized as a stochastic distributed random variable that are governed by the Bernoulli distribution. With all of this as a backdrop, the appropriate delay‐dependent constraints are expressed in the context of linear matrix inequalities by employing the Lyapunov stability theory. In line with the predetermined criteria, the relations for computing the required gain matrices are also formulated. Ultimately, the simulation analysis is carried out using two distinct numerical examples to confirm the importance of the proposed control mechanism from the perspective of theory as well as practice. [ABSTRACT FROM AUTHOR]

Summary: In this article, we address the problem of achieving predefined‐time control for a class of nonlinear dynamical systems with parameter uncertainties. We introduce an adaptive predefined‐time control algorithm based on integrator backstepping for n$$ n $$th order nonlinear systems. Using Lyapunov's stability theory, we establish that the proposed predefined time control approach, combined with an adaptive law, ensures the boundedness of all signals within the closed‐loop system. A notable advantage of our method is its potential to achieve convergence within a predetermined time frame. To validate our approach's efficacy, we present a practical example involving a 2 DOF helicopter, demonstrating the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this article, an explicit solution of the homogeneous fractional delay oscillation difference equation of order 1<ι<2$$ 1<\iota <2 $$ is given by constructing discrete sine‐ and cosine‐type delayed Mittag‐Leffler functions. Then, the discrete Laplace transform technique as an effective tool for solving the nonhomogeneous term, which is utilized to explore the solution of corresponding nonhomogeneous equation. Next, finite‐time stability of the homogeneous equation is studied based on the representation of the solution. Furthermore, we show a numerical example to elaborate the correctness of stability theory. Finally, an exact solution for the nonhomogeneous fractional difference equation with 0<ι<1$$ 0<\iota <1 $$ is further presented via using the discrete two‐parameter delayed Mittag‐Leffler function. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered-based cluster-delay consensus control problem is investigated for leader-following nonlinear multi-agent systems (MASs). In control design, both state triggering in the agents' network and constant time-delay in the leaders' communication network are considered. Under the framework of Lyapunov function stability theory, the Lipschitz condition is used to overcome the influence caused by time-delay. In order to further effectively utilize data transmission resources, and reduce the communication load of the topology network between each agent, an event-triggered mechanism is established. Subsequently, a robust cluster consensus control strategy is proposed based on event-triggered mechanism, which can ensure all signals of the controlled system are bounded, and the tracking errors converge to zero. In addition, it can also effectively avoid the Zeno behavior. Finally, the effectiveness of the presented control method and theory is verified by a simulation example. [ABSTRACT FROM AUTHOR]

The robust synchronization of uncertain master–slave Lur'e systems based on time-delayed feedback control is further investigated. A less conservative synchronization stability criterion and a less conservative robust synchronization stability criterion than some recent published references are proposed via Lyapunov stability theory. First, an augmented delay-dependent Lyapunov–Krasovskii functional (LKF) is constructed, where some single integral terms are augmented to the integrand component of a single-integral subfunction. This not only increases some coupling information on some system variables but also increases the coupling information on some necessary variables contained in the inequality lemmas, which can make full use of the inequality lemmas and reduce the conservatism of the synchronization stability criterion. Second, to overcome the nonlinear phenomena in the synchronization criterion, the novel negative definite inequality equivalent transformation lemma is used to transform the nonlinear inequalities to the linear matrix inequalities (LMIs) equivalently, which can be easily solved by the MATLAB LMI-Toolbox. Finally, some common numerical examples are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this study, a method for fault detection of a permanent magnet synchronous generator (PMSG) wind turbine is proposed. The dynamic model of the wind energy conversion system is simulated and the system's fault is diagnosed using a proposed terminal sliding mode observer (TSMO). The nonlinear state-space equations of the closed-loop wind turbine are derived, which include a robust adaptive controller that is implemented for maximum power capture and a PI controller that is designed for pitch angle control. Then, utilising a new approach, a TSMO is designed for estimating the states and faults in a finite time. The stability and convergence of the states and fault estimation error are investigated via the Lyapunov stability theory. A $ 3kw $ 3 kw PMSG wind turbine is simulated and using TSMO the states are estimated and a blade imbalance fault (BIF) fault is detected. The state and fault estimation errors converge to zero in a finite time. [ABSTRACT FROM AUTHOR]

This study proposes a new control strategy for mitigating the libration in a partial space elevator (PSE). First, a libration-free or coupling-free analytical speed function is derived by assuming no in-plane and out-of-plane libration in the cargo transportation phase. Subsequently, a thrust is applied at the PSE's end body to counter any libration during this phase. A new set of geometric measures - bending and departure angles - are introduced to characterize the libration motion in PSE's dynamic equation. Based on these measures, two separate proportional-derivative (PD) stabilizing feedback laws are proposed. These PD laws individually control the bending and departure angles by thrust at the end body to suppress the libration that deviates from the libration-free trajectory. Due to the dynamic coupling between the bending and departure modes, they dominate alternatively. Accordingly, a novel fuzzy logic control law is proposed to switch between two PD controls based on the state of these two angles. Finally, a thrust vectoring control is proposed to combine in-plane and out-of-plane thrusting into a single actuation control. The asymptotic stability of the proposed control scheme is proved by Lyapunov's stability theory. Comprehensive numerical analyses demonstrate the effectiveness of the new geometric representation of the libration and the proposed new control strategy, highlighting their ability to suppress libration with bounded control inputs efficiently. • Derived new coupling-free analytical speed function for libration-free cargo transfer trajectory. • Introduced a new set of geometric measures, bending and departure angles, to describe libration motion. • Proposed a Fuzzy logic law to switch control between bending and departure angles. • Proposed a thrust vectoring control to combine in-plane and out-of-plane thrusting into one actuation. [ABSTRACT FROM AUTHOR]

Indonesia's geographic location and position with its sovereign rights and territorial sovereignty from land, sea, and air geopolitically and geostrategically has a form of high vulnerability from traditional and non-traditional threats in violations of maritime territory and regional stability. This research aims to provide an analysis of defense resource empowerment strategies to support the Indonesia Armed Forces (TNI) main tasks in maintaining regional stability. this research is supported by the resource theory, defense theory, and stability theory approaches. The method used is qualitative descriptive statistics supported by SWOT analysis and analytical hierarchy process (AHP). Based on the results of the SWOT analysis, there are 15 internal factors in the form of strengths and 20 external factors in the form of opportunities. Of the 15 sub-items, the sub-item Foreign policy system, free and active from political aspects, is the most influential with a weight of 0.08. Meanwhile, for the obstacle/threat factor, there were 20 sub-items. The results of the SWOT and AHP analysis show that the steps for optimizing defense resources to support the main task of the TNI in resolving territorial violations are a diversification strategy, namely empowering all national resource forces for defense in resolving threats/obstacles. [ABSTRACT FROM AUTHOR]

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This paper proposes a fixed-time prescribed performance control technique to address the challenge of precise trajectory tracking control for unmanned surface vessels (USVs) in the presence of external time-varying disturbances and input saturation. To begin with, a fixed-time disturbance observer is created to handle the time-varying external interference. The observer can accurately estimate and compensate for the disturbance in a fixed time, which effectively improves the robustness of the system. Furthermore, to guarantee both the transient and steady-state response of the system, we employed a specific control technology that ensures the trajectory tracking error remains within a preset bounded range. Then, combined with the fixed-time disturbance observer, the command filter, the prescribed performance control technology, and the fixed-time stability theory, a fixed-time trajectory tracking control law is designed to make the trajectory tracking error of the system converge in a fixed time. Finally, an experiment was designed to validate the suggested control scheme. The results show that under the same conditions, compared with the nonlinear controller and the finite-time controller, the absolute error tracking index of this paper is the lowest, which means that the presented control scheme has higher accuracy. [ABSTRACT FROM AUTHOR]

Excellent self-righting performance is important to guarantee the normal navigation of Unmanned Surface Vehicles (USVs) after overturning, and the restoring time is an important index in design requirements. Traditionally, the static stability method and experiments on full-scale vehicles were used to analyze the large-angle stability of the USV. However, when it comes to the analysis of self-righting performance, the traditional static stability method will cause improper integration, and experiments are not convenient. To solve these problems, an improved static stability method was proposed, and a whole self-righting process simulation of a physical model was finished. The numerical simulation method was used to predict the self-righting process of a USV under four working conditions. Firstly, a midpoint average method based on the static stability theory was adopted to compute the static restoring time, and the results were compared with the results of the references, which verifies the effectiveness of the midpoint average method. Also, the midpoint average method is convenient because it only needs the restoring arm curve, the width and the gravity center height. Then, a numerical simulation of a physical model in static water was finished, and an experiment for a physical model in a towing tank was conducted. Comparing the restoring time of the midpoint average method, the numerical simulation and the experiment, the results show that the numerical simulation has high accuracy. Moreover, the numerical simulation was used to predict the self-righting process and analyze the self-righting performance of a USV under four working conditions. [ABSTRACT FROM AUTHOR]

This work mainly studies the issue of predefined time and accuracy adaptive fault-tolerant control for strict-feedback nonlinear systems with multiple faults. The faults in the controlled system include actuator faults and external system faults. The unknown functions for nonlinear systems are approximated by fuzzy logic systems (FLSs). And then, according to the backstepping technique and the predefined time stability theory, an adaptive fuzzy control algorithm is presented, which can make sure that all closed-loop system signals remain predefined time bound and the tracking error converges to a predefined accuracy within the predefined time. Ultimately, the effectiveness of the presented control algorithm is proved through two simulation examples. [ABSTRACT FROM AUTHOR]

The radiation generated around a uniform high-voltage transmission line can be regarded as an external problem in the two dimensional unbounded region. The natural boundary element (NBE) method is one of the most effective approaches to solve the external problem. But the NBE model for the external problem includes a lot of unknowns. Hence, in this paper, we employ a proper orthogonal decomposition to reduce the dimension of finite element space in the NBE model for the external problem. We first develop an NBE reduced-dimension recurrence (NBERDR) model for the external problem. We then use the Hahn-Banach theorem in functional analysis to link the NBE method with the NBERDR method to establish the theory of the existence and stability as well as convergence for the NBERDR solutions. We finally employ some numerical experiments to verify the correctness of theoretical results. As far as we know, there have been not similar reports. Therefore, this paper can facilitate the theoretical study and applications of NBERDR method for the uniform high-voltage transmission line. [ABSTRACT FROM AUTHOR]

The tapping-mode atomic force microscope (TM-AFM) is widely used today; however, improper matching between the operating medium and the sampling time may lead to inaccurate measurement results. The relationship between the damping coefficient and the steady state of the TM-AFM microcantilever is investigated in this paper using multiple stability theory. Firstly, the effects of changes in dimensionless linear damping coefficients and dimensionless piezoelectric film damping coefficients on the motion stability of the system are examined using bifurcation diagrams, phase trajectories, and domains of attraction. Subsequently, the degrees of effect of the two damping coefficients on the stability of the system are compared. Finally, the bi-parametric bifurcation characteristics of the system under a specific number of iterative cycles are investigated using the bi-parametric bifurcation diagram in conjunction with the actual working conditions, and the boundary conditions for the transition of the system's motion from an unstable state to a stable state are obtained. The results of the study show that to ensure the accuracy and reliability of the individual measurement data in 500 iteration cycles, the dimensionless linear damping coefficient must be greater than 0.01014. Our results will provide valuable references for TM-AFM measurement media selection, improving TM-AFM imaging quality, measurement accuracy and maneuverability, and TM-AFM troubleshooting. [ABSTRACT FROM AUTHOR]

In this paper, the clustering component synchronization of nonlinearly coupled complex dynamical networks with nonidentical nodes was investigated. By applying feedback injections to those nodes who have connections with other clusters, some criteria for achieving clustering component synchronization were obtained. A numerical simulation was also included to verify the correctness of the results obtained. [ABSTRACT FROM AUTHOR]

This study employed an event-triggered control (ETC) strategy to investigate the problems of fixed-time stabilization (FTS) and preassigned-time stabilization (PTS) for state-dependent switching neural networks (SDSNNs) that involved mixed time delays. To enhance the network's generalization capability and accelerate convergence stabilization, a more intricate weight-switching mechanism was introduced, then to mitigate transmission energy consumption, this paper proposed a tailored event-triggering rule that triggered the ETC solely at predetermined time points. This rule ensured the stability of the system while effectively reducing energy consumption. Using the Lyapunov stability theory and various inequality techniques, this paper presented new results for FTS and PTS of SDSNNs. The validity of these findings was supported by conducting data simulations in two illustrative examples. [ABSTRACT FROM AUTHOR]

In this article, with the help of Laplace transform, the existence of solution was established in a finite dimensional setting for nonlinear ψ-Hilfer fractional stochastic equation with both retarded and advanced arguments driven by multiplicative and fractional noises, with Hurst index H∈(1/2,1). At first, we obtained the existence and uniqueness results by using the Banach fixed point theorem (FPT). Second, the existence result was also obtained by applying Schaefer's fixed point theorem with less conservative conditions. Furthermore, we investigated the Hyers Ulam Rasisas stability for the aforementioned system. At the end, an example was illustrated to validate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In a meta-analysis of longitudinal analyses of the theory of planned behaviour, we tested a series of extended or auxiliary theory-consistent hypotheses: construct stability, theory predictions within and between occasions, consistency over time or stationarity in theory effects and reciprocal effects among constructs. We also tested the effects of moderators on theory effects: measurement lag, health behaviour type (protection, risk) and specific health behaviours (alcohol, dietary and physical activity). A systematic search identified 87 studies eligible for inclusion. Meta-analytic structural equation models supported construct stability and theory effects within and between occasions. Only the perceived behavioural control–intention effect exhibited stationarity. We found little evidence of reciprocal effects, and theory effects were small after accounting for reciprocal effects. We observed theory-consistent effects for the behaviour-type moderators, but no variation in model effects for the measurement lag moderators. Findings advance knowledge of the correlates of intentional behaviour and associated processes over time. [ABSTRACT FROM AUTHOR]

In light of the problem of trajectory tracking control in vehicle servo systems with system model uncertainty and external time-varying disturbance, an effective trajectory tracking control method that can handle system model uncertainty and external time-varying disturbances is proposed. To achieve this goal, a novel composite robust integral of the sign of the error (RISE) control method is introduced that combines a multi-layer neural network and an extended state observer. Specifically, multi-layer neural networks are utilized to approximate the uncertainty of the system model, while an extended state observer is employed to estimate the fitting near-error and the external time-varying interference, which are used as feedforward compensation. Finally, the RISE controller is implemented as a robust feedback controller. By applying Lyapunov theory for stability analysis and conducting experiments, the results demonstrate that the proposed approach exhibits excellent performance and robustness in addressing the uncertainties and disturbances involved in trajectory tracking control for vehicle servo systems. • Develop a composite controller for vehicle-mounted servo system with uncertainties and time-varying disturbances. • Multilayer neural networks and extended state observers is integrated into the feedforward compensation term of RISE control. • Comparative experimental results verify the validity and priority of the proposed control method. [ABSTRACT FROM AUTHOR]