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This research explores the efficacy of integrating nonlinear single-degree-of-freedom systems in the vibration control of rod coupling systems. By interlinking two rods with a nonlinear single-degree-of-freedom system as the intermediary, the study employs the Lagrange method (LM) to forecast nonlinear vibrational behaviors. The findings, substantiated by numerical analyses, affirm the precision of LM in gauging the amplitude responses when such a nonlinear system is utilized. The nonlinear dynamics, characterized by intricate vibrational patterns, peak jumping phenomena, and the migration of resonance zones, are induced by the nonlinear single-degree-of-freedom system. By fine-tuning the system's parameters, significant alterations in the vibrational states of the rod coupling system are achievable. This suggests that the application of a nonlinear single-degree-of-freedom system is a viable strategy for modulating vibrations in rod systems. Furthermore, optimal parameterization of this system is proven to effectively dampen vibrations, showcasing its potential as a sophisticated mechanism for vibration suppression in coupled rod configurations. [ABSTRACT FROM AUTHOR]

Fluctuation dynamics of an experimentally measured observable offer a primary signal for nonequilibrium systems, along with dynamics of the mean. While universal speed limits for the mean have actively been studied recently, constraints for the speed of the fluctuation have been elusive. Here, we develop a theory concerning rigorous limits to the rate of fluctuation growth. We find a principle that the speed of an observable's fluctuation is upper bounded by the fluctuation of an appropriate observable describing velocity, which also indicates a tradeoff relation between the changes for the mean and fluctuation. We demonstrate the advantages of our inequalities for processes with non-negligible dispersion of observables, quantum work extraction, and the entanglement growth in free fermionic systems. Our results open an avenue toward a quantitative theory of fluctuation dynamics in various non-equilibrium systems encompassing quantum many-body systems and nonlinear population dynamics. Fluctuation dynamics of an observable offers a primary signal for understanding non-equilibrium statistical mechanics. Here, the author derives a principle that the speed of an observable's fluctuation is upper bounded by the fluctuation of an observable describing velocity, which is valid for various non-equilibrium systems from quantum many-body systems to nonlinear population dynamics. [ABSTRACT FROM AUTHOR]

In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton's principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam's multidimensional system. [ABSTRACT FROM AUTHOR]

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables. For a high dimensional nonparametric nonlinear system, however, identifying whether a variable contributes or not is not easy. Therefore, based on the Fourier spectrum of density-weighted derivative, one novel variable selection approach is developed, which does not suffer from the dimensionality curse and improves the identification accuracy. Furthermore, a necessary and sufficient condition for testing a variable whether it contributes or not is provided. The proposed approach does not require strong assumptions on the distribution, such as elliptical distribution. The simulation study verifies the effectiveness of the novel variable selection algorithm. [ABSTRACT FROM AUTHOR]

This work investigates the Kraenkel-Manna-Merle (KMM) system, which models the nonlinear propagation of short waves in saturated ferromagnetic materials subjected to an external magnetic field, despite the absence of electrical conductivity. The study aims to explore and derive new solitary wave solutions for this system using two distinct methodological approaches. In the first approach, the KMM system is transformed into a system of nonlinear ordinary differential equations (ODEs) via Lie group transformation. The resulting ODEs are then solved analytically using a similarity invariant approach, leading to the discovery of various types of solitary wave solutions, including bright, dark, and exponential solitons. The second approach involves applying wave and Galilean transformations to reduce the KMM system to a system of two ODEs, both with and without damping effects. This reduced system is further analyzed to investigate its bifurcation behavior, sensitivity to initial conditions, and chaotic dynamics. The analysis reveals the presence of strange multi-scroll chaotic dynamics in the presence of damping and off-boosting dynamics without damping. In addition to these approaches, the study also applies the planar dynamical theory to obtain further new soliton solutions of the KMM system. These solitons include bright, kink, dark, and periodic solutions, each of which has been visualized through 3D and 2D graphs. The results of this research provide new insights into the dynamics of the KMM system, with potential applications in magnetic data storage, magnonic devices, material science, and spintronics. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework combining proper generalized decomposition (PGD) with the shooting method to determine the steady-state response of nonlinear dynamical systems upon a general periodic input. The proposed PGD approximates the response as a low-rank separated representation of the spatial and temporal dimensions. The Galerkin projection is employed to formulate the subproblem for each dimension, then the fixed-point iteration is applied. The subproblem for the spatial vector can be regarded as computing a set of reduced-order basis vectors, and the shooting problem projected onto the subspace spanned by these basis vectors is defined to obtain the temporal coefficients. From this procedure, the proposed framework replaces the complex nonlinear time integration of the full-order model with the series of solving simple iterative subproblems. The proposed framework is validated through two descriptive numerical examples considering the conventional linear normal mode method for comparison. The results show that the proposed shooting method based on PGD can accurately capture nonlinear characteristics within 10 modes, whereas linear modes cannot easily approximate these behaviors. In terms of computational efficiency, the proposed method enables CPU time savings of about one order of magnitude compared with the conventional shooting methods. [ABSTRACT FROM AUTHOR]

Saturation nonlinearity exists widely in various practical control systems. Modeling and parameter estimation of systems with saturation nonlinearity are of great importance for analyzing their characteristics and controller design. This paper focuses on the identification issue of the input nonlinear Box–Jenkins systems with saturation nonlinearity. The input saturation nonlinearity is presented as a linear parametric expression through the application of a switching function, then the identification model of the system is derived by using the key term separation technique. Based on this model and the data filtering technique, the filtering identification model of the system is given by changing the system structure without changing the relationship between the input and output, which can reduce the interference of the colored noise and improve the identification accuracy. Then a data filtering-based maximum likelihood gradient-based iterative algorithm is proposed to estimate the unknown parameters. The maximum likelihood gradient-based iterative algorithm is provided for comparison. The feasibility and superiority of the proposed approach are emphasized by a simulation example. [ABSTRACT FROM AUTHOR]

This paper deals with the local bifurcation analysis of a nanotube with a nanostring passing through it. Eringen's two-phase local/nonlocal model and Eringen's differential model are employed as constitutive equations. The governing equations are derived as two nonlinear first-order systems of ordinary differential equations. Nonlinear analysis is performed by using the Lyapunov–Schmidt method. The influence of the small length scale parameter and the phase parameter on critical buckling load, type of bifurcation and post-buckling shape of the nanotube is examined for both types of constitutive equations. Depending on the values of the small length scale parameter and the phase parameter, the critical buckling load corresponding to Eringen's two-phase local/nonlocal model can be greater or less than that corresponding to Eringen's differential model. It is shown that for both models supercritical pitchfork bifurcation occurs. The post-buckling shapes of nanotube, obtained by numerical integration, exhibit a qualitative difference between the two models. [ABSTRACT FROM AUTHOR]

This paper aims to propose a more efficient control algorithm for improving the control performance of uncertain nonlinear systems. A novel improved Takagi–Sugeno–Kang (TSK) wavelet type-2 fuzzy brain emotional learning controller (ITSKWT2FBC) is proposed. The proposed ITSKWT2FBC contains a brain emotional learning controller (BELC) combined with an improved TSK wavelet type-2 fuzzy system. By taking the advantages of BELC and the improved wavelet type-2 TSK fuzzy system, the control performance of this controller can be improved. The adaptive laws of controller parameters are derived from the defined Lyapunov function and gradient descent method. Moreover, the system stability can be guaranteed based on the Lyapunov stability theory. Finally, three nonlinear systems, a double inverted pendulum system, a Mackey–Glass time series prediction (TSP) and a four dimensional (4D) chaotic system synchronization are simulated to illustrate the effectiveness of the proposed method. The simulation results have demonstrated the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

As an essential tool for processing fuzzy or chaotic information, the main feature of the first-order Takagi–Sugeno (T–S) neuro-fuzzy model is utilizing a set of IF-THEN fuzzy rules to represent non-linear systems, showcasing commendable non-linear approximation ability and significant interpretability. However, the coexistence of linear rules and the affiliation function of fuzzy sets makes the integer-order gradient descent method (IOGDM), commonly used in training the first-order T–S neuro-fuzzy model, fail to accurately capture the intricate relationships among weights, resulting in the error function struggling to converge rapidly to low values. To enhance the convergence speed and training accuracy of the first-order T–S neuro-fuzzy model during the training process, a fractional-order gradient descent method (FOGDM) is proposed to update the fuzzy rule parameters and neural network weights of the model in this paper. By subdividing the gradient into fractional orders, FOGDM exhibits heightened flexibility in gradient adjustments, thus better capturing the complex non-linear relationships among parameters during the optimization process. The weak and strong convergence of the proposed approach is meticulously demonstrated in this paper, ensuring that the weight of error functions converges to a constant value and that the gradient of the error functions tends toward zero, respectively. Simulation results analysis indicates that, compared to IOGDM, FOGDM exhibits faster convergence speed and more significant generalization capabilities. [ABSTRACT FROM AUTHOR]

This work reflects on a fast finite-time control issue of nonlinear systems. Both the unmeasurable states of system and unknown nonlinearities are consideblack in this article. A state observer is constructed to eliminate the constraint that the states of system need to be measublack. By utilizing the fuzzy logic systems (FLSs), the unknown nonlinearities are coped with. The singularity issue from the virtual controllers design is skillfully tackled by constructing the smooth piecewise function. The practical fast finite-time stability criterion (fast FTS criterion) is firstly established. Then, a fast finite time output feedback controller is established. By means of the proposed stability criterion, the fast finite time stability of the closed-loop system is guaranteed. Eventually, two examples demonstrate the efficacy of the proposed control strategy. [ABSTRACT FROM AUTHOR]

To maintain the vibrations of the gyroscope proof mass, an adaptive super-twisting sliding mode control (STSMC) of a micro gyroscope based on a two-loop recursive fuzzy neural network (TLRFNN) is designed. In order to estimate the unknown parameters of the nonlinear system online, an adaptive technology is adopted based on the parameter linearization of the nonlinear model. In response to the problem of system chattering caused by ordinary sliding mode control, the STSMC with the advantages of high order sliding mode and conventional sliding mode is introduced. Aiming at the problem of uncertainty in system parameters, a two-loop recursive fuzzy neural network approximation with the competence over the storage of a priori information is utilized. All adaptive laws are obtained under the Lyapunov stability framework which contributes to the stability of the system. The simulation research shows the system exhibits good tracking performance and maintains a small tracking error under the control of the suggested control system. The effect is measured by calculating the root mean square error (RMSE) parameter of the tracking error and the proposed control system achieves a tracking effect of and in the x and y directions, respectively. [ABSTRACT FROM AUTHOR]

This paper presents a novel numerical approach for approximating the solution of the model describing the infection of C D 4 + T -cells by the human T-cell lymphotropic virus I (HTLV-I).The proposed method utilizes the operational matrix along with spectral method to convert the fractional model into a system of nonlinear algebraic equations. The Levenberg-Marquardt algorithm efficiently solves these equations. The study includes theoretical convergence analysis and error bounds to establish the validity of the proposed method. Through several test problems, we demonstrate the effectiveness and accuracy of the approach. We compare its performance and reliability to other existing methods in the literature. The results indicate that the proposed method is a reliable and efficient approach for solving the model. [ABSTRACT FROM AUTHOR]

In this research article, a fractional-order nonlinear Proportional plus Integral plus Derivative (FONPID) controller is incorporated into a complex surge tank system where the gains of the controller are tuned through a machine learning control approach to control the nonlinear variations in level setpoints. Obtaining a proper output response from a non-linear system is challenging and demanding for researchers. In this case, nonlinear Proportional plus Integral plus Derivative (NPID) and conventional Proportional plus Integral plus Derivative (PID) controllers are not sufficient for obtaining desired output robustness in the system performances. Hence, to fulfill the need for an adaptive controller for a spherical surge tank system, FONPID can be a better choice. The machine learning control is applied to the gains of the FONPID controller with the Cuckoo Search Optimization Algorithm (CSA), a swarm-intelligence algorithm mostly known for its levy flights and searching pattern for best quality eggs. The whole idea of using machine learning control is to tune the gains to make the controller adaptive towards parametric variation and uncertainties. The machine learning control uses the Integral of Absolute Error (IAE) performance index criteria as the minimum objective function of CSA for tuning of gain constraints of the controllers. The proposed FONPID controller is then compared with NPID and conventional PID controllers to stabilize level setpoint variations. The results demonstrate that the FONPID controller gives better, robust, and optimum results over NPID and PID controllers. In comparison to NPID and PID controllers, the FONPID controller performs significantly better, with gains ranging from 11.68% to 215.31% across various operational modes and system parametric variations. [ABSTRACT FROM AUTHOR]

This study proposes a novel method for predicting the axial stress of bolts by analyzing their nonlinear ultrasonic characteristics. We first derive the theoretical relationship between the relative nonlinear coefficient and stress. Then, we build a detection system based on nonlinear ultrasonic technology to measure the axial stress of bolts. We find that the relative nonlinear coefficient of bolts increases with the stress, and the increase rate becomes faster when the stress exceeds a certain value. This indicates that the relative nonlinear coefficient is very sensitive to the stress change and can be used to accurately characterize the bolt axial stress. We normalize the relative nonlinear coefficient and fit the experimental data to create a bolt axial stress prediction model. We also use both nonlinear ultrasonic and linear ultrasonic methods to predict the bolt axial stress. The prediction results shows that when the axial stress exceeds 200 MPa, the prediction error of nonlinear ultrasonic is less than 5%, indicating that the prediction accuracy is significantly better than that of the linear ultrasonic method. In summary, this study demonstrates the effectiveness of nonlinear ultrasonic technology in detecting axial stress in bolts and offers a novel approach for the evaluation and prediction of bolt axial stress under service conditions. [ABSTRACT FROM AUTHOR]

Cardiac rhythms are related to heart electrical activity, being the essential aspect of the cardiovascular physiology. Usually, these rhythms are represented by electrocardiograms (ECGs) that are useful to detect cardiac pathologies. Essentially, the heart activity starts in the sinoatrial node (SA) node, the natural pacemaker, propagating to the atrioventricular node (AV), and finally reaching the His-Purkinje complex (HP). This paper investigates the control of cardiac rhythms in order to induce normal rhythms from pathological responses. A mathematical model that presents close agreement with experimental measurements is employed to represent the heart functioning. The adopted model comprises a network of three nonlinear oscillators that represent each one of the cardiac nodes, connected by delayed couplings. The pathological behavior is induced by an external stimulus in the SA node. An adaptive controller is proposed acting in the SA node considering an strategy based on the signal obtained by the natural pacemaker and its regularization. The incorporation of adaptive compensation in a Lyapunov-based control scheme allows the compensation for the unknown dynamics. The controller ability to deal with interpatient variability is evaluated by assuming that the heart model is not available to the controller design, being used only in the simulator to assess the control performance. Results show that the adaptive term can reduce the control effort by around 3% while reducing the tracking error by 20%, when compared to the conventional feedback approach. Additionally, the controller can avoid abnormal rhythms, turning the ECG closer to the expected normal behavior and preventing critical cardiac responses. Therefore, this work demonstrates that an adaptive controller can be used to regulate the ECG signal without prior information about the system and disregarding inter- and intrapatient variability. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for a class of unknown heterogeneous nonlinear multi-agent systems via a network with random packet dropouts. Based on the dynamic linearization technique, novel model-free adaptive consensus protocols with the data compensation mechanism are designed for both leaderless and leader-following cases. The advantage of this approach is that only neighborhood input and output data of the agents are required in the protocol design. For the stability analysis, a new Squeeze Theorem based method is developed to derive the theoretic results instead of the traditional contraction mapping principle used in model-free adaptive control. It is shown that the consensus can be achieved for both leaderless and leader-following cases if the communication topology is strongly connected. Finally, numerical simulations verifying the correctness of the theoretical results are given. [ABSTRACT FROM AUTHOR]

The existence of nonautonomous solitons on a continuous wave background in an inhomogeneous nonlinear medium with temporally varying dispersion, cubic nonlinearity, quintic nonlinearity, and self-steepening effect is reported. Further, the precise conditions for the formation of these localized waves in the nonlinear system are determined. It is found that these nonautonomous solitons nicely exhibit a frequency chirp property which originates from the self-steepening process. It is also demonstrated that the velocity of these chirped nonautonomous solitons is time-dependent, and it can be controlled more efficiently by selecting the appropriate profile of the varying-in-time dispersion parameter. The results reveal that interesting motion trajectories of nonautonomous solitons including the acceleration, deceleration, reversion of propagation direction, and stopping behaviors can be achieved through different dispersion profiles. [ABSTRACT FROM AUTHOR]

In this paper, a novel data-driven distributed optimal control (DDOC) scheme via neighbourhood optimization is proposed for affine nonlinear interconnected systems with unknown dynamics. In this scheme, each subsystem merely broadcasts its local information to its neighbours, and receives information only from them. The proposed distributed method is established based on a hybrid structure mainly consisting of both algebraic and analytical parts, in which two neural networks (NN) are simultaneously tuned in an online manner by using neighbourhood information for each subsystem. To tackle the unknown dynamics, a new distributed data-driven model is established to reconstruct subsystem dynamics and estimate system states. Moreover, by using the Hamilton–Jacobi–Bellman (HJB) based formulation, a distributed NN-based optimal control is designed to minimize both the performance of the corresponding subsystem and its neighbours, in the presence of unknown dynamics. Through Lyapunov's direct method, the uniformly ultimately boundedness (UUB) of the overall closed-loop system is guaranteed, and the provided results of the stability are exploited to find updating rules for the NN-based observer and controller. Finally, two illustrative examples are investigated to certify the efficacy of the new distributed optimal control (DOC). [ABSTRACT FROM AUTHOR]

This paper deals with the attraction–repulsion chemotaxis system with nonlinear productions and logistic source, u t = ∇ ⋅ (D (u) ∇ u) − ∇ ⋅ (Φ (u) ∇ v) + ∇ ⋅ (Ψ (u) ∇ w) + f (u) , v t = Δ v + α u k − β v , τ w t = Δ w + γ u l − δ w , τ ∈ { 0 , 1 } , in a bounded domain Ω ⊂ R n (n ≥ 1 ), subject to the homogeneous Neumann boundary conditions and initial conditions, where D , Φ , Ψ ∈ C 2 [ 0 , ∞) are nonnegative with D (s) ≥ (s + 1) p for s ≥ 0 , Φ (s) ≤ χ s q , ξ s g ≤ Ψ (s) ≤ ζ s j , s ≥ s 0 , for s 0 > 1 , the logistic source satisfies f (s) ≤ s (a − b s d) , s > 0 , f (0) ≥ 0 , and the nonlinear productions for the attraction and repulsion chemicals are described via α u k and γ u l , respectively. When k = l = 1 , it is known that this system possesses a globally bounded solution in some cases. However, there has been no work in the case k , l > 0 . This paper develops the global boundedness of the solution to the system in some cases and extends the global boundedness criteria established by Tian, He, and Zheng (2016) for the attraction–repulsion chemotaxis system. [ABSTRACT FROM AUTHOR]

We provide the well-posedness for a partially dissipative viscous system of balance laws in smooth Sobolev spaces under the same assumptions as in the case of inviscid balance laws. A priori estimates for coupled hyperbolic-parabolic linear systems with coefficients having limited regularity are derived using Friedrichs regularization and Moser-type estimates. Local existence for nonlinear systems will be established using the results of the linear theory and a suitable iteration scheme. The local existence theory is then applied to the Kuznetsov–Westervelt equation with damping for nonlinear wave acoustic propagation. Existence of global solutions for small data and their asymptotic stability are established. [ABSTRACT FROM AUTHOR]

Nonlinear vibration isolators can offer a high static stiffness alongside a low dynamic stiffness and so they have better isolation performance than conventional linear devices. In this paper, the models of the one-degree-of-freedom (DOF) and two-DOF bottom-springs grounded (BG) nonlinear vibration isolators with quasi-zero stiffness (QZS) characteristic are analyzed. In order to further improve the isolation performance of the 2-DOF BG nonlinear QZS vibration isolator, the H-infinity optimal control problem based on output feedback is studied. The nonlinear element of the vibration isolator is linearized by Taylor series expansion and ignoring the higher order term and then the whole nonlinear system is decomposed into linear part and nonlinear part. The output feedback H-infinity optimal controller designed for the linear part is proved to be the H-infinity optimal controller of the original nonlinear system. The controller has constraints, and the constraint equation contains input-related terms. The solution methods recorded in the existing literature are invalid for this situation. Therefore, a new linear matrix inequality for solution is given in this paper. To test the performance of the controller, numerical simulation is studied under the typical harmonic excitation. The results show that the designed controller for the 2-DOF BG nonlinear QZS vibration isolator has a good vibration isolation effect. [ABSTRACT FROM AUTHOR]

The industrial standard in the design and development process of NVH(Noise Vibration Harshness) characteristic of brakes is the application of Finite Element(FE) models with a high number of degrees of freedom in the range of one or several millions. Nevertheless, parallel experimental investigations are still indispensable. On the other hand, minimal models with, due to the inclusion of the self-excitation process, at least two degrees of freedom are well known to be capable to explain qualitatively phenomena as instability of the desired non-vibrating solution or limit cycle oscillation but are in general very inaccurate in predicting the dynamics of a specific real brake. This is because the underlying physical assumptions are already too restrictive and model parameters (especially those referring to nonlinearities) are widely unknown. To overcome this problem, the data-driven modeling approach SINDy(Sparse Identification of Nonlinear Dynamics) is applied to identify appropriate nonlinear functions for a brake squeal minimal model. A problem thereby is the limited database. It turns out that the naive implementation of the method yielding the lowest possible residuum does not necessarily provide physically meaningful models and results, respectively. Instead, a constrained model that incorporates physical knowledge is used to robustly identify parameters and reproduce realistic dynamic behavior. Thereby, several appropriate models with coexisting limit cycles and stationary equilibrium are identified. In particular, it was found that the angular position of the brake drum has a significant influence on the model parameters and therefore must be taken into account in a model with long-term validity. [ABSTRACT FROM AUTHOR]

In this paper, a new dynamic event-triggered control solution is presented for state-constrained strict-feedback nonlinear systems. The current barrier Lyapunov function is required to assume or remove the feasibility conditions for virtual control signals. In this paper, a new scheme is proposed to guarantee the designed virtual control signals satisfy feasibility conditions. By introducing a dynamic variable into the event-triggered schedule, the dynamic event-triggered control scheme is established by using backstepping iterative design procedure. Moreover, the theoretical analysis illustrates that the proposed control solution can ensure the boundedness of all signals in SNS. Finally, simulation example is given to showcase the availability of the developed method. [ABSTRACT FROM AUTHOR]

Solving nonlinear problems stands as a pivotal domain in scientific exploration. This study introduces a novel method comprising basic and multi-step components. The proposed iterative method has a convergence order of 2 m + 1 , where m is the step number for m ≥ 2 . Since our proposed method has only one Fréchet derivative evaluation and its inversion, the method has a higher efficiency index than previous methods. To comprehensively evaluate the method's performance in efficiency, accuracy, and attraction basin behavior, numerical tests are presented. Furthermore, we applied the proposed method to solve renowned equations like Hammerstein's integral equation and Berger's equation after transforming them into nonlinear systems. [ABSTRACT FROM AUTHOR]

In this paper, efficient algorithms will be studied for solving nonlinear saddle point problems from the elliptic optimal control problems. Based on the preconditioned inexact Uzawa (PIU) algorithmic framework, an improved preconditioned inexact Uzawa (I-PIU) algorithmic framework will first be constructed for solving a class of block-structured nonlinear systems, which possess a more general form of the nonlinear saddle point systems. When the I-PIU algorithmic framework is used for solving the block-structured nonlinear systems, a detailed theoretical analysis of the global convergence properties is proposed under the case that the nonlinear operator is single-valued. Besides, a special I-PIU method is established based on a new matrix splitting technique at the first iterative step of the I-PIU algorithmic framework, and then we establish the detailed theoretical results of the convergence. Finally, some numerical experiments are given to demonstrate the efficiency of the I-PIU method. [ABSTRACT FROM AUTHOR]

In the fault-tolerant control tasks of nonlinear systems, unmeasurable states, time delay and actuator faults are considered to be the main factors hindering effective controller design and tracking performance improvement. To solve these problems, firstly, a state observer is established to estimate the unmeasurable of the system and the prescribed performance control based on error transformation is presented to maintain system efficiency and reliability. Secondly, the problem of controller design caused by input delay is effectively solved by constructing an auxiliary tracking error and auxiliary system and combining with the well-designed Lyapunov-Krasovskii functionals. Thirdly, the newly employed damping term in the intermediate control law is utilized to compensate for the possibly unlimited number of faults. Then, it is proved that all signals are semi-global practical finite-time stable based on the backstepping technique. Meanwhile, the tracking error can converge to a specified range within finite time. Finally, comparative simulations are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The present study focuses on the master–slave synchronization issue for switched nonlinear time-delay systems based on quantization and switching event-triggered strategy (ETS). The logarithmic quantizer and the switching ETS that is represented by a transition between the periodic sampled-data control and the general continuous ETS are adopted to improve resource utilization and adjust data transmission. According to the event-triggered sampled signal, the synchronization error system with asynchronous switching signal is modeled. In virtue of multiple Lyapunov functional approach, the sufficient conditions are obtained to guarantee the error system is exponentially stable by developing some linear matrix inequalities (LMIs), from which the synchronizing controller is orchestrated. Lastly, the reliability of the proposed methods is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In the paper, a dynamic surface-based adaptive fuzzy fixed-time fault-tolerant control scheme is developed for nonstrict feedback nonlinear systems with non-affine faults. Firstly, the computational complexity is reduced by adopting dynamic surface control technique, and unknown nonlinear functions are approximated with the help of fuzzy logic systems. Secondly, non-affine faults involving system states and controller output are taken into account and treated by transforming it into nonlinear in the unknown parameters. Then, under the framework of fixed-time stability, a novel adaptive fuzzy fault-tolerant control strategy is designed so that the closed-loop system is semi-globally practically fixed-time stable. Finally, a numerical simulation and a model simulation are given to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of predictor-based fast finite-time fuzzy dynamic surface control for the nonlinear systems with strict-feedback structure is considered. Different from the traditional fuzzy dynamic surface control method, the proposed method utilizes prediction errors to update learning parameters for improving fuzzy logic systems learning behaviors in this paper. This technique can estimate the system unknown function smoothly and cannot result in high-frequency oscillations due to the existence of the overlarge adaptive gains. In addition, based on fast finite-time theorem and backstepping control technique, the developed controller can ensure all signals of the closed-loop are bounded at a finite time. Eventually, the illustrative examples are given to validate the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

In this article, an adaptive prescribed performance tracking control scheme is proposed for switched nonlinear systems with output dead zone and unmeasured state variables using an adaptive fuzzy approach. Fuzzy logic systems are utilized to learn the unknown nonlinear functions. The output nonlinearity is resolved via introducing Nussbaum function. The novelty of this article is that a shift function is utilized to break the strict restriction that the initial value of the tracking error must be within the initial value of the finite-time performance function. In addition, a switched observer is adopted to reduce the conservativeness caused by the use of a common observer. Then, by combining the average dwell time scheme and the backstepping technology, a novel observer-based fuzzy adaptive controller is developed, which can assure that all the closed-loop signals of the switched systems are bounded under a type of slowly switching signals and the tracking error converges to a pre-specified range in finite time even if the initial value of the tracking error is greater than the performance function. Finally, the simulation results are shown to verify the feasibility of the presented control scheme. [ABSTRACT FROM AUTHOR]

Tracking is a crucial problem for nonlinear systems as it ensures stability and enables the system to accurately follow a desired reference signal. Using Takagi–Sugeno (T–S) fuzzy models, this paper addresses the problem of fuzzy observer and control design for a class of nonlinear systems. The Takagi–Sugeno (T–S) fuzzy models can represent nonlinear systems because it is a universal approximation. Firstly, the T–S fuzzy modeling is applied to get the dynamics of an observational system in order to estimate the unmeasurable states of an unknown nonlinear system. There are various kinds of nonlinear systems that can be modeled using T–S fuzzy systems by combining the input state variables linearly. Secondly, the T–S fuzzy systems can handle unknown states as well as parameters known to the indirect adaptive fuzzy observer. A simple feedback method is used to implement the proposed controller. As a result, the feedback linearization method allows for solving the singularity problem without using any additional algorithms. A fuzzy model representation of the observation system comprises parameters and a feedback gain. The Lyapunov function and Lipschitz conditions are used in constructing the adaptive law. This method is then illustrated by an illustrative example to prove its effectiveness with different kinds of nonlinear functions. A well-designed controller is effective and its performance index minimizes network utilization—this factor is particularly significant when applied to wireless communication systems. [ABSTRACT FROM AUTHOR]

In this manuscript, a general class of Jacobian-free iterative schemes for solving systems of nonlinear equations is presented. Once its fourth-order convergence is proven, the most efficient sub-family is selected in order to make a qualitative study. It is proven that the most of elements of this family are very stable, and this is checked by means on numerical tests on several problems of different sizes. Their performance is compared with other known Jacobian-free iterative procedure, being better in the most of results. [ABSTRACT FROM AUTHOR]

We present a novel data-driven Model Predictive Control (MPC) algorithm for nonlinear systems. The method is based on recent extensions of behavioural theory and Willem's Fundamental Lemma for nonlinear systems by the means of adequate Input–Output (IO) quasi-Linear Parameter-Varying (qLPV) embeddings. Thus, the MPC is formulated to ensure regulation and IO constraints satisfaction, based only on measured datasets of sufficient length (and under persistent excitation). The main innovation is to consider the knowledge of the function that maps the qLPV realisation, and apply an extrapolation procedure in order to generate the corresponding future scheduling trajectories, at each sample. Accordingly, we briefly discuss the issues of closed-loop IO stability and recursive feasibility certificates of the method. The algorithm is tested and discussed with the aid of a numerical application. [ABSTRACT FROM AUTHOR]

This article presents an improved data-driven adaptive control structure to address the problem of input and output saturation in unknown nonlinear systems with multiple inputs and multiple outputs. In the suggested structure, a virtual model of the controlled system is initially built utilizing a multi-layered group method of data handling neural network. The control signal is then applied to this virtual model to predict the output before being applied to the system. If the predicted output is saturated, the control signals are readjusted to prevent saturation and are then applied to the system. By using this proposed structure, the performance of model-free adaptive control against input/output saturation phenomena is improved and the occurrence of saturation is prevented. Based on Lyapunov's theory, the stability of the suggested structure is proven. The controller has been applied to an interconnected three-tank system and a subway train which results clearly illustrate the advantages of the suggested method over the traditional form of model-free adaptive control design. [ABSTRACT FROM AUTHOR]

Vibrations in mechanical systems with geometric symmetry have been studied. It has been shown that, in systems with a low level of asymmetry, stratification of multiple natural frequencies occurs, which leads to instability of forced vibrations in this frequency range, as well as to beats occurring in the course of natural vibrations. In the case of mechanical systems, symmetrically arranged structural elements usually have several degrees of freedom or represent separate subsystems. Therefore, block symmetry operators and basis vectors that characterize the interactions between these structural elements determined by the symmetry conditions have been introduced. It has been shown that, for systems with a symmetry hierarchy, the resulting symmetry operator represents the product of the operators corresponding to each symmetry group. It has been found that the basis vectors for a given type of symmetry remain the same for nonlinear systems with the same type of symmetry. Their use makes it possible to divide the initial equations with an odd nonlinearity function into independent nonlinear equations, each of which describes its own coordinate. The mathematical apparatus of the theory of group representation is used. [ABSTRACT FROM AUTHOR]

Multi-year La Niña events cause prolonged climate disruptions worldwide, but a systematic understanding of the underlying mechanisms is not yet established. Here we show using observations and models from the sixth phase of Coupled Model Intercomparison Project that a greater frequency of consecutive La Niña events is tied to the upper equatorial Pacific Ocean when it favors more rapid heat discharge. The propensity for heat discharge is underscored by negative skewness in upper-ocean heat content, underpinned by southward tropical Pacific wind shift during austral summer. Models with stronger westerly anomalies south of the equator simulate steeper east-to-west upward tilt of the thermocline that is favorable for a greater discharge rate. This highlights the crucial role of the southward wind shift in the nonlinear system of the El Niño-Southern Oscillation. The large inter-model spread in multi-year La Niña processes underscores the need in constraining models for reliable climate prediction and projection. [ABSTRACT FROM AUTHOR]

We consider a system of two nonlocal and nonlinear partial differential equations that describe some aspects of yeast cell-cell communication. We study local and global existence and uniqueness of solutions. We consider mild solutions and we perform bilinear and trilinear fixed point arguments in suitable functional spaces. [ABSTRACT FROM AUTHOR]

We investigate the interior regularity to nonlinear subelliptic systems in divergence form with drift term for the case of superquadratic controllable structure conditions in the Heisenberg group. On the basis of a generalization of the A -harmonic approximation technique, C 1 -regularity is established for horizontal gradients of vector-valued solutions to the subelliptic systems with drift term. Specially, our result is optimal in the sense that in the case of Hölder continuous coefficients we directly attain the optimal Hölder exponent for the horizontal gradients of weak solutions on the regular set. [ABSTRACT FROM AUTHOR]

This paper explores nonlinear control systems within a finite dimensional Euclidean space. To guide the system towards a compact set at a specific time instant, the approach presented in this paper relies on the construction of approximate solvability sets. The Runge–Kutta methods, coupled with distance clustering, is employed to construct these approximate solvability sets. Simultaneously, the corresponding controls are recorded. The effectiveness of our theoretical results is demonstrated through simulation results. [ABSTRACT FROM AUTHOR]

Turnpike phenomena of nonlinear port-Hamiltonian descriptor systems under minimal energy supply are studied. Under assumptions on the smoothness of the system nonlinearities, it is shown that the optimal control problem is dissipative with respect to a manifold. Then, under controllability assumptions, it is shown that the optimal control problem exhibits a manifold turnpike property. [ABSTRACT FROM AUTHOR]

Four control systems are generated using Matlab software based on different regulators for the granulation process in a fluidized bed: PID controller and optimal LQR for linear systems and MPC and those based on fuzzy logic for nonlinear systems. For each control system, transient characteristics are obtained and system efficiency indicators are given. [ABSTRACT FROM AUTHOR]

We obtain new Lyapunov-type inequalities for a nonlinear system including a p-relativistic operator and a q-prescribed curvature operator under the Dirichlet or antiperiodic boundary condition. [ABSTRACT FROM AUTHOR]

We consider the problem of controlling the nonlinear 5-dimensional systems that are induced by horizontal vector fields and which together with their commutators generate some Cartan algebra depending linearly on two piecewise constant controls. We also study the properties of solutions to the systems on interpreting a solution as a horizontal -broken line on the canonical Cartan group , where the segments of are segments of integral curves of the vector fields of the form with . As regards , we prove that 4 is the minimal number such that every two points can be joined by some with . Thus, we obtain the best version of the Rashevskii–Chow theorem on the Cartan group. We also show that the minimal number of segments of a closed horizontal broken line on equals 6. [ABSTRACT FROM AUTHOR]

This article focuses on the fixed-time stability of a class of nonlinear systems with uncertain disturbances and time-varying delays. Different from other papers, the second-order sliding mode control algorithm (SOSMCA) is developed in this article to study the fixed-time stability of nonlinear systems for the first time. Additionally, the novel sliding mode surface (SMC) and second-order SMC are presented. And the stability and reachability of the sliding-mode dynamics under a faster settling time are demonstrated. Finally, the applicability and validity of the obtained SOSMCA are demonstrated by a simulation example with the F-404 aircraft engine model. [ABSTRACT FROM AUTHOR]

Based on the significant weather report, CG lightning, composite radar reflectivity, and ERA5 reanalysis data, we first studied the spatiotemporal distribution characteristics of four types (only severe convective wind (SCW); SCW and hail; SCW and short-duration heavy rainfall (SDHR); and SCW, hail, and SDHR) of convective weather events related to SCW during the warm season (May to September) from 2011 to 2018 in North China. Second, severe convective cases producing SCW were selected to statistically analyze the initiation, decay, lifetime, and organizational characteristics of convective systems. Finally, using ERA5 reanalysis data and conventional surface observation data, preconvective soundings were constructed to explore the differences in environmental conditions for initiating convective systems between SCW and non-SCW. The results indicate that mixed-type of SCW and SDHR events occur more frequently over plains, while other types of convective weather occur more frequently over mountains. The frequency peak of SCW occurs in June, while mixed convective weather peaks in July. The initiation time of convective systems is concentrated between 1000 and 1300 BST, with apeak at 1200 BST. Over mountains, the daily peaks of ordinary and significant SCW generally occur at 1700–1800 BST and 1600–1700 BST, respectively, while over plains, the peak of ordinary SCW typically lags behind that of mountains by 1–2 hours. Additionally, SCW systems are mainly initiated over mountains, with most lifetimes lasting 7–13 hours. Nonlinear convective systems produce the most SCW events, followed by trailing-stratiform convective systems. The convective available potential energy (CAPE), downdraft convective available potential energy, and the temperature difference between 850 and 500 hPa can all distinguish between SCW systems and non-SCW systems occurring over plains. Compared to non-SCW convective systems, SCW convective systems over mountains are more likely to occur in environments with less precipitable water, while SCW convective systems over plains are more likely to occur in environments with higher CAPE and stronger deep-layer wind shear. [ABSTRACT FROM AUTHOR]

This study presents the development of sliding mode control (SMC) using the diagonal recurrent neural network (DRNN) for nonlinear systems. Firstly, the SMC for linear systems is developed for nonlinear coupled tank system. Second, the DRNN is used to design the equivalent part of the SMC law, which is performed to approximate the dynamics of a controlled process. Third, the sliding surface for the switching control is developed using the DRNN. The DRNN parameters are tuned using Lyapunov function to achieve the controlled process stability. For the developed scheme, discontinuous signum function is used to compensate the chattering phenomenon. The developed scheme is applied for controlling the uncertain nonlinear coupled tank system. The simulation results indicate that the developed scheme can respond to the effects of system uncertainties compared to other existing schemes. [ABSTRACT FROM AUTHOR]

Optimal control of multivariable systems is a complex dynamic process that minimizes the cost function to obtain the optimal control strategy. Unfortunately, for nonlinear systems, it is not possible to use the traditional linear quadratic regulator (LQR), which would be optimal over the entire range of parameter variation. The problem of nonlinear multivariable systems and their optimal control is very momentous. The solution presented in this paper is based on the application of Reinforcement Learning (RL) networks in controlling a five-degree-of-freedom overhead crane system. Additionally, unlike the classical approach, the algorithm is adapted to directly analyze tabular data of inputs and outputs of the controlled model instead of analyzing its state as feedback (model-free). Implementing the new control structure for the multivariable system improved control quality compared to the classical LQR controller with linearization at the operating point. In addition to quality, the resource indicators, which in the LQR controller are represented by the matrix R, have been significantly improved. The architecture of the neural control system is presented, ensuring that over the entire range of nonlinearity, the quality of control is preserved while reducing the cost of its resource intensity. Obtaining optimal control with reduced resources for its implementation induces a wide range of applications of such neural control in engineering systems. The effectiveness of the proposed control system has been demonstrated in simulation studies. The simulation results present the system's excellent control performance and adaptability over the entire range of object nonlinearity. The neural algorithm resulted in significantly shorter adjustment time and better control quality with significantly less system resource consumption and increased system dynamics. [ABSTRACT FROM AUTHOR]

This study focuses on addressing the challenge of adaptive fuzzy tracking control for stochastic nonlinear systems while considering full-state constraints. To tackle this issue, we introduce a fuzzy logic system to approximate the unknown nonlinear terms in the system. Additionally, a barrier Lyapunov function is utilized to confine the system state within a specific range. In order to design a novel tracking controller, the backstepping design method and the fuzzy control approach are combined. To optimize system performance, a hysteresis quantizer is integrated. To evaluate the effectiveness of the proposed control strategy, two simulation examples are presented. The simulation results demonstrate that the proposed control strategy effectively limits all state variables to a predefined range. Additionally, the tracking error of the system steadily converges to a negligible range near zero. [ABSTRACT FROM AUTHOR]

In this paper, tracking control of a class of series elastic actuators subject to unknown time-varying input delay and additive disturbances is investigated. To address the input delay, a novel predictor-like method is proposed in the control input which uses a predictor to compensate for the delay. Lyapunov-Krasovskii functions are applied within Lyapunov-based stability analysis to show semi-globally uniformly ultimately bounded tracking errors. The control scheme is extended to the case that the input delay is unknown and time-varying. A constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error. Numerical simulation results illustrate the performance of the developed robust controller. [ABSTRACT FROM AUTHOR]