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Summary: This paper studies a coordinated rotor speed control of flywheel energy storage matrix systems (FESMS) in the presence of model uncertainties and unknown disturbances. We consider the scenarios that the torque variation during the operation of flywheel energy storage system (FESS) cannot be accurately measured and the coordinated operation of FESMS is realized without the measurements of accurate rotor speeds. We design a distributed extended state observer (ESO) only using local rotor position measurements to estimate the rotor speeds and unknown disturbances. Based on the estimated states, a coordinated control strategy with the compensation of model uncertainties and unknown disturbances is proposed. The proposed control strategy has the advantage of speed‐free feature and active disturbance rejection. By using Lyapunov stability theory, sufficient conditions are given to ensure that the FESMS can achieve the reference tracking. The performance of the control strategy is verified by simulations. [ABSTRACT FROM AUTHOR]

This article investigates the problem of adaptive decentralized fixed‐time tracking control for strong interconnected nonlinear systems with full‐state constraints and input quantization. During the control design process, the assumption that the strong interconnection terms are bounded is removed via an inherent feature of the Gaussian function in neural networks. Unlike presvious nonlinear state‐dependent function (NSDF) that can only handle a single constraint, a novel form of NSDF is introduced to cope with more types of state constraints in this article. Meanwhile, the introduced NSDF is still available when the system states are unconstrained. Simultaneously, quantized input is directly handled by utilizing the intrinsic characteristics of the hysteresis quantizer. Then, based on the Lyapunov stability theory, all signals in the closed‐loop systems and tracking error are guaranteed to be bounded within fixed‐time. Finally, the feasibility of the proposed control scheme is illustrated by simulation results. [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]

The problem of fixed‐time formation control for a class of second‐order nonlinear multi‐agent systems is studied. For a class of such systems, a control algorithm is proposed to maintain the connections among the agents while avoiding collisions. Furthermore, a radial basis function neural network is used in the design to precisely approximate the nonlinear function for the nonlinear terms in the model. Then, a dynamic sliding mode control method is proposed to suppress the chattering phenomenon that may arise due to the sliding mode control. A sufficient condition for the system to achieve fixed‐time formation is obtained by using different methods, such as Lyapunov stability. Finally, the effectiveness of the proposed algorithm is verified by example. Simulation experiments reveal that the proposed method has faster error convergence and better robust control than conventional algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the problem of attitude tracking control for a class of vertical take-off landing (VTOL) aircraft in the presence of uncertain disturbances is addressed. The active disturbance rejection control (ADRC) method is utilized to address uncertain disturbances, while the radial basis function (RBF) neural network is considered for handling unknown nonlinear dynamics. By incorporating a modified tracking differentiator, a nonlinear state error feedback controller, and an extended state observer, the disturbance observation problem in the aircraft system is solved. These disturbances, seen as a combined disturbance in the aircraft system, are counteracted through the extended state observer. Furthermore, the unknown nonlinear dynamics within the aircraft system are approximated using the RBF neural network. Subsequently, the paper suggests adaptive ADRC strategies based on neural network and formulates adaptive control laws to estimate unknown parameters. The Lyapunov stability theory proves the effectiveness of the proposed control strategies. The simulation results show that the attitude tracking control problem of VTOL aircraft can be achieved under the proposed control strategies and adaptive control laws. [ABSTRACT FROM AUTHOR]

This article concentrates on the fixed-time synchronization (FXTS) of fractional-order complex-valued delayed neural networks with discontinuous activation functions. On the basis of the nonsmooth analysis, differential inclusion theory, Lyapunov stability theorem and complex function theory, some sufficient conditions are developed to guarantee the FXTS of such system by designing a novel fractional-order complex-valued controller. The fixed-time synchronization can make up the limitation of the previous finite-time synchronization results, that is, fixed-time synchronization time relies on the parameters of controller, which is independent of initial values. Additionally, the upper limit of synchronization time is estimated accurately. Furthermore, our results improve some finite-time synchronization and fixed-time synchronization ones. Finally, the effectiveness of theoretical results is demonstrated by some numerical simulations. [ABSTRACT FROM AUTHOR]

This article primarily focuses on the finite‐time fault‐tolerant tracking control problem of quadrotor unmanned aerial vehicle (UAV) systems. Our main innovation points are: (1) A simple cubic form of Lyapunov function is applied to the design of the position ring controller of the quadrotor UAV; (2) The command filtering technology effectively solves the challenge of derivation of complex coupling matrixs in the controller design process; (3) An improved disturbance observer and a variable threshold event‐triggered mechanism are applied in the Quadrotor UAV system. In summary, the overall approach combines the backstepping method and finite‐time Lyapunov stability to prove the finite‐time stability of all the signals in the system. Finally, the effectiveness and rationality of the algorithm are verified through simulation experiments and its application on an actual simulation platform. [ABSTRACT FROM AUTHOR]

The present paper proposes the use of fractional derivatives in the definition of sliding function, giving a new mode control applied to induction motor drives in electric vehicle (EV) applications. The proposed Fractional-Order Sliding Mode Direct Torque Control-Space Vector Modulation (FOSM-DTC-SVM) strategy aims to address the limitations of conventional control techniques and mitigate torque and flux ripples in induction motor systems. The paper first introduces the motivation for using fractional-order control methods to handle the nonlinear and fractional characteristics inherent in induction motor systems. The core describes the proposed FOSM-DTC-SVM control strategy, which leverages a fractional sliding function and the associated Lyapunov stability analysis. The efficiency of the proposed strategy is validated via three scenarios. (i) The first scenario, where the acceleration of the desired speed is defined by pulses, leading to Dirac impulses in its second derivative, demonstrates the advantage of the proposed control approach in tracking the desired speed while minimizing flux ripples and generating pulses in the rotor pulsation. (ii) The second scenario demonstrates the effectiveness of filtering the desired speed to eliminate Dirac impulses, resulting in smoother rotor pulsation variations and a slightly slower speed response while maintaining similar flux ripples and stator current characteristics. (iii) The third scenario consists of eliminating the fractional derivatives of the pulses existing in the expression of the control, leading to the elimination of Dirac impulses. These results demonstrate the potential of the FOSM-DTC-SVM to revolutionize the performance and efficiency of EVs. By incorporating fractional control in the control scheme for PV-powered EVs, the paper showcases a promising avenue for sustainable transportation. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a robust kinematic controller based on sliding mode theory designed to solve the trajectory tracking problem and also the formation control using the leader–follower strategy for nonholonomic differential-drive wheeled mobile robots with a PD dynamic controller. Design/methodology/approach: To deal with classical sliding mode control shortcomings, such as the chattering and the requirement of a priori knowledge of the limits of the effects of disturbances, an immune regulation mechanism-inspired approach is proposed to adjust the control effort magnitude adaptively. A simple fuzzy boundary layer method and an adaptation law for the immune portion gain online adjustment are also considered. An obstacle avoidance reactive strategy is proposed for the leader robot, given the importance of the leader in the formation control structure. Findings: To verify the adaptability of the controller, obstacles are distributed along the reference trajectory, and the simulation and experimental results show the effectiveness of the proposed controller, which was capable of generating control signals avoiding chattering, compensating for disturbances and avoiding the obstacles. Originality/value: The proposed design stands out for the ability to adapt in a case involving obstacle avoidance, trajectory tracking and leader–follower formation control by nonholonomic robots under the incidence of uncertainties and disturbances and also considering that the immune-based control provided chattering mitigation by adjusting the magnitude of the control effort, with adaptability improved by a simple integral-type adaptive law derived by Lyapunov stability analysis. [ABSTRACT FROM AUTHOR]

In this study, it is considered that the question of adaptive tracking control of nonlinear systems containing unknown time‐varying parameters. To optimize the control effect, a fixed‐time control strategy is adopted, in which the upper bound of the settling time is connected with the designed parameters, but not to the initial conditions. In the design, the unknown time‐varying parameters are treated as the multiplication of known and unknown vectors, and the adaptive laws are constructed to estimate the mean value of the components in the unknown ones, which availably solve the difficulty of unknown control gains. Besides, the application of command filtered technique, which combined with the compensation signals containing the adaptive parameters, effectively avoids the "complexity explosion" problem. Further, Lyapunov stability theory verifies that the tracking error can always be kept within the boundaries of the performance functions, and converges to a designated neighbourhood of the origin within a fixed time, beyond that all signals of the closed‐loop system are bounded. Finally, the simulation results prove the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

We proposed an online identification and adaptive control framework for the nonlinear dynamical systems using a novel hybrid‐feed‐forward recurrent neural network (HFRNN) model. The HFRNN is a combination of a feed‐forward neural network (FFNN) and a local recurrent neural network (LRNN). We aim to leverage the simplicity of FFNN and the effectiveness of RNN to capture changing dynamics accurately and design an indirect adaptive control scheme. To derive the weights update equations, we have applied the gradient‐descent‐based Back‐Propagation (BP) technique, and the stability of the proposed learning strategy is proven using the Lyapunov stability principles. We also compared the proposed method's results with those of the Jordan network‐based controller (JNC) and the local recurrent network‐based controller (LRNC) in the simulation examples. The results demonstrate that our approach performs satisfactorily, even in the presence of disturbance signals. [ABSTRACT FROM AUTHOR]

In this article, a fault-tolerant tracking control technique is developed for the ascent of hypersonic vehicles (HSV) experiencing wing damage and time-varying state constraints. The difficulty of control problem lies in handling state constraints associated with both state and time, while determining the unknown control directions of the multi-input multi-output (MIMO) nonlinear system. The presence of constraints in both state and time complicates the design of the control algorithm. This paper proposes the construction of a novel state transition function to establish a new unconstrained system, thereby eliminating the conservative feasibility conditions of Barrier Lyapunov Function (BLF) and integral BLF methods when dealing with time-varying constraints. The fusion of time-varying scaling functions and Nussbaum-type functions not only resolves the issue of unknown control directions in the MIMO nonlinear system but also enhances the transient and steady-state performance of the closed-loop system. Neural Networks are employed to approximate the unknown nonlinear functions. Using Lyapunov stability theory, it is proven that state constraints are not violated, and all signals in the closed-loop system are bounded. Simulation results demonstrate the merits of the designed fault-tolerant control (FTC) algorithm. • A unified fault-tolerant control scheme for the ascent hypersonic vehicle is designed. • Wing damage and function constraints on states are considered. • Nonlinear mapping eliminates the feasibility conditions in barrier Lyapunov functions. • The unknown control direction issue in multivariable nonlinear systems is resolved. [ABSTRACT FROM AUTHOR]

In recent decades, impulse control has been increasingly applied as a discontinuous control method across diverse domains such as satellite orbit transfers, financial market regulation, chaos synchronization, and communication security. This paper investigates an impulse synchronization strategy specifically tailored for chaotic financial systems. We propose a novel strategy grounded in Lyapunov stability theory and the maximum Lyapunov exponent, designed to synchronize chaotic financial systems effectively. Simulation experiments are conducted to validate the efficacy of our proposed approach. [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]

In this paper, we study the multi-target tracking problem of networked robotic systems (NRSs) within predefined time under a directed interaction topology considering disturbances and physical parameter uncertainties. On the basis of non-singular sliding-mode surface, a new predefined-time estimator-based hierarchical control algorithm is put forward so as to address the tracking problem under the case of multiple moving targets. Using the time base generator (TBG), a distributed estimator algorithm is designed to ensure that the followers can estimate different target states within a predefined-time. Certain sufficient conditions of predefined-time multi-target tracking of NRSs are presented using the Lyapunov stability and neighbor information interaction principle. In the end, numerical simulation experiments are offered to indicate the availability and correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path. [ABSTRACT FROM AUTHOR]

A model-free control method based on iterative learning law combined with adaptive super-twisting is proposed to realize the synchronous coordination control of multi-lift overhead crane system for the problems of inaccurate modeling, system parameter variation, and disturbance uncertainty that exist in multi-lift overhead crane system. First, a load-coupling model of the double-container overhead crane considering the deformation tangential force in the interlocking mode is established. Second, a time-varying sliding mode surface (TSMC) designed using nonlinear functions effectively improves the convergence speed of the system state. The method of iterative learning control is introduced to compensate the system dynamics to achieve model-free control, and the dynamic iterative learning control (DILC) is designed to improve the convergence speed of the error of the system and the steady-state performance. To suppress uncertainty disturbances and avoid control gain overestimation, an adaptive gain is added to the generalized super-twisting algorithm, which has the advantages of both finite-time convergence and chattering suppression, and improves the robustness and tracking performance of the multi-lift overhead crane system. The stability of the controlled system is analyzed using Lyapunov stability theory. The simulation experiments illustrate the effectiveness of the proposed synchronization control scheme. [ABSTRACT FROM AUTHOR]

Summary: This article delves into the adaptive heading tracking control of unmanned surface vehicle (USV) by incorporating an event‐triggered mechanism and signal quantization. The primary objective is to save communication resources while alleviating the burden of signal transmission. To address time‐varying external perturbations inherent in the control system, a disturbance observer is employed for precise estimation. Additionally, a linear model is introduced to delineate the procedure of quantization. By furnishing the controller with purpose‐designed quantized control input, the adaptive tracking control system can effectively track desired input without requiring any prior knowledge of the quantized parameters. The article substantiates its claims by demonstrating the system's stability in the absence of quantization considerations and the bounded nature of quantization errors through a series of presented lemmas. Further, the stability of the USV heading control system, integrated with an event‐triggered mechanism and signal quantization, is proofed in accordance with Lyapunov stability theory. Finally, the proposed strategy's efficacy and practical applicability are validated through experimental simulations. [ABSTRACT FROM AUTHOR]

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]

• Introduce a novel low-thrust constellation reconfiguration control method using artificial potential function. • Assure the Lyapunov stability including phase control and in the presence of perturbations. • Combine collision avoidance with reconfiguration simultaneously, lowering the risk of collision significantly. • Carry out comprehensive numerical simulations under diverse scenarios, including mega-constellation case. The configuration control of constellations which consist of numerous satellites presents significant challenges. Such space systems demand the capability for autonomous reconfiguration to accomplish specific missions. Individual satellites within constellations are primarily equipped with low-thrust systems, rendering traditional impulse control methods for satellite formation and mission planning ineffective. To address this issue, this paper proposes a low-thrust constellations reconfiguration control method utilizing an artificial potential function. Relying exclusively on neighboring state information, satellites can dynamically modulate their control efforts in real-time. The stability of the proposed reconfiguration control method is established under modelable, bounded perturbation using Lyapunov theory. Furthermore, a repulsive potential function is formulated to ensure collision avoidance among satellites. Numerical results indicate that the proposed method is stable, computationally efficient, and guarantees the safe distance during maneuvers. Consequently, this method is ideally suited for reconfiguration tasks across a spectrum of large space systems, including mega-constellations. [ABSTRACT FROM AUTHOR]

This paper studies the approximate optimal event-triggered tracking control problem for a class of second-order nonlinear systems with prescribed performances. By employing a prescribed performances function, restrictions on tracking errors are removed for prescribed performances including convergence rate, maximum overshoot, and steady-state error. On this basis, a complex optimal tracking control problem can be transformed into an optimal stabilising control problem by constructing an augmented system. Subsequently, an event-triggered mechanism is introduced to reduce communication resources. Then, an adaptive critic learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation, where the weights in the critic networks are tuned through the gradient descent approach and experience replay technology. Through the developed learning method, the persistence of excitation condition is released, and the data efficiency is improved. The Lyapunov stability theory is introduced to verify the stability of the close-loop system and the tracking errors are uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is devoted to the observer-based adaptive robust control for fractional-order Takagi–Sugeno (T-S) fuzzy systems with input uncertainties and output disturbances. By combining system states and output perturbations as new state variables, an augmented fuzzy system whose state variables are unknown is built. Furthermore, an observer is devised to simultaneously estimate unmeasurable system states together with unknown external disturbances. Two stability theorems are derived to prove the asymptotic stability of the error system based on linear matrix inequalities and Lyapunov stability theory. Finally, simulation results are provided to demonstrate the effectiveness of the designed method. [ABSTRACT FROM AUTHOR]

Reconfigurable variable stiffness actuator (RVSA) has attracted increasing attention in robotics due to its safety, compliance, and robustness. However, the control of the RVSA is challenging due to nonlinear factors such as high-order nonlinear dynamic, model uncertainties, time-varying model parameters, and disturbances. In this paper, firstly, a lightweight RVSA structure with both passive and active nonlinear variable stiffness characteristic is developed. Secondly, a dynamic surface backstepping control method based on a radial basis neural network and disturbance observer (DSBC-RBFNN-DOB) is proposed to achieve position control of the lightweight RVSA with matched and unmatched uncertainties. To address solve the "complexity explosion" and noise problems in traditional backstepping control, the dynamic surface backstepping control (DSBC) method is used to design the controller. Then, a method based on radial basis neural network (RBFNN) and disturbance observer (DOB) are used to compensate for the matched and unmatched uncertainties in the link and motor. In this method, the matched uncertainties are compensated using RBFNN, and the DOB is integrated to compensate RBFNN approximation errors and unmatched uncertainties. Through Lyapunov stability analysis, the semi-global boundedness of the controller is proven. Finally, the proposed method is simulated and actually implemented, verifying the effectiveness of the method. Simulation and experimental results show that the root mean square error (RMSE) of the proposed method is only 0.97277° and 0.6418°, respectively. Compared with PID, DSBC, and DSBC-RBFNN, the error reduction percentages in simulation (experiment) are 85.6 % (88.9 %), 49.4 % (88.4 %) and 36.1 % (80.0 %) respectively. • A lightweight reconfigurable variable stiffness actuator with smaller mass and more compact structure is proposed.. • A dynamic surface backstepping control method based on neural network and disturbance observer is proposed. • A method of uncertainty and disturbance estimation combining neural network and disturbance observer is proposed. • Experiments and simulations were conducted under the condition of actively changing stiffness. [ABSTRACT FROM AUTHOR]

Mathematical models, especially complex nonlinear systems, are always difficult to analyze and synthesize, and researchers need effective and suitable control methods to address these issues. In the present work, we proposed a hybrid method that combines the well-known Takagi-Sugeno fuzzy model with wavelet decomposition to investigate nonlinear systems characterized by the presence of mixed nonlinearities. Here, one nonlinearity is super-linear and convex, and other is sub-linear, concave, and singular at zero, which leads to difficulties in the analysis, as is known in PDE theory. Linear and polynomial fuzzy models were combined with wavelets to ensure an improvement in both methods for investigating such problems. The results showed a high performance compared with existing methods via error estimates and Lyapunov theory of stability. The model was applied to a prototype nonlinear Schrodinger dynamical system. [ABSTRACT FROM AUTHOR]

In this article, a finite‐time optimal containment control method is proposed for nonlinear multi‐agent systems with prescribed performance. First, a neural network‐based reinforcement learning algorithm is developed under the optimized backstepping framework. The algorithm employs an identifier‐critic‐actor architecture, where the identifiers, critics and actors are used to estimate the unknown dynamics, evaluate the system performance, and optimize the system, respectively. Subsequently, in order to guarantee the transient performance of the tracking error, the original system is converted into an equivalent unconstrained system. Then, the tracking errors are allowed to converge to a prescribed set of residuals in finite time by combining prescribed performance control and finite‐time optimal control techniques. Furthermore, by using the Lyapunov stability theorem, it is verified that all signals are semi‐globally practical finite‐time stable, and all followers can converge to a convex region formed by multiple leaders. Finally, the effectiveness of the proposed scheme is demonstrated by a practical example. [ABSTRACT FROM AUTHOR]

In this article, the cluster synchronization control for a complex dynamic network (CDN) with mutually coupled nodes subsystem (NS) and connection relations subsystem is investigated. The process of cluster synchronization is segmented into three dynamic continuous stages: first, the free movement, then the task‐oriented clustering, and finally the cluster synchronization. The control scheme, founded on the clustering nodes of CDN, is proposed, such that the cluster synchronization arises when clustering all the nodes into two different sub‐networks (SNs). This approach originates from the flight motion for a group of autonomous aircrafts. At a certain moment, free flight is interrupted, and all the aircrafts split into two SNs according to the given clustering rules. Then the two controlled SNs are required to achieve cluster synchronization, that is, every SN converges to the same in speed. In order to split all the nodes into two different SNs, a clustering algorithm according to the "central nodes" is proposed. Based on Lyapunov stability theory, by designing the suitable inner cluster links, the adaptive controller of NS for each SN is synthesized to guarantee the stability of the error system. It is shown that the eventual inner topology of each SN is displayed in the pre‐given form when the cluster synchronization achieves. Finally, the merits and effectiveness of the proposed control scheme are verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this article, the problem of adaptive optimal tracking control is studied for nonlinear strict‐feedback systems. While not directly measurable, the states of these systems are subject to both time‐varying and asymmetric constraints. Bypassing the conventional barrier Lyapunov function method, the constrained system is transformed into its unconstrained counterpart, thereby obviating the need for feasibility conditions. A specially designed reinforcement learning (RL) algorithm, featuring an observer‐critic‐actor architecture, is deployed in an adaptive optimal control scheme to ensure the stabilization of the converted unconstrained system. Within this architecture, the observer estimates the unmeasurable system states, the critic evaluates the control performance, and the actor executes the control actions. Furthermore, enhancements to the RL algorithm lead to relaxed conditions of persistent excitation, and the design methodology for the observer overcomes the restrictions imposed by the Hurwitz equation. The Lyapunov stability theorem is applied for two primary purposes: to ascertain the boundedness of all signals within the closed‐loop system, and to ensure the accuracy of the output signal in tracking the desired reference trajectory. Finally, numerical and practical simulations are provided to corroborate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this article, a distributed controller based on adaptive dynamic programming is proposed to solve the minimum loss problem of flywheel energy storage systems (FESS). We first formulate a performance function aiming to reduce total losses of FESS in power distribution applications. Then we use the Hamilton–Jacobi–Bellman (HJB) equation to solve this optimal control problem. The solution of the HJB equation is approximated by neural networks. To achieve distributed control, we estimate the global variables in the HJB equation by using the dynamic average consensus algorithm. A barrier Lyapunov function and a saturation function are introduced to handle the issue of state and input constraints, respectively. Then the stability of the system is proved through the Lyapunov stability analysis. Finally the effectiveness of the proposed strategy is verified by simulations. Simulation results show that FESS can track the power command while minimizing total power losses by interacting with neighbors. The proposed algorithm leads to a loss reduction of 1.13%$$ 1.13\% $$ compared to the equal power distribution strategy. [ABSTRACT FROM AUTHOR]

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This paper primarily investigates a neural-network-based safe control scheme for solving the optimal control problem of continuous-time (CT) nonlinear systems with asymmetric input constraints under non-zero-sum (NZS) differential game scenarios. Initially, by constructing a novel non-quadratic function, the issue of asymmetric input constraints in the non-zero-sum differential game controllers is addressed. Subsequently, the safe Hamilton-Jacobi-Bellman (HJB) equation is derived from the direct integration of the control barrier function (CBF) into the traditional cost function, ensuring that the system states remain within a safe region. Then, the safe learning control scheme based on single critic neural network (NN) and adaptive dynamic programming (ADP) is proposed to approximate the optimal control strategy, differing from the dual-network update method commonly used in traditional ADP. Based on the constructed neural network weight adjustment rules, the optimal solution to the HJB equation can be derived within the safe learning control framework. Following this, Lyapunov's stability theory demonstrates that the errors in neural network weights and all signals within the closed-loop system are uniformly ultimately bounded (UUB). Finally, the effectiveness of the developed neural-network-based safe learning control method is validated through two simulation results. [ABSTRACT FROM AUTHOR]

This paper focuses on the containment control problem for a class of nonlinear multi-agent systems (MASs) with sampled-data. To enhance the efficiency of utilizing communication resources, a new distributed sampled-data-based event-triggered transmission strategy is proposed. This event-driven strategy requires that event detector works only at periodic sampling instants. By employing the techniques such as input delay method, inequality technique and the Lyapunov stability theory, sufficient criteria are derived to ensure that each follower converges to the convex hull spanned by the leaders. A convex optimization method is employed to search for the desired controller gain by maximizing the maximum-allowable bound of sampling intervals. Additionally, for some special scenarios, to reduce computational complexity, the matrix decoupling technique is utilized to reduce the dimension of matrix inequalities, thereby facilitating application to large-scale MASs. Finally, the effectiveness of the proposed theory is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Summary The thesis studies a stochastic H∞$$ {H}_{\infty } $$ finite‐time bounded (SH∞$$ {H}_{\infty } $$FTB) filter design method for time‐varying delay Markov jump systems (MJSs) with partially unknown transition rates. First, a Lyapunov–Krasovskii functional with triple integral is built, the free weight matrix is added for lowering the conservatism. And the condition of SH∞$$ {H}_{\infty } $$FTB of the error system is analyzed. Then, according to linear matrix inequalities (LMIs), a new filter design method is presented. Moreover, the dimension of the filter obtained is free, and the filter ensures that the error system is SH∞$$ {H}_{\infty } $$FTB. Finally, the validity and effectiveness of the conclusion of this paper are demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

This paper mainly concerns on the tracking control problem for event‐triggered networked control systems (NCSs) with diversified cyber‐attacks. An event‐triggered mechanism (ETM) is exploited to decrease the amount of redundant transmissions, thus saving communication resources. In addition, a novel tracking error model for NCSs is built with consideration of ETM and diversified cyber‐attacks, which involves deception attacks and Denial‐of‐Service (DoS) attacks. On the basis of Lyapunov stability theory and linear matrix inequalities (LMIs), the stability criterion of the tracking error system is constructed, and the controller is designed to ensure the tracking performance of the system. In the end, simulation examples are provided to testify the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Highly active antiretroviral therapy (HAART) stands out as the most effective treatment for human immunodeficiency virus type-1 (HIV-1). While total eradication is still difficult, HAART can dramatically lower the virus's plasma viral level below the detection threshold. The activation of latently infected cells is considered to be the main obstacle to the total eradication of HIV-1 infection. This study investigates the dynamic characteristics of two generalized HIV-1 infection models taking into account the impairment of cytotoxic T lymphocytes (CTLs). These models include CD4+T cells that are latently infected and equipped with the capability to engage in cell-to-cell infection and elude immune responses. We introduce models featuring three infection pathways: virus-to-cell (VTC), latent cell-to-cell (L-CTC), and active cell-to-cell (A-CTC). The three pathways' infection rates are characterized by general functions, which cover the many types of infection rates documented in the literature. The second model integrates three distinct types of distributed-time delays. We demonstrate the validity of the suggested models, through their well-posedness. We determine the basic reproduction ratio (RO) of the systems. Lyapunov functions and LaSalle's invariance principle are employed to verify that the global stability of both the virus-free steady state (O0) and the virus-persistence steady state (Ο1). More precisely, O0 achieves global asymptotic stability when R0 ≤ 1 whereas Ο1 attains global asymptotic stability when R0 > 1-To demonstrate the impact of the parameter values on R0 we examine the sensitivity analysis. It is illustrated that R0 comprises three components, namely R0Ɛ, R0P, and R0K corresponding to the transmissions of VTC, L-CTC, and A-CTC, respectively. Thus, if the L-CTC pathway is disregarded in the HIV-1 infection model, R0 be underestimated, which could lead to inadequate or erroneous medication therapy focused on eradicating HIV-1 within the body. To demonstrate the associated mathematical outcomes, we conduct numerical simulations through an illustrative example. Specifically, we delve into how the dynamics of HIV-1 are influenced by both immune impairment and time delay. Our findings suggest a significant role of reduced immunity in the progression of the infection. Furthermore, time delays possess the potential to markedly reduce R0, thereby impeding the replication of HIV-1. [ABSTRACT FROM AUTHOR]

Permanent magnet synchronous motor (PMSM) is a multivariable and highly coupled nonlinear system, which is prone to chaotic behavior during actual operation. In order to suppress the chaotic behavior of the PMSM, this work designs a free-will arbitrary time adaptive controller based on the inverse step derivation, adaptive control theorem and Lyapunov stability theory. Firstly, the corresponding coordination transformations are designed according to the PMSM. Secondly, the bounded problem of the controlled system is analyzed by using the Lyapunov stability theory, and the free-will arbitrary time adaptive controller is designed by backstepping derivation. Finally, numerical simulation verifies that the designed controller quickly stabilizes the system state variables to the output signals and proves that the controller is free-will arbitrary time stable for all closed-loop signals. [ABSTRACT FROM AUTHOR]

This article presents a discrete‐time robust model reference adaptive controller and adaptive sigmoid super‐twisting sliding mode (RMRAC‐ASSTSM) and its stability analysis using Lyapunov stability theory. This control structure is robust to matched and unmatched dynamics. In addition, the chattering phenomenon tends to be suppressed in the steady state due to adaptive super‐twisting sliding mode action using a sigmoid function. The performance of the proposed control structure is corroborated with simulation results, considering a second‐order non‐minimum phase unstable plant, where it can be seen that RMRAC‐ASSTSM regulation errors converge to a finite residual set when the plant presents unmodeled dynamics. A comparison is also presented with a similar RMRAC‐based control structure with an adaptive super‐twisting sliding mode implemented with a sign function. [ABSTRACT FROM AUTHOR]

This study investigates analytically the stability analysis of a nonlinear convective boundary layer (BL) flow of the nanofluids GO-EG and GO-W on a shrinking surface in the presence of a magnetic field and viscous dissipation. We provide a second-order nonlinear ordinary differential equation (NODE) for temperature distribution (TD) and a third-order NODE for velocity profile (VP) coupling based on the thermophysical characteristics of the base fluid and nanofluid as well as similarity transformations (STs) in the fundamental governing equations of momentum and energy. The analytical method HAM is used to answer the equations that have been gathered. In many different industries, such as manufacturing, automotive, microelectronics, and defense, cooling of various types of equipment and devices has very important challenges. To fulfill the demands of the engineering and industrial industries, it is hoped that this issue would significantly improve the heat transformation ratio. [ABSTRACT FROM AUTHOR]

This article investigates the consensus problem of nonlinear leader-following multi-agent systems (MASs) via adaptive impulsive control. A distributed impulsive controller is employed, in which an adaptive updating law in the discrete-time setting is designed for the impulsive gain. Moreover, in order to reduce the communication cost, a distributed self-triggered strategy is proposed to determine when the impulsive instant occurs. Some criteria are derived to guarantee consensus of leader-following MASs based on Lyapunov stability theory and algebraic Riccati equation. It is proved that the self-triggered impulsive sequence does not exhibit Zeno behaviour. Finally, an illustrative example is presented to empirically validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Intersecting disciplines, as an important trend in the development of modern academic research and education, have exerted a profound and positive influence on scientific research activities. Based on control theory and fractional-order theory, this paper presents a novel approach for the speed regulation of a permanent magnet synchronous motor (PMSM) in the presence of uncertainties and external disturbances. The proposed method is a composite control based on a model-free sliding mode and a fractional-order ultra-local model. The model-free sliding mode is a control strategy that utilizes the sliding mode control methodology without explicitly relying on a mathematical model of the system being controlled. The fractional-order ultra-local model is a mathematical representation of a dynamic system that incorporates the concept of fractional-order derivatives. The core of the controller is a new type of fractional-order fast nonsingular terminal sliding mode surface, which ensures high robustness, quick convergence, while preventing singularity. Moreover, a novel fractional-order nonlinear extended state observer is proposed to estimate both internal and external disturbances of the fractional-order ultra-local model. The stability of the system is analyzed using both the Lyapunov stability theory and the Mittag–Leffler stability theory. The analysis confirms the convergence stability of the closed-loop system under the proposed control scheme. The comparison results indicate that the proposed composite control based on the fractional-order ultra-local model is a promising solution for regulating the speed of PMSMs in the presence of uncertainties and disturbances. [ABSTRACT FROM AUTHOR]

The global stability of a nonautonomous 3-species ratio-dependent diffusive predator-prey model is studied in this paper. Firstly, some easily verifiable sufficient conditions which guarantee the existence of the strictly positive space homogenous periodic solution (SHPS) of the ratio- dependent predator-prey model (RDPPM) with diffusive and variable coefficient are achieved by using a comparison theorem of differential equation and fixed point theorem. At the same time, some new analysis techniques are developed as a byproduct. Secondly, some sufficient conditions ensuring the globally asymptotically stability of the strictly positive SHPS of the diffusive nonautonomous predator-prey model are given by using the method of upper and lower solutions (UALS) for the parabolic partial differential equations and Lyapunov stability theory. In addition, two numerical examples are given to validate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

Summary The primary objective of this paper is to enhance the efficient utilization of communication resources. To achieve this, the paper delves into the disturbance observer based adaptive heading control strategy for Unmanned Marine Vehicles with event‐triggered and input quantization. Furthermore, in order to mitigate the impact of slow time‐varying external disturbances within the control system, the disturbance observer is employed for estimation. Within the context of a networked control, control input is subjected to quantization via an input quantizer, and the process of input quantization is described by using a linear analytical model. Importantly, no foreknowledge of quantization parameters is necessary for the quantized feedback controllers. Subsequently, the sliding mode control method is combined with event‐triggered mechanismss to design quantization feedback control system. The stability of the closed‐loop system is established in line with the fundamental tenets of Lyapunov stability theory, validating the bounded nature of both observation and heading tracking control errors. The effectiveness of the proposed heading control scheme is further underscored through a series of simulation experiments. [ABSTRACT FROM AUTHOR]

We consider the problem of stability of nonzero integral manifolds of a nonlinear finitedimensional system of ordinary differential equations whose right-hand side is a periodic vector-valued function of the independent variable containing a parameter. We assume that the system has a trivial integral manifold for all values of the parameter and the corresponding linear subsystem does not possess the property of exponential dichotomy. The aim of this work is to find sufficient conditions for stability, instability, and asymptotic stability of a local nonzero integral manifold. For this purpose, we use the method of Lyapunov functions modified to the problem considered and singularities of the right-hand sides of the system. [ABSTRACT FROM AUTHOR]

This study explores fault-tolerant consensus in leader–following heterogeneous multi-agent systems, focusing on actuator failures in uncrewed aerial vehicles (UAVs) and uncrewed ground vehicles (UGVs). An optimization-based fault-tolerant consensus algorithm is proposed. The algorithm utilizes the Euler–Lagrange formula to ensure system consistency under actuator failures, with the Lyapunov stability theory proving the asymptotic stability of the consistency error. The algorithm is applied to heterogeneous multi-agent systems of UAVs and UGVs to derive optimal fault-tolerant consensus control laws for each vehicle type. Simulation experiments give evidence for the feasibility of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this study, a novel control scheme based on spiking neural networks (SNNs) has been proposed to accomplish the trajectory tracking of quadrotor unmanned aerial vehicles (UAVs). The update rules for the network parameters have been derived using the Lyapunov stability theorem. Three different trajectories have been utilized in the simulated and experimental studies to verify the efficacy of the proposed control scheme. The acquired results have been compared with the responses obtained for proportional–integral–derivative (PID) and traditional neural network controllers. Simulated and experimental studies demonstrate that the proposed SNN-based controller is capable of providing better tracking accuracy and robust system response in the presence of disturbing factors. [ABSTRACT FROM AUTHOR]

The number of Methicillin-resistant Staphylococcus aureus (MRSA) cases in communities and hospitals is on the rise worldwide. In this work, a nonlinear deterministic model for the dynamics of MRSA infection in society was developed to visualize the significance of awareness in interventions that could be applied in the prevention of transmission with and without optimal control. Positivity and uniqueness were verified for the proposed corruption model to identify the level of resolution of infection factors in society. Furthermore, how various parameters affect the reproductive number R 0 and sensitivity analysis of the proposed model was explored through mathematical techniques and figures. The global stability of model equilibria analysis was established by using Lyapunov functions with the first derivative test. A total of seven years of data gathered from a private hospital consisting of inpatients and outpatients of MRSA were used in this model for numerical simulations and for observing the dynamics of infection by using a non-standard finite difference (NSFD) scheme. When optimal control was applied as a second model, it was determined that increasing awareness of hand hygiene and wearing a mask were the key controlling measures to prevent the spread of community-acquired MRSA (CA-MRSA) and hospital-acquired MRSA (HA-MRSA). Lastly, it was concluded that both CA-MRSA and HA-MRSA cases are on the rise in the community, and increasing awareness concerning transmission is extremely significant in preventing further spread. [ABSTRACT FROM AUTHOR]

Nonholonomic constrained wheeled mobile robot (WMR) trajectory tracking requires the enhancement of the ground adaptation capability of the WMR while ensuring its attitude tracking accuracy, a novel dual closed-loop control structure is developed to implement this motion/force coordinated control objective in this paper. Firstly, the outer-loop motion controller is presented using Laguerre functions modified model predictive control (LMPC). Optimised solution condition is introduced to reduce the number of LMPC solutions. Secondly, an inner-loop force controller based on adaptive integral sliding mode control (AISMC) is constructed to ensure the desired velocity tracking and output driving torques by combining second-order nonlinear extended state observer (ESO) with the estimation of dynamic uncertainties and external disturbances during WMR travelling process. Then, Lyapunov stability theory is utilised to guarantee the consistent final boundedness of the designed controller. Finally, the system is numerically simulated and practically verified. The results show that the double-closed-loop control strategy devised in this paper has better control performance in terms of complex trajectory tracking accuracy, system resistance to strong interference and computational timeliness, and is able to realise effective coordinated control of WMR motion/force. [ABSTRACT FROM AUTHOR]

This article investigates the issue of data‐based distributed consensus optimal control for a class of affine nonlinear multi‐agent systems (MASs) under switching topology with external disturbances. With the help of the game theory, the distributed adaptive optimal consensus control issue can be formulated into a zero‐sum (ZM) game problem. In control design, a data‐based integral reinforcement learning (IRL) algorithm is used to solve the coupled Hamilton–Jacobi–Isaac (HJI) equation with unknown drift dynamics. Meanwhile, to relax the persistent excitation (PE) condition in the traditional optimal control design, the experience replay (ER) technique is introduced. Combining IRL algorithm and single critic neural network (NN), a distributed adaptive optimal consensus control approach is designed. The stability of the closed‐loop system is proved by combining the Lyapunov stability theory and the average dwell time method. Finally, a simulation example is given to illustrate the effectiveness of the developed optimal consensus control approach. [ABSTRACT FROM AUTHOR]

The stability of systems of linear autonomous functional differential equations of neutral type is studied. The study is based on the well-known representation of the solution in the form of an integral operator, the kernel of which is the Cauchy function of the equation under study. The definitions of Lyapunov, asymptotic, and exponential stability are formulated in terms of the corresponding properties of the Cauchy function, which allows us to clarify a number of traditional concepts without loss of generality. Along with the concept of asymptotic stability, a new concept of strong asymptotic stability is introduced. The main results are related to the stability with respect to the initial function from the spaces of summable functions. In particular, it is established that strong asymptotic stability with initial data from the space L1 is equivalent to the exponential estimate of the Cauchy function and, moreover, exponential stability with respect to initial data from the spaces Lp for any p ≥ 1. [ABSTRACT FROM AUTHOR]

The goal of this article is to investigate the bipartite tracking control problem using a prescribed‐time convergence method for Euler–Lagrange systems (ELSs) with external disturbances. Agent interactions are represented by a matrix‐weighted signed directed graph. There are not only cooperative but also adversarial interactions. An essential component of the system, the prescribed‐time hierarchical control (PTHC) algorithm, including a more general time‐varying function, is newly developed to guarantee that all agents converge to the same leader state but with opposite signs within a prescribed time. The salient feature of the introduced method lies in the fact that the convergence time of the control objective can be prespecified by the user. The state transformation, the property of the matrix‐weighted Laplacian, and the generalized Lyapunov stability argument are employed to theoretically validate the proposed algorithms. Finally, the effectiveness of the algorithm is confirmed through the execution of numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach that simultaneously enables photovoltaic (PV) inversion and flexible arc suppression during single-phase grounding faults. Inverters compensate for ground currents through an arc-elimination function, while outputting a PV direct current (DC) power supply. This method effectively reduces the residual grounding current. To reduce the dependence of the arc-suppression performance on accurate compensation current-injection models, an adaptive fuzzy neural network imitating a sliding mode controller was designed. An online adaptive adjustment law for network parameters was developed, based on the Lyapunov stability theorem, to improve the robustness of the inverter to fault and connection locations. Furthermore, a new arc-suppression control exit strategy is proposed to allow a zerosequence voltage amplitude to quickly and smoothly track a target value by controlling the nonlinear decrease in current and reducing the regulation time. Simulation results showed that the proposed method can effectively achieve fast arc suppression and reduce the fault impact current in single-phase grounding faults. Compared to other methods, the proposed method can generate a lower residual grounding current and maintain good arc-suppression performance under different transition resistances and fault locations. [ABSTRACT FROM AUTHOR]