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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]

This work investigates the stability for the wave equation with damping γ (t , x) (− Δ x) α ∂ t u defined on a bounded domain Ω ⊂ R d , d ≥ 1. The damping coefficient γ (t , x) ≥ 0 may degenerate to zero at some (t , x) ∈ [ τ , + ∞) × Ω. In contrast to the classical geometric control condition (GCC), we give the integral control condition (ICC) which means γ only has a positive lower bound in the sense of integral. [ABSTRACT FROM AUTHOR]

A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a perturbation drags solutions into solutions and the dragged perturbed solutions can be expanded in a series with respect to the flow parameter, hence it contains perturbations at any order. Mechanics is included as a special case. As a simple application, we recover the well-known discussion about stability of geodesics on a sphere S 2 . [ABSTRACT FROM AUTHOR]

This paper investigates the problems of exponential stability for a class of quaternion‐valued memristor‐based neural networks. By using M‐matrix theory and fixed point theorem, the existence and uniqueness of the equilibrium point of quaternion‐valued neural network are proved, respectively. Then, by combining M‐matrix with exponential stability theory, a non‐factorization method is obtained by using some inequality techniques to give the effective conditions of global exponential stability of quaternion‐valued memristor‐based neural network with time‐varying delay. Finally, numerical examples are given to demonstrate the validity of the derived results. [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]

In this paper, finite-time and fixed-time function projective synchronization of competitive neural networks with time-varying delays and noise perturbation is studied. Firstly, different from the existing papers, a more flexible Lyapunov function is constructed based on p-norm and two hybrid controllers are designed in this paper. Secondly, based on the finite-time and fixed-time stability theory and stochastic analysis theory, some new and useful finite-time and fixed-time function projective synchronization criteria are obtained. Furthermore, the settling time is derived with the help of some lemmas and mathematical inequalities under the appropriate control scheme. Finally, illustrative examples are given to show the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension‐one and codimension‐two bifurcation analysis, and chaos control in a predator‐prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension‐two 1 : 2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results. [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]

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]

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]

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]

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]

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]

The dynamic nature of multilingual families and their language policies has been touched upon by numerous studies. Adding to the field, the present study assesses the stability of family language policy in a standardised and quantitative manner. To this end, a linguistically heterogenous sample consisting of 488 multilingual families raising young children in Belgium's Flemish Community was surveyed twice, eighteen months apart. Based on the collected longitudinal survey data, the present study offers statistically verifiable evidence for the (partially) dynamic character of family language policy. Firstly, parental beliefs in a multilingual advantage were strengthened and a change was found in language-specific beliefs regarding children's language acquisition. Secondly, the families' practices demonstrate a shift towards the Dutch institutional language, particularly in parental language use when communicating with each other and with their child, and in the child's overall exposure. The observed shift in practices and beliefs underscores not only parents' continuous assessment of their children's linguistic needs and development, but also the societal environment influencing this assessment and adjustment. However, while significant changes in language beliefs and practices were uncovered, the more conscious and explicit component of language management proved stable across time, corroborating the independent character of the three family language policy components. [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]

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]

In this article, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method can be applied to real diagonalizable matrices, is provably convergent with acceleration in the symmetric case, and does not require a priori spectral knowledge. We review and extend background results on previously developed static momentum accelerations for the power iteration through the connection between the momentum accelerated iteration and the standard power iteration applied to an augmented matrix. We show that the augmented matrix is defective for the optimal parameter choice. We then present our dynamic method which updates the momentum parameter at each iteration based on the Rayleigh quotient and two previous residuals. We present convergence and stability theory for the method by considering a power‐like method consisting of multiplying an initial vector by a sequence of augmented matrices. We demonstrate the developed method on a number of benchmark problems, and see that it outperforms both the power iteration and often the static momentum acceleration with optimal parameter choice. Finally, we present and demonstrate an explicit extension of the algorithm to inverse power iterations. [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]

A novel controller using fixed‐time sliding mode (FTSM) and fixed‐time disturbance observer (FTDO) is proposed to achieve trajectory tracking control of robotic manipulators. First, the mathematical model is established for robots with dynamic model uncertainties and external disturbances. An FTSM control strategy is presented where the integral terms of position errors are introduced into the existing sliding mode surface (SMS) to reduce the steady‐state error of the system. The exponential form in the integral terms can provide an appropriate control force for tracking systems when the position errors are far from the sliding surface for a long time. Then, an FTDO is designed to obtain a precise estimation of lumped disturbances which can be used to weaken the impact of disturbances on the control accuracy. Finally, the fixed‐time convergence properties of the tracking control system are demonstrated using Lyapunov stability theory. Simulation research is carried out to illustrate that the proposed control strategy has strong robustness and fast‐tracking speed. [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]

Recent years have seen high penetration of renewable energies, which have significantly reduced the inertia of bulk power systems. As a result, the frequency behaviour of power systems is becoming more complex. To resolve this technical challenge, there is a particularly strong interest in developing analytical solutions for frequency dynamics studies. This study first describes a second‐order frequency dynamics model for power systems with renewable energies. A non‐linear perturbation approach is suggested to drive the analytical solution of the model. It is shown that, under many circumstances, frequency dynamics can be effectively approximated using a linear model. Subsequently, the article describes a fourth‐order linear frequency dynamics model that takes into account governor‐turbines. A polynomial eigenvalue method is proposed to identify the dominant and non‐dominant modes of the solution of the four‐order model. It is demonstrated that the dominant mode has a decisive impact on frequency behaviour, while the non‐dominant modes influence the relative frequency oscillations only. Finally, the study derives the analytical expressions of the standard frequency performance metrics and examines the impact of damping and inertia parameters. The introduced results are verified using two test systems, demonstrating the accuracy and effectiveness of the suggested method. [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]

In this paper, we consider a nonlinear boundary-value problem proposed as the simplest model for describing oscillations in a gas flow. We analyze the stability of the trivial (zero) equilibrium state and find a critical value of the speed of the incoming gas flow. Exact solutions of the problem are found in the form of time-periodic functions and their stability is examined. All the results are obtained analytically based on the qualitative theory of infinite-dimensional dynamical systems. [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]

This paper focuses on the finite‐time synchronization issue for reaction‐diffusion competitive neural networks (RCNNs) with different time scales and time‐varying delays. To reduce the waste of network resources, a periodically intermittent control strategy is presented based on two time scales (short and long memory) and time‐varying delay. By constructing the Lyapunov–Krasovskii functional, with the help of Lyapunov stability theory and auxiliary inequality technique, the finite‐time synchronization can be guaranteed and the settling time is exactly estimated. Finally, an exhaustive numerical analysis is presented to illustrate the effectiveness of the controller and the correctness of theoretical results. [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 purpose of this research is to address the problem of synchronization between two identical biological hyperchaotic snap oscillator systems with unknown parameters at a fixed time, as well as to design a new theory for synchronizing two different chaotic systems. Firstly, we designed an adaptive controller using Lyapunov stability and fixed-time stability theory to achieve synchronization between two identical biological hyperchaotic snap oscillator in fixed time under unknown parameters. Among the results obtained, we found that the synchronization time for system states occurred in a very short time compared to results in previous research. Secondly, we extended and generalized synchronization between non-identical chaotic systems by creating a theory for achieving synchronization in which adaptive control and fixed-time stability are combined. Through the new theory, the unknown parameters in chaotic systems were estimated, and the settling time was determined, which turned out to be very short and independent of the initial conditions of the system states. One of what makes the scheme important is that it can be easily applied to most chaotic and even hyperchaotic systems in the shortest possible time. Finally, we gave examples of different systems to test the feasibility and effectiveness of the scheme that was designed. [ABSTRACT FROM AUTHOR]

This research endeavour's primary attention is on the problems of stabilization and multiple disturbance rejection for a class of interval type-2 fuzzy stochastic systems that are prone to parameter uncertainties and multiple disturbances. Specifically, the multiple disturbances are classified into two aspects: the first aspect is matched disturbances, which emanate from an exogenous system, while the second aspect is norm-bounded mismatched disturbances. Further, to provide a precise estimation of the matched disturbances, a fuzzy rule-based multiple disturbance observer is built. Based on the estimated information from the framed observer, a disturbance estimation-based resilient control is devised that can withstand the effects of disturbances. Besides, the footprints of mismatched kind of disturbances are handled by employing the $ (\mathcal {Q},\mathcal {S},\mathcal {R})-\tilde \varsigma $ (Q , S , R) − ς ~ dissipative performance. Moreover, to insure the attainment of the foremost objective of this analysis, a collection of suitable criteria has been developed by means of linear matrix inequalities with the satisfied disturbance attenuation index through Lyapunov's theory of stability. In addition, under the lighting of adequate conditions, the gain matrices of the configured controller and the framed observer can be determined. Finally, two simulation examples are supplied as a conclusion to the examination, each serving to illustrate the potency and viability of the designed control scheme and the presented theoretical findings. [ABSTRACT FROM AUTHOR]

This research explores the complex dynamics of a Novel Four-Dimensional Fractional Supply Chain System (NFDFSCS) that integrates a quadratic interaction term involving the actual demand of customers and the inventory level of distributors. The introduction of the quadratic term results in significantly larger maximal Lyapunov exponents (MLE) compared to the original model, indicating increased system complexity. The existence, uniqueness, and Ulam–Hyers stability of the proposed system are verified. Additionally, we establish the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the system. Numerical simulations and MATLAB phase portraits demonstrate the chaotic nature of the proposed system. Furthermore, a dynamical analysis achieves verification via the Lyapunov exponents, a bifurcation diagram, a 0–1 test, and a complexity analysis. A new numerical approximation method is proposed to solve non-linear fractional differential equations, utilizing fractional differentiation with a non-singular and non-local kernel. These numerical simulations illustrate the primary findings, showing that both external and internal factors can accelerate the process. Furthermore, a robust control scheme is designed to stabilize the system in finite time, effectively suppressing chaotic behaviors. The theoretical findings are supported by the numerical results, highlighting the effectiveness of the control strategy and its potential application in real-world supply chain management (SCM). [ABSTRACT FROM AUTHOR]

The critical lateral buckling load of cantilever beams with IPE cross-section was calculated using analytical closed-form equations and numerical finite element analyses within the scope of the research. The equations suggested in the specifications for simply supported beams were used to calculate the buckling load of cantilever beams. The rationality of the values calculated due to this is not fully known. In the research, a single loading was made to the shear center at the free end of the cantilever beam. Cantilever length and section height were kept variable. As a result, it has been determined that there are partial differences in the analysis result obtained from the elastic stability theory and finite element method. Accordingly, the results obtained from ANSYS and SAP2000 analyses confirm each other. On the other hand, the results obtained using the formulation of Timoshenko and Gere, the calculation results made according to the AISC and DCCPSS regulations, and the results obtained from the LTBeam program confirm each other. However, it differs from the FEA analysis due to the cantilever beam length’s shortening and the section height increase. Thus, to obtain accurate and reliable results in the buckling load calculation of cantilever beams, the equations used in analytical calculations were optimized according to finite element analysis (FEA) results. As a result of the study conducted according to the error criteria, it was determined that the updated equation results gave similar results to the FEA results. [ABSTRACT FROM AUTHOR]

The dynamic vibration absorber with inerter and grounded stiffness (IG-DVA) is used to control a two-scale system subject to a weak periodic perturbation. The vibration suppression effect is remarkable. The amplitude of the main system coupled with absorber is significantly reduced, and the high frequency vibration completely disappears. First, through the slow-fast analysis and stability theory, it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system. After adding the dynamic vibrator absorber, the center in the autonomous system changes to an asymptotically stable focus, consequently suppressing the vibration in the non-autonomous system. Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system, thereby regulating the stability of the system. Transitioning from a qualitative standpoint to a quantitative approach, a comparison of the solutions before and after the introduction of the dynamic absorber reveals that, when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal, the high-frequency part in the analytical solution disappears. As a result, this leads to a reduction in the amplitude of the trajectory, achieving a vibration reduction effect. [ABSTRACT FROM AUTHOR]

Creating stable oscillations in the nonlinear dynamic of thermoacoustic stirling engines is an essential challenge for researchers. Hence, investigating this challenge is the main objective of this paper. In this regard, a novel systematic and parametric method using the practical stability theory is presented to investigate the stable oscillations (sufficient condition) of thermoacoustic stirling engines for the first time. In this regard, the goals of the problem, which included stable oscillations of the pistons are determined. In the following, based on the desired objectives of the nonlinear dynamic equations, the engine error is extracted. Based on the practical stability theory, a Lyapunov function is selected according to the dynamics of the problem. Then, a time derivative of the Lyapunov candidate function and its sign is determined later. According to the conditions presented for the practical stable theory (the positive definiteness of the Lyapunov function and the negative definiteness of its derivative), nine parametric conditions for the error dynamics of the thermoacoustic stirling engine are presented. Once these nine conditions are met, sufficient conditions (stable motion) will occur in engine dynamics. The noteworthy point is that the presented method is completely parametric, and this will make it possible to easily evaluate the effect of each parameter of the engine to reach sufficient conditions. Another interesting feature of the presented idea is to determine the accuracy of the design process, which can be determined using the value of the ultimate bound. In other words, the lower the value of the ultimate bound, the better the accuracy of the design. As a result, the design is close enough to the problem's objectives. Hence, in this work, the effect of the important parameters of the engine on the value of the ultimate bound is also evaluated. It is worth mentioning that in order to verify the effectiveness of the presented method, the data extracted from the constructed engine is used to check the sufficient condition and the effect of the parameters on the ultimate bound. The obtained results showed that the presented parametric method can examine the mentioned cases appropriately. In the end, it can be said that the main innovation and finding of this work is to investigate the sufficient condition of the thermoacoustic stirling engines using a parametric method (presenting nine parametric conditions). Through the utilization of this method, researchers can not only assess the sufficient condition but also investigate the impact of engine parameters on its performance before construction. This approach helps in reducing costs and time associated with the study. [ABSTRACT FROM AUTHOR]

This article revisits saturated stabilization of the feed‐forward systems that are subject to lower‐order perturbations, with the purpose of providing new analysis approaches. To carry out the saturation reduction analysis, we do not use the existing time‐interval based contradiction approach, but propose a Lyapunov function method; to deal with the reduced system (the closed‐loop system that does not contain saturation any longer), we do not use the "adding a power integrator" backstepping scheme, but propose an approach which is established by jointly using the vector Lyapunov function theory, a matrix measure stability theory and the switching systems theory. As a result, a quite number of inequality computations can be avoided, and the stability conditions summarized in two analysis procedures can be expressed by directly using the system parameters. This article also shows that the established approaches are applicable to the uncertain feedforward systems subject to linear input perturbation and consequently, allows to present new stabilizing control laws for several intractable under‐actuated systems. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the problem of adaptive tracking control for multi‐input and multi‐output (MIMO) non‐strict feedback systems with unmodeled dynamics and full state time‐varying constraints. To tackle the interference of unmodeled dynamics, the dynamic signal generated by the auxiliary system is used. Hyperbolic tangent function is used as a nonlinear mapping tool to transform the constrained system into an unconstrained one. Hysteresis quantizer is introduced to mitigate the chattering phenomenon and quantization error in the quantization signal. The derivative of virtual signal can be approximated more efficiently by command filter. Furthermore, an error compensation mechanism is established to mitigate the error introduced by the command filter. Unknown nonlinear functions are approximated by radial basis function neural networks (RBFNNs). Stability analysis of the proposed controller is performed through the Lyapunov stability theory and the output tracking error can be constrained within a specified range. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this investigation, we delve into the influence of throughflow on the phenomenon of bi-disperse convection within Rivlin-Ericksen fluid. In the context of examining bi-disperse convection within this specific type of fluid, the throughflow effect is considered to have a uniform vertical distribution. The primary focus of this study centers on evaluating the system’s linear stability. To achieve this, we employ normal mode analysis to compute the Darcy-Rayleigh number at the onset of convection. This Darcy-Rayleigh number is computed for both stationary and oscillatory convection modes. Furthermore, we conduct a comprehensive analysis and present the results in graphical form to illustrate the impact of various parameters, including Peclet number and kinematic viscoelastic parameter, on both stationary and oscillatory convection. Our research findings demonstrate that when Peclet number Pr1 < 0, it leads to destabilising effect on both stationary and oscillatory convections. Conversely, when Peclet number Pr1 > 0, it induces stabilising effect on both stationary as well as oscillatory convections. [ABSTRACT FROM AUTHOR]

Climate change is increasing the proportion of river networks experiencing flow intermittence, which in turn reduces local diversity (i.e., α‐diversity) but enhances variation in species composition among sites (i.e., β‐diversity), with potential consequences on ecosystem stability. Indeed, the multiscale theory of stability proposes that regional stability can be attained not only by local processes but also by spatial asynchrony among sites. However, it is still unknown whether and how scale‐dependent changes in biodiversity associated with river flow intermittence influence stability across spatial scales. To elucidate this, we here focus on multiple metacommunities of French rivers experiencing contrasting levels of flow intermittence. We clearly show that the relative contribution of spatial asynchrony to regional stability was higher for metacommunities of intermittent than perennial rivers. Surprisingly, spatial asynchrony was mainly linked to asynchronous population dynamics among sites, but not to β‐diversity. This finding was robust for both truly aquatic macroinvertebrates and for taxa that disperse aerially during their adult stages, implying the need to conserve multiple sites across the landscape to attain regional stability in intermittent rivers. By contrast, metacommunities of truly aquatic macroinvertebrates inhabiting perennial rivers were mainly stabilized by local processes. Our study provides novel evidence that metacommunities of perennial and intermittent rivers are stabilized by contrasting processes operating at different spatial scales. We demonstrate that flow intermittence enhances spatial asynchrony among sites, thus resulting in a regional stabilizing effect on intermittent river networks. Considering that climate change is increasing the proportion of intermittent rivers worldwide, our results suggest that managers need to focus on the spatial dynamics of metacommunities more than on local‐scale processes to monitor, restore, and conserve freshwater biodiversity. [ABSTRACT FROM AUTHOR]

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time adaptive practical tracking control for a class of high-order nonlinear systems with full-state constraints and input saturation. The state constraints are handled by applying nonlinear transformed functions (NTFs) and the input saturation is estimated by an auxiliary hyperbolic tangent function. On the basis of adding a power integrator technique and adaptive control method, an adaptive state feedback controller is designed for the closed-loop system. With the aid of finite-time stability theory, the tracking error converges to a bounded neighbourhood of the origin in a finite time, and all the signals in the closed-loop system are bounded. At last, a simulation example and a practical example are presented to show the effectiveness of the proposed control procedure. [ABSTRACT FROM AUTHOR]

In this study, dynamic formation tracking and interception are performed by controlling multi-agent using a Euler-like Lagrangian model. The purpose is to use the distance-based rigid graph method to control multi-agent, and ultimately achieve dynamic formation tracking and target interception of multi-agent. Initially, distance-based graph stiffness and back-stepping techniques were considered to address the formation control challenge. This method helps achieve the initial expected formation and effectively complete the formation mission. Leaders continue to chase the moving target, while followers stick to the expected arrangement. The leader then precisely tracks the moving target and surrounds it within the formation. By using Lyapunov stability theory with adaptive control, it is ensured that the total distance meets finite and consistent error limits. Finally, the numerical simulation of the interception plan was carried out by 6 multi-agents and 1 target at different times to verify the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

To improve the ride comfort and driving stability of automobiles, an optimal sliding mode control (OSMC) strategy based on the enhanced African vultures optimization algorithm (EAVOA) is proposed. Firstly, the structure and operating principle of a semi-active suspension system (SASS) with a magnetorheological damper (MRD) is comprehensively introduced. Secondly, the OSMC is designed based on a quarter-vehicle suspension model with two degrees of freedom (DOF) to meet the Hurwitz stability theory. Simultaneously, the EAVOA is employed to optimize the control coefficients of the sliding mode surface and the control law parameters. Finally, the EAVOA-OSMC control strategy is utilized to construct the simulation model in MATLAB/Simulink (R2018b), providing a comprehensive analysis for passive suspension systems (PSSs) and suspensions with SMC control. The simulation results demonstrate that the EAVOA-OSMC control strategy outperforms SMC controllers, offering a better control performance in real application. [ABSTRACT FROM AUTHOR]

To expand the application prospects of quadrotors in challenging scenes such as those with dense obstacles and narrow corridors, task-driven reconfigurable quadrotors are highly desirable. Aiming to address hazard missions, in this paper, translational reconfigurable quadrotors and rotational reconfigurable quadrotors are proposed with their assumptions and mathematical models. Related motion control laws were designed using model reference adaptive control (MRAC) theory based on Lyapunov stability theory, whose validity was demonstrated by sufficient numerical simulations. The simulation results verify the feasibility of the proposed control laws and reveal the important effect of time delay on the stability of the motion control system. Additionally, the dependence of motion control's stability on the time constant of reference system was discussed. [ABSTRACT FROM AUTHOR]

With the application of the two-tier capital agreement and the introduction of the three-tier capital agreement, the discussion of the role of banks’ capital in the monetary transfer mechanism and banks’ lending decisions has become more important. In this regard, in this research, the effect of the legal requirements of the Basel III Agreement on the lending power and financial stability of the banking sector in Iran has been investigated using the system of simultaneous equations. For this purpose, the data from 19 selected banks and financial institutions were used during the period of 2011-2019. The findings of the research showed that the legal requirements of Basel III had negative and significant effects on bank lending. It was also observed that the legal requirements of Basel III had positive and significant effects on the financial stability of banks. [ABSTRACT FROM AUTHOR]

A H ∞ robust adaptive nonlinear observer for state and parameter estimation of a class of Lipschitz nonlinear systems with disturbances is presented in this work. The objective is to estimate parameters and monitor the performance of nonlinear processes with model uncertainties. The behavior of the observer in the presence of disturbances is analyzed using Lyapunov stability theory and by considering an H ∞ performance criterion. Numerical simulations were carried out to demonstrate the applicability of this observer for a semi-active car suspension. The adaptive observer performed well in estimating the tire rigidity (as an unknown parameter) and induced disturbances representing damage to the damper. The main contribution is the proposal of an alternative methodology for simultaneous parameter and actuator disturbance estimation for a more general class of nonlinear systems. [ABSTRACT FROM AUTHOR]