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Summary This article addresses the position control issue of multi‐quadrotor unmanned aerial vehicle (QUAV) formation. Concerning the translational dynamic of a multi‐QUAV system, on the one hand, it is an under‐actuation dynamic; on the other hand, it does not satisfy the matching condition. These features will cause inevitable thorny in the formation position control design. Furthermore, because of the state coupling problem, the formation control of multi‐QUAV system is more challenging and knotty than the control of single QUAV system. To achieve this control, both backstepping technique and neural network (NN) approximation strategy are combined by introducing an intermediary control, where NN is employed to compensate the system uncertainty. However, since the traditional adaptive NN control methods need to train a large number of adaptive parameters for the high approximation accuracy, it will cause the heavy computing burden if traditional adaptive method is used for the QUAV formation control. The proposed adaptive NN strategy in this paper only requires training a scalar adaptive parameter, which is generated from the norm of NN weight vector or matrix, thereby significantly reducing computational burden. Finally, according to Lyapunov stability proof and computer simulation, it is demonstrated that the control tasks can be successfully accomplished. [ABSTRACT FROM AUTHOR]

In this paper, the impact of the strong Allee effect and ratio-dependent Holling–Tanner functional response on the dynamical behaviors of a predator–prey system is investigated. First, the positivity and boundedness of solutions of the system are proved. Then, stability and bifurcation analysis on equilibria is provided, with explicit conditions obtained for Hopf bifurcation. Moreover, global dynamics of the system is discussed. In particular, the degenerate singular point at the origin is proved to be globally asymptotically stable under various conditions. Further, a detailed bifurcation analysis is presented to show that the system undergoes a codimension- 1 Hopf bifurcation and a codimension- 2 cusp Bogdanov–Takens bifurcation. Simulations are given to illustrate the theoretical predictions. The results obtained in this paper indicate that the strong Allee effect and proportional dependence coefficient have significant impact on the fundamental change of predator–prey dynamics and the species persistence. [ABSTRACT FROM AUTHOR]

• A preassigned finite-time attitude synchronization controller is proposed for multiple rigid spacecraft systems by using two designed barrier Lyapunov functions. • The convergence time of the designed controller can be preassigned according to different space task requirements and it is independent of the initial condition of the system states and control parameters. • The steady-state error of the closed-loop system can be limited to a certain range by the appropriate choice of the controller parameters. This paper investigates the preassigned finite-time attitude synchronization control for the spacecraft formation with a dynamic virtual leader under an undirected connected graph. Each follower is described by a rigid spacecraft model subjects to parameter uncertainty, actuator saturation, and the disturbance. First, two fixed-time sliding mode estimators are introduced to estimate the reference attitude variable and the reference angular velocity, respectively. Then, by selecting the attitude errors as the system states, an attitude tracking error system for the spacecraft formation is established. An extended state observer is applied for computing the total disturbance in the attitude tracking error system. Based on the estimations of the extended state observer and two sliding mode estimators, a novel distributed controller is proposed to force the states of the established attitude tracking error system converge to a small region in preassigned finite time by using two modified time-varying barrier Lyapunov functions. The practical preassigned finite-time stability of the resulting closed-loop system is proven by Lyapunov stability theory. Finally, some simulations are provided to illustrate the effectiveness and advantages of the developed preassigned finite-time attitude synchronization control scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the mean-square bounded consensus issue in a two-layer multi-agent network under deception attacks. The two-layer network is composed of the leader and follower layers with a switching topology. Employing an impulsive control method, the mean-square bounded consensus for the leader layer and the node-to-node mean-square bounded consensus of the two-layer network are analyzed. Based on the knowledge of graph theory, Lyapunov stability theory, and linear matrix inequalities, sufficient conditions for the mean-square bounded consensus of multi-agent systems in the two-layer network are derived. Finally, the practicability and efficacy of the theoretical outcomes are corroborated via the provided numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, we deal with finite‐time optimal control of the Euler–Lagrange (E–L) multi‐body mechanism under: uncertain its kinematics and dynamics, displacement blocking of the damaged joint caused by the actuator failure, undesirable forces/torques exerted on the end‐effector and unknown friction forces originating from joints directly driven by the actuators, as well as completely unstructured forces arising from the kinematic singularities appearing on the mechanism trajectory. Based on the suitably defined task space non‐singular terminal sliding manifold and the Lyapunov stability theory, we propose a class of new fault tolerant estimated generalized Jacobian controllers, which seem to be effective in reducing (minimizing) the joint velocity jumps as well as in counteracting the unstructured forces/torques. On account of the fact, that the multi‐body mechanism is a redundant one, a useful criterion function (energy consumption +$$ + $$ manipulability measure) has been utilized in our controller to temporarily optimally track a desired trajectory. The proposed controllers' performance is demonstrated by computer simulations conducted on a redundant manipulator in conditions of unexpected actuator failure and the corresponding joint lock. Additionally, numerical comparisons are also provided with other representative controllers, found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the control problem of auto-berthing marine surface vessels (MSVs) within a predefined, finite time in the restricted waters of a port, in the face of internal and external uncertain dynamics and actuator faults. We first use radial basis function neural networks to reconstruct the internal uncertainties of the system; then, using the minimum learning parameter method, we transform the weights of the neural networks, the external disturbances of the system, and the bias fault factors into an indirect single-parameter neural learning mode. We also apply a robust depth information adaptation technique to estimate the upper bound on the composite disturbances online. Dynamic surface control technology alleviates the burden of virtual control derivative calculations. Finite-time convergence of the system is guaranteed by a predetermined finite-time function based on a time-based generator (TBG). Based on these methods, we design a finite-time fault-tolerant auto-berthing control scheme based on TBG. The stability of the system is analysed based on Lyapunov stability theory. Finally, we verify the effectiveness of the proposed control scheme through simulation. [ABSTRACT FROM AUTHOR]

Due to the Jacobian matrix rank reduction near singularities, applying numerical methods to study PMs' motion stability at singularities is quite difficult. As a result, there is a scarcity of literature on the investigation of PMs' dynamic behaviors near singularities and the influence of kinematic parameters on the motion stability of PMs. To address the research gap related to the above issues, based on the Gerschgorin perturbation method, Hurwitz exact approach, and the Lyapunov dynamic stability theory, the influence of kinematic parameters and external loads on a PM's motion stability at singularities is studied for the first time. The theoretical analysis results reported in this paper reveal many previously undiscovered features beyond those derived from previous numerical methods, and indicate the limitations of some widely accepted statements. For example, increasing the angular speed of the movable platform can expand the range of the external loads that meet the motion stability at singular configurations. The prevailing notion in prior research that PMs are unable to support external loads in the direction of the gained DoF at singular configurations is only partially accurate. This pioneering research establishes a theoretical foundation for exploring a new real-time approach to avoid dynamic singularities by fully exploiting the influence mechanisms of kinematic parameters on PMs' dynamic stability at singularities. [ABSTRACT FROM AUTHOR]

Considering the situation of limited resources in practical applications, it is significant to design control algorithms with high resource utilization rates for a class of nonlinear systems subject to mismatched disturbances. In contrast to common recursive methods, this paper proposes a novel event-triggered tracking control approach by co-designing the triggering event and the controller within a non-recursive design framework that combines disturbance estimation techniques and feedforward compensation strategies. Through rigorous Lyapunov stability analysis, the global boundedness of each state in the closed-loop system is demonstrated, and the absence of the Zeno phenomenon is further verified. A representative numerical simulation and a practical implementation for speed regulation of permanent magnet synchronous motor (PMSM) system confirm the effectiveness and simplicity of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Feature selection (FS) stability is an important topic of recent interest. Finding stable features is important for creating reliable, non-overfitted feature sets, which in turn can be used to generate machine learning models with better accuracy and explanations and are less prone to adversarial attacks. There are currently several definitions of FS stability that are widely used. In this paper, we demonstrate that existing stability metrics fail to quantify certain key elements of many datasets such as resilience to data drift or non-uniformly distributed missing values. To address this shortcoming, we propose a new definition for FS stability inspired by Lyapunov stability in dynamic systems. We show the proposed definition is statistically different from the classical record-stability on ( n = 90 ) datasets. We present the advantages and disadvantages of using Lyapunov and other stability definitions and demonstrate three scenarios in which each one of the three proposed stability metrics is best suited. [ABSTRACT FROM AUTHOR]

This paper presents a new control approach of trajectory tracking for quadrotor unmanned aerial vehicle (UAV) systems under external disturbances and parameter uncertainties. The integral fast terminal sliding mode control (IFTSMC) approach applying state-dependent Riccati equation (SDRE) observer is presented for this purpose. As a result, the nonlinear SDRE observer is designed to estimate the non-measurable states. Afterward, employing the estimated states of the SDRE observer, the proposed IFTSMC controller is designed for trajectory tracking of the perturbed quadrotor UAV. Besides, applying Lyapunov's stability theory, the finite-time convergence and robustness of the closed-loop UAV system are assured. Based on the numerical simulation results, the proposed controller successfully tracked various reference trajectories of quadrotor UAVs despite external disturbances and parametric uncertainty. [ABSTRACT FROM AUTHOR]

Summary: In the presented study, the solution of the fuzzy nonlinear optimization problems (FNLOPs) is calculated using a recurrent neural network (RNN) model. Since there is a few research for solving FNLOP by RNN's, we give a new approach to solve the problem. By reducing the original program to an interval problem and then weighting problem, the Karush–Kuhn–Tucker (KKT) conditions are given. Moreover, we use the KKT conditions into a RNN as an important tool to solve the problem. Besides, the global convergence properties and the Lyapunov stability of the dynamic model are studied in this study. In the final step, some illustrative examples are considered to establish the obtained results. Reported results are compared with some others network models. [ABSTRACT FROM AUTHOR]

Summary: The cluster synchronization problem of stochastic two‐layer networks with infinite distributed delays is concerned. Firstly, we study the cluster synchronization of the first layer (leader‐layer) network with the average state of each cluster of sets as synchronization target. Secondly, we design a delayed pinning impulsive controller to synchronize the second layer (follower‐layer) network to the first layer network in a mean square cluster sense. Based on stochastic impulsive analysis and Lyapunov stability theory, some sufficient conditions for cluster synchronization are obtained. Finally, the effectiveness of the theoretical results is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: This article studies robust adaptive control for a class of autonomous vehicle platoons. In particular, two innovative adaptive control laws are proposed to address both position and velocity tracking for a vehicle platoon. In addition, it is shown that robust asymptotic string stability can be delivered by the underlying adaptive control laws for the vehicle platoon, in the sense that these adaptive control laws are capable of mitigating parameter uncertainties involved in the nonlinear vehicular dynamics and achieving truly cooperative adaptive cruise control while ensuring the required safety spacing between each neighboring vehicle pair asymptotically. It is also shown that the control performance of the vehicle platoon can be further improved if the operating equilibrium points of all vehicles can be adaptively estimated, leading to two linear time‐invariant control laws for individual vehicles under both position and velocity controls and for the vehicle platoon. Simulation studies illustrate the effectiveness of the proposed control method, validating the results obtained for the class of vehicle platoons. [ABSTRACT FROM AUTHOR]

Summary: The issues of cluster synchronization and state estimation for a class of nonlinear complex dynamical networks are concurrently focused in this study. In precise, led by the design of complex dynamical networks, a proportional integral‐based observer is implemented for achieving robustness, by the virtue of which the states of examined networks are estimated. Thereupon, a proportional integral observer‐based hybrid triggered control scheme is proposed, wherein, the switch‐over between time‐ and event‐ triggered scheme is governed through a Bernoulli distributed random variable. Further, with the application of mixed H∞$$ {H}_{\infty } $$ and passivity performance technique, the external disturbances for the addressed complex dynamical networks are reduced. Based on the Lyapunov stability theory, the requisite sufficient conditions in respect of linear matrix inequalities are provided which ensures the discussed complex dynamical network's synchronization phenomenon. In a further, the presented criteria are exploited for the attainment of required controller, proportional and integral gain matrices. In conclusion, the applicability of proposed results and efficacy of the undertaken strategy are evidently proven with the illustration of two numerical examples with Chua's circuit and Goodwin oscillator model. [ABSTRACT FROM AUTHOR]

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 work developed an adaptive fuzzy tracking control strategy for pure-feedback nonlinear multi-agent systems via backstepping. The relevant unknown functions are addressed by fuzzy logic systems (FLSs), which take into account entirely unknown nonlinearities. The non-affine pure-feedback form is dealt with a Butterworth low-pass filter (BLF), and the converted systems can be used to construct a controller. The implementation of the first-order sliding-mode differentiator overcomes the difficulty of calculation explosion. The backstepping method is applied to design the virtual controller step by step, and the actual controller is designed successfully. Furthermore, through Lyapunov stability theory, the stability of systems is ensured, and that the tracking error is kept to a minimum. Finally, the simulation result shows the validity of the designed control strategy. [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]

Using Hybrid optimization algorithms for nonlinear systems analysis is a novel approach. It is a powerful technique that uses the exploitation ability of one algorithm and the exploration ability of another algorithm, to find the best solution. Literature survey reveals that hybrid algorithms not only show quality response but also give faster convergence of error for nonlinear systems. In this paper, hybrid optimization techniques based proportional integral derivative (PID) controller is used for benchmark problems: Continuous stirred tank reactor (CSTR), Inverted pendulum and blood glucose system. Two recent hybrid algorithms: Particle swarm optimization‐Gravitational search algorithm (PSO‐GSA) and Particle swarm optimization‐Grey wolf algorithm (PSO‐GWO) are implemented to control the temperature and concentration of CSTR, pendulum angle of inverted pendulum, glucose concentration and insulin level of blood glucose system. In PID and PSOGWO algorithms, the exploration abilities of GSA and GWO combined with the exploitation ability of PSO have been used. The performance of these algorithms is then compared with individual PSO, GSA, and GWO algorithms proving their superiority. Stability is ensured using the Lyapunov approach while the robustness of the systems is checked using the parameter perturbation technique. Simulation results show substantial improvement in the performance of these systems by using these meta‐heuristic hybrid optimization techniques. A comparative analysis of these algorithms has also been done. [ABSTRACT FROM AUTHOR]

The stability of each train, high control accuracy, and minimum safe separation distance are important indexes to measure the performance of the cooperative control system of multiple trains. In this article, aiming at the problem of low accuracy of multiple trains cooperative control with nonlinear running resistance and external disturbance, the distributed cooperative robust adaptive control scheme for multiple trains with RBFNN position output constraints based on train running curve tracking is proposed. Multiple different control techniques are offered for different trains, and that they are based on local knowledge of position, speed, and acceleration. The leading train's speed and position precisely match the planned operation curve, while the following train keeps the tracking interval at the minimum safe distance between two trains. In order to reduce the influence of the uncertainty of basic resistance parameters and external interference on the cooperative control of multiple trains, the parameter uncertainties are compensated by adding a robust adaptive law to the multiple trains control based on position output constraints. The lumped exogenous disturbances (additional resistance, external interference, measurement noise, etc.) are estimated using an RBFNN approximator for the unknown term of the cooperative system. The stability of the cooperative operation of multiple trains is confirmed using the Lyapunov stability theorem. The performance of the proposed scheme was evaluated by the cooperative control system of multiple trains in predecessor following (PF) and bidirectional control (BC) modes. [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, sliding mode control (SMC) strategy is reported for frequency stabilization in microgrid (MG) using event-triggering mechanism (ETM) subject to load disturbances and uncertainties. The MG systems are characterized as systems affected by large computation and data transmission between different components in a control loop. This acts as a major constraint in a resource-limited network control systems (NCSs). Therefore, an ET-SMC is proposed in this article which not only ensures system stability under uncertainties and disturbance but also effective utilization of communication channel resources in terms of lesser computation and data transmission. The ET approach utilizes a requirement-based control strategy, wherein the control signal is updated and activated solely upon the violation of a predefined triggering condition. It is observed that an ETC approach saves approximately around 80% resources compared to time-triggered approach while maintaining system stability. The proposed design undergoes validation against system parameter variation and energy system nonlinearities, demonstrating that the frequency response remains within acceptable limits. The proposed design is also seen to provide better frequency stabilization with larger average inter-event time and lesser triggering number. Theoretical proof of stability is established through the application of a Lyapunov function, while its verification is conducted via simulation in MATLAB. [ABSTRACT FROM AUTHOR]

This paper analyzes the problem of simultaneous fault detection and control of the six-rotor unmanned aerial vehicle control system, considering external disturbance, measurement disturbance, and actuator fault. The integral event trigger mechanism is introduced in the control side and sensor side of the system. Based on Lyapunov stability and H∞ control theory, the sufficient conditions to make the fault system asymptotically stable and have certain performance indexes are given by means of linear matrix inequalities; at the same time, the design criteria of event trigger parameters are also given. The linear matrix inequality is decoupled, and the calculation method of gain matrix of simultaneous fault detection and control module is given. The effectiveness of the proposed method is verified by simulation experiments. [ABSTRACT FROM AUTHOR]

Seasonality is repetitive in the ecological, biological and human systems. Seasonal factors affect both pathogen survival in the environment and host behavior. In this study, we considered a five-dimensional system of ordinary differential equations modeling an epidemic in a seasonal environment with a general incidence rate. We started by studying the autonomous system by investigating the global stability of steady states. Later, we proved the existence, uniqueness, positivity and boundedness of a periodic orbit in a non-autonomous system. We demonstrate that the global dynamics are determined using the basic reproduction number ℛ0 which is defined by the spectral radius of a linear integral operator. We showed that if ℛ0 < 1, then the disease-free periodic solution is globally asymptotically stable and if ℛ0 > 1, then the trajectories converge to a limit cycle reflecting the persistence of the disease. Finally, we present a numerical investigation that support our results. [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 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]

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]

This paper investigates the fixed-time adaptive event-triggered control problem for a class of nonlinear multiagent systems with full-state constraints. The problem of full-state constraints is solved for multiagent systems by utilising a one-to-one nonlinear mapping. The design conditions of the controllers are more easily satisfied than the existing barrier Lyapunov functions strategy. A fixed-time adaptive control scheme is proposed for unconstrained systems that are converted from constrained systems. In contract with the existing finite-time control schemes that rely on the initial states, this restriction condition can be removed in this paper. An improved event-triggered mechanism with an adaptable switching threshold is designed to provide flexible switching between fixed threshold and variable threshold policies, resulting in reduced execution and sampling. It is proved via the Lyapunov stability method that all signals of the closed-loop systems are semi-global practical fixed-time stable. Finally, the effectiveness of the proposed control strategy is verified by some simulation results. [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: This article investigates the devise issue of a practical finite‐time output‐tracking control for uncertain nonlinear nonstrict‐feedback systems subject simultaneously to time‐varying output constraints (TVOC), actuator saturation, and bounded unmatched disturbances. An adaptive fuzzy approximator‐based control system is devised using the dynamic surface control (DSC) concept. System output constraints are addressed by employing an appropriate barrier Lyapunov function. Adaptive fuzzy disturbance observers are constructed to practically deal with time‐varying unmatched but bounded disturbances. It is verified via Lyapunov stability analysis and simulation experiments that all closed‐loop signals remain bounded, the output tracking error practically converges in finite time to a tiny but adjustable neighborhood around the origin, and the system output stays within its required time‐varying bounds. [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]

Summary: In this article, the leader‐following consensus of a kind of linear homogeneous MASs (multi‐agent systems) with input time delay is investigated. To realize leader‐following consensus, a novel distributive input control protocol based on dynamic event‐triggered mechanism is proposed. In this novel protocol, internal dynamic variables are employed to reduce the burden of communication and exclude the Zeno phenomenon. By utilizing the graph algebra, stability analysis and Lyapunov theory, some sufficient conditions have been obtained for the consensus of this MASs. The effectiveness of our approach is illustrated by some simulation examples. Compared with the given achievements, the obtained results have better ability in accelerating convergence rate and reducing the burden of communication. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time and fixed-time bipartite consensus problem of multiple Euler–Lagrange systems (MELSs) under directed interaction topologies, considering external disturbances. Two novel distributed hierarchical control algorithms are developed to address the challenging problems. Specifically, a new distributed estimator is designed to estimate the states of agents in finite/fixed-time. Moreover, based on the obtained estimations, the finite/fixed-time controller is presented to accomplish the bipartite consensus of the MELSs in the local control layer. By utilizing Lyapunov stability and the nearest neighbor-interactions theory, sufficient conditions for achieving the designed performance of the MELSs are derived. Simulation examples are provided to illustrate the effectiveness of the proposed algorithms. [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]

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 focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases. [ABSTRACT FROM AUTHOR]

This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results. [ABSTRACT FROM AUTHOR]

Memristors have several chaotic dynamic models and have been used successfully in various fields, including secure communication systems, information storage, and artificial neural networks. The memristor-based four-dimensional chaotic (FDMC) systems generate unpredictable and intricate time domain signals. Parameter fluctuations in the FDMC system may give birth to chaos, making it difficult to suppress. Stabilizing chaos in the FDMC system improves the circuit's performance. This paper synthesizes a novel time-efficient chatter-free nonlinear robust adaptive control (NLRAC) technique that stabilizes chaos in the FDMC system affected by time-varying unknown bounded exogenous disturbances and model uncertainties. The proposed NLRAC strategy decimates the time-varying unknown bounded exogenous disturbances and model uncertainties effects; it establishes a faster, smoother state-variable trajectories convergence to the zero vicinity. The theoretical analysis and mathematical proofs are based on the Lyapunov stability technique. Computer simulation results show that the proposed NLRAC technique effectively brings the FDMC system's state-variable trajectories to zero with reduced fluctuations for control input signals and state-variable trajectories. This feedback controller's attribute enhances closed-loop stability performance, improves precision, and reduces risk overshoot. The paper includes comparative computer simulation results to endorse the proposed controller performance. [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]

In this paper, a fixed-time sliding mode control scheme is developed to fulfill the trajectory tracking task of a marine surface vehicle with unknown dynamics. To restrain the adverse effects of the unknown dynamics including the parameter inaccuracy and exogenous disturbances, a fixed-time disturbance observer is designed to estimate the lumped uncertainties using the bi-limit homogeneous theory without requiring any knowledge of the model uncertainties. Then, a nominal tracking controller is proposed to stabilize the error dynamic model in the sense of fixed-time Lyapunov stability, based on which a novel integral-type sliding mode manifold with bi-limit homogeneity is constructed to drive tracking error convergence in fixed time. To enhance the robustness of the vessel control system, a disturbance observer–based fixed-time integral sliding mode tracking controller is finally proposed, and the chattering phenomenon is effectively alleviated by direct estimation compensations. The analysis of Lyapunov stability indicates that the closed-loop system is fixed-time stable. Numerical simulations on a model vessel are carried out to validate theoretical results of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, we consider the electron beam focusing system guided by an axially symmetric periodic magnetic field with unshielded cathode. Based on the third‐order approximation method and some quantitative methods, we establish two different sufficient conditions for the existence of twist periodic solutions of the system. Such twist periodic solutions are stable in the sense of Lyapunov. Some results in the literature are generalized and improved. [ABSTRACT FROM AUTHOR]

Phenomenon of cluster synchronization has captured the curiosity of scientists in the study of nonlinear dynamics over the last few decades. It is a well-known and intriguing aspect of complex systems that has garnered significant attention in research. Many researchers have significantly addressed the synchronization of cluster-based networks with identical and non-identical systems in the literature. This review paper presents a detailed summary of overall developments in the domain of cluster synchronization of chaotic system networks. After introducing the chaotic systems and concept of cluster synchronization initially; the applicability of synchronization in several fields including secure communication, information processing, and the synchronization of complex networks, has been highlighted in the later part of the paper. In general, for meeting out the goal of cluster synchronization, several strategies including standard Lyapunov design- based approach, pinning control, observer-based control, time-delayed feedback control, adaptive synchronization etc. are prominently used in literature. The article briefly discusses these approaches and reviews their advantages and disadvantages along with some possible applications. The overarching goal of this literature review is to provide a comprehensive summary of current research on cluster synchronization in chaotic systems and to point the way toward promising avenues for further investigation. The overarching goal of this literature review is to provide a comprehensive summary of current research on cluster synchronization in chaotic systems and to point the way toward promising avenues for further investigation. [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]

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]

This paper addresses the $ H_{\infty } $ H ∞ static output feedback control of discrete-time semi-Markov jump systems (S-MJSs) with mismatched modes in finite-time horizon. Different from the existing relevant work, transient dynamics in short-time is focused instead of the Lyapunov stability over infinite-time horizon. Considering the immeasurable system states, output control strategy is developed subject to mismatched modes. Firstly, S-MJSs in closed-loop form are established by designing a hidden mode-dependent output feedback controller. Based on the closed-loop system (CLS), new Lyapunov function relies on both system mode and elapsed-time are created, according to which fresh analysis criteria ensuring FTB and $ H_{\infty } $ H ∞ FTB are derived. To circumvent the non-convex difficulty arising in controller design, a separation technique is introduced such that the design prerequisites are obtained from the above performance analysis conditions. Finally, the boost converter circuit and a numerical example are borrowed to test the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]