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In this paper, the μ-state estimation issue for Markovian switching complex-valued neural networks with mixed delays has been addressed. To conserve communication resources, an effective event-triggered mechanism is proposed, which relays on a Markovian switching positive threshold. By resorting to Lyapunov stability theory, stochastic analysis method and matrix inequalities technique, some sufficient criteria are established to guarantee the estimation error system is stochastic μ-stable in the mean sense. Moreover, the expected estimator gain matrices can be accurately achieved by solving some obtained matrix inequalities. Besides, it is should be pointed that the μ-stability involves exponential, power, and logarithmic stability, which expands a mass of existed relevant results. In the end, for power stability, one numerical example is provided to substantiate the effectiveness and credibility of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This article is concerned with the practical stability performance of nonlinear impulsive stochastic functional differential systems driven by G-Brownian motion (G-ISFDSs). Comparing with traditional Lyapunov stability theory, practical stability can portray qualitative behaviour and quantitative properties of suggested systems. By employing G-Itô formula, Lyapunov–Razumikhin approach and stochastic analysis theory, some novel conditions for pth moment practical exponential stability and quasi-sure global practical uniform exponential stability of G-ISFDSs are established. The obtained results show that impulses may influence dynamic behaviour of the addressed system. Two numerical examples are given to verify the validity of our developed results. [ABSTRACT FROM AUTHOR]

In this article, by considering the existence of unavailable state, external disturbance, and denial of service (DoS) attacks, an anti‐disturbance trajectory tracking controller is proposed for the air‐ground system composed of unmanned autonomous helicopter (UAH) and unmanned ground vehicle (UGV). Initially, by combining the advantages of conventional event‐triggered scheme (ETS) and memory ETS, a switching‐like event‐triggered mechanism is put forward, which can induce less data transmissions without reducing control performance, and effectively restrain the DoS attacks. Second, by dividing the DoS attacks into active intervals and sleep ones, the concept of acknowledgement character technology (ACK) is presented to define the suitable types of time intervals. Third, a switching‐like dynamic ETS is introduced for the sleep intervals of DoS attacks while the ETS with fixed triggered‐threshold is exploited for the active intervals. Fourth, based on the occurrence of DoS attacks, a switching‐like observer and a normal one are respectively proposed to estimate the UGV state, the UAH state, the reference input of the UGV, and the disturbance of the UAH, which are further utilized to design the tracking controller. Fifth, an augmented closed‐loop system consisting of observation errors and tracking error is established and its stability is analyzed by using Lyapunov stability theory. Then, a sufficient condition on co‐designing the parameters of switching‐like ETS, observers, and tracking controller is presented in terms of linear matrix inequalities (LMI). Finally, the validity and superiority of the proposed control scheme are verified by resorting to simulations and comparisons. [ABSTRACT FROM AUTHOR]

This paper focused on fault estimation in Lipschitz nonlinear systems by providing an improved intermediate estimator (IIE). The core feature of an intermediate estimator is to simultaneously estimate the fault and states of the system without considering the matching condition. Since fault estimation is the first step of the process to compensate for its effect, the system performance can be further improved by making more accurate fault estimation. The structure of the nominal intermediate estimator (NIE) was modified by being inspired by the proportional‐integral (PI) controller to improve the performance characteristics of the estimator, such as convergence rate, overshoot, and steady‐state error. The estimation equation was assumed as such in the proposed estimator structure that the estimated fault would have a PI structure of the output estimation error. This has increased the number of design parameters, improving the estimator performance in transient and steady‐state. The NIE can be indeed known as a particular case of the IIE since the proposed estimator benefits from all the advantages of an NIE while improving the estimation performance. The states of the error system were proven to be uniformly ultimately bounded according to Lyapunov stability theory and using the LMI method, as well as the appropriate selection of parameters. The analysis of the theory, simulation, and comparing the results of the proposed method with the NIE method reveal the capabilities and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

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]

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]

Summary: This work primarily concentrates on the design of fault‐tolerant anti‐disturbance control for synchronization of multiple memristor‐based neural networks subject to time delay, matched and mismatched disturbances. Moreover, in the addressed network model, we consider parameter uncertainties and actuator faults. Firstly in order to estimate the matched disturbances generated by the exogenous system, a disturbance observer is devised. Whereas, the mismatched part is tackled by employing the mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passivity performance indexes. Subsequently, a unified controller is designed by incorporating error feedback control and the disturbance estimate. Further, with the assistance of Lyapunov stability theory and linear matrix inequality technique, an adequate criteria is procured to ascertain the required synchronization criteria for the assayed network model with the mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passivity performance indexes. Following this, by basing on the established conditions, the explicit form of the controller and observer gain matrices is obtained. In the end, a numerical example with simulation results is shown to confirm the potential and usefulness of the conclusions acquired from the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, a distributed diffusion Kalman filtering algorithm with event‐triggered communication (DDKF‐E) is studied for discrete‐time nonlinear systems. According to the event‐triggered communication protocol, the data between sensors and estimators are transmitted only when the predefined conditions are satisfied. Considering the characteristic of event‐triggered method and truncated error by linearization, an upper bound of the estimation error covariance matrix is obtained by using the variance‐constrained method. The Kalman gain is designed to minimize the upper bound and then two Riccati equations are obtained. Furthermore, the stochastic stability theory is used to prove the stability of DDKF‐E, and it is derived that the estimation error of DDKF‐E is exponentially bounded in mean square. Finally, numerical simulations validate the effectiveness of the DDKF‐E algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the observer‐based security control problem for interval type‐2 nonlinear networked control systems with deception attacks and replay attacks. Firstly, to alleviate the communication burden of the network, a novel adaptive event‐triggered communication (ETC) mechanism is proposed. Compared with existing observer‐based adaptive ETC security control techniques, the threshold of the proposed adaptive ETC scheme can be adjusted dynamically depending on the value of adjustable parameters and estimation error. In particular, the adjustable parameters can change the sensitivity of the threshold flexibly. Then, taking the influence of the adaptive ETC mechanism and cyber attacks into consideration, an observer‐based security controller is developed under the co‐designed method. Furthermore, by utilizing the Lyapunov stability theory, sufficient conditions for asymptotically mean‐square stable of the closed‐loop system are obtained. Ultimately, the feasibility of the designed control approach can be proved via a simulation example. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an event‐triggered control strategy for stochastic interconnected nonlinear systems with unknown control directions. Firstly, a new lemma is proposed for stochastic nonlinear systems with multiple time‐varying unknown control directions, which guarantees the boundedness of Nussbaum function parameter variables. Different from the existing results, each subsystem is allowed to have multiple time‐varying unknown control directions. Then, by using the backstepping method, a novel controller is proposed based on the relative threshold event‐triggered strategy. The controller not only reduces the communication burden but also eliminates the interference of unknown control directions. Based on Lyapunov stability theory, it is proved that the controller can make all signals in the closed‐loop system be bounded in probability and the system state variables converge to zero in probability. Finally, two simulation examples are presented to certify the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this article, we investigate the mean‐square consensus tracking problem of nonlinear MASs subjected to external disturbances under stochastic switching topologies. An aperiodically intermittent control strategy is proposed to guarantee consensus tracking in the mean‐square sense, which depends only on the local state information of the neighbors and the leader. The stochastic switching signal of the interaction topologies is modeled as a continuous‐time Markov process, and the aperiodically intermittent control method is driven by a discrete‐time series of stochastic samples, that are independent of each other. Moreover, several sufficient conditions are established to ensure the feasibility of the control strategy. The proofs are given by employing matrix inequality theory and Lyapunov stability theory. Finally, numerical simulations are provided to verify the feasibility of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a physical parameter m, which characterizes the constitutive relation between density and pressure. Based on these models, we employ the Bayesian inversion framework to infer parametric and nonparametric unknowns that affect tumor growth from noisy observations of tumor cell density. We establish the well-posedness and the stability theories for the Bayesian inversion problem and further prove the convergence of the posterior distribution in the so-called incompressible limit, m → ∞. Since the posterior distribution across the index regime m ∈ [2, ∞) can thus be treated in a unified manner, such theoretical results also guide the design of the numerical inference for the unknown. We propose a generic computational framework for such inverse problems, which consists of a typical sampling algorithm and an asymptotic preserving solver for the forward problem. With extensive numerical tests, we demonstrate that the proposed method achieves satisfactory accuracy in the Bayesian inference of the tumor growth models, which is uniform with respect to the constitutive relation. [ABSTRACT FROM AUTHOR]

The present study introduces a new adaptive control framework that aims to attain exponential stability in complex‐valued neural network systems utilizing memristors while accounting for time‐varying delays. The control issues in systems of this nature are mostly attributed to the presence of memristors and time‐varying latency. To overcome these challenges and achieve stabilization outcomes, a methodology is employed that integrates adaptive control approaches inside a matrix‐based framework. This study employs Lyapunov's stability theory to establish exponential stabilization conditions and conduct convergence analysis. The efficacy of the suggested control algorithm in achieving exponential stabilization and robustness under varied delays is demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

The results of studies on a trajectory-tracking problem affected by false data injection attacks (FDIAs) and internal and external uncertainties are presented in this paper. In view of the FDIAs experienced by the system, we compensate for the serious navigation deviation caused by malicious attacks by designing an online approximator. Next, we study the internal and external uncertainties introduced by environmental factors, system parameter fluctuations, or sensor errors, and we design adaptive laws for these uncertainties to approximate their upper bounds. To further enhance the response velocity and stability of the system, we introduce finite-time technology to ensure that the unmanned underactuated surface vessels (USVs) reach the predetermined trajectory-tracking target within finite time. To further reduce the update frequency of the controller, we introduced event-triggered control (ETC) technology. This saves the system's communication resources and optimizes the system. Through Lyapunov stability theory, a strict and complete stability analysis is provided for the control scheme. Finally, the effectiveness of the control scheme is verified using two sets of simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the H ∞ consensus problem of discrete-time Markov jump fractional-order multiagent systems (DTMJFOMASs) under denial-of-service (DoS) attacks. By applying the short-memory principle, we can obtain discrete-time Markov jump multiagent systems with partially unknown probabilities. A novel quantized event-triggering mechanism (QETM), based on a mode-dependent logarithmic quantizer, is proposed to enhance transmission efficiency among multiagents. A distributed controller with quantized output is developed. Sufficient conditions are provided to ensure the system achieves H ∞ consensus through Lyapunov stability theory. Finally, two examples are given to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

The free-stream turbulence induced transition occurring under typical low-pressure turbine flow conditions is investigated by comparing linear stability theory with wind tunnel measurements acquired over a flat plate subjected to high turbulence intensity. The analysis was carried out, accounting for three different Reynolds numbers and four different adverse pressure gradients. First, a non-similarity-based boundary layer (BL) solver was used to compute base flows and validated against pressure taps and particle image velocimetry (PIV) measurements. Successively, the optimal disturbances and their spatial transient growth were calculated by coupling classical linear stability theory and a direct-adjoint optimization procedure on all flow conditions considered. Linear stability results were compared with experimental particle image velocimetry measurements on both wall-normal and wall-parallel planes. Finally, the sensitivity of the disturbance spatial transient growth to the spanwise wavenumber of perturbations, the receptivity position, and the location where disturbance energy is maximized were investigated via the built numerical model. Overall, the optimal perturbations computed by linear stability theory show good agreement with the streaky structures surveyed in experiments. Interestingly, the energy growth of disturbances was found to be maximum for all the flow conditions examined, when perturbations entered the boundary layer close to the position where minimum pressure occurs. [ABSTRACT FROM AUTHOR]

This paper concerns a class of coupled competitive neural networks, subject to disturbance and discontinuous activation functions. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results. [ABSTRACT FROM AUTHOR]

Path dependence has become a multi-disciplinary concept, employed across various literatures to explain why the past matters for decision-making. Debate within 'new institutionalist' scholarship has provided a detailed critique of the term over several decades. Some scholars argue that it is hampered by poor conceptual clarity and highlight its limitations in explaining institutional reform. Yet, this paper demonstrates how neglecting antecedent conditions and associated decision pathways is particularly inappropriate for politico-spatial issues like disaster risk and natural resource governance. Doing so risks omitting key material and perceptual contingencies influencing contemporary institutions. Examining southeast Queensland's flooding disaster of 2011, the paper proposes that path contingency provides a useful theoretical bridge between institutionalist theories of stability and reform, and the geographic contexts within which disaster risk governance proceeds. The analysis then addresses the potential generalisability of path contingency beyond its application to disaster management, for consideration across a broader range of institutionalist research. [ABSTRACT FROM AUTHOR]

The event-triggered formation control of first-order continuous multi-agent systems is studied based on complex Laplacian in this paper. Periodic event-triggered control is designed in which continuous communication between agents is not required. For each agent, two different triggering conditions are discussed. The first one relies on the inter-neighboring communication at each verification time, while the second one only need the broadcast states of neighbors at their triggering instants. According to the Lyapunov stability theory and algebraic graph theory, consensus conditions on the verification period and parameters in the triggering conditions are also provided. It is demonstrated that the maximum verification period under two triggering conditions are two times larger than the existing results. And a certain amount of communication between neighbors can be further reduced in the second one. Finally, the simulation examples prove the validity of the results proposed. [ABSTRACT FROM AUTHOR]