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In light of the complex behavior of vibrating structures, their reliable modeling plays a crucial role in the analysis and system design for vibration control. In this paper, the reverse-path (RP) method is revisited, further developed, and applied to modeling a nonlinear system, particularly with respect to the identification of the frequency response function for a nominal underlying linear system and the determination of the structural nonlinearities. The present approach aims to overcome the requirement for measuring all nonlinear system states all the time during operation. Especially in large-scale systems, this might be a tedious task and often practically infeasible since it would require having individual sensors assigned for each state involved in the design process. In addition, the proper placement and simultaneous operation of a large number of transducers would represent further difficulty. To overcome those issues, we have proposed state estimation in light of the observability criteria, which significantly reduces the number of required sensor elements. To this end, relying on the optimal sensor placement problem, the state estimation process reduces to the solution of Kalman filtering. On this ground, the problem of nonlinear system identification for large-scale systems can be addressed using the observer-based conditioned RP method (OBCRP) proposed in this paper. In contrast to the classical RP method, the current one can potentially handle local and distributed nonlinearities. Moreover, in addition to the state estimation and in comparison to the orthogonal RP method, a new frequency-dependent weighting is introduced in this paper, which results in superior nonlinear system identification performances. Implementation of the method is demonstrated on a multi-degree-of-freedom discretized lumped mass system, representing a substitute model of a physical counterpart used for the identification of the model parameters. [ABSTRACT FROM AUTHOR]

This paper explores two sample-based methods for analysing multistable systems: basin stability and basin entropy. Both methods rely on many numerical integration trials conducted with diverse initial conditions. The collected data is categorised and used to compute metrics that characterise solution stability, phase space structure, and system dynamics predictability. Basin stability assesses the overall likelihood of reaching specific solutions, while the basin entropy measure aims to capture the structure of attraction basins and the complexity of their boundaries. Although these two metrics complement each other effectively, their original procedures for computation differ significantly. This paper introduces a universal approach and algorithm for calculating basin stability and entropy measures. The suitability of these procedures is demonstrated through the analysis of two non-linear systems. [ABSTRACT FROM AUTHOR]

The variational theory is an inextricable part of both continuum mechanics and physics, and plays an important role in mathematics and nonlinear science, however it is difficult to find a variational formulation for a nonlinear system, and it is more difficult for a fractional differential system. This paper is to search for a variational formulation for the Schrödinger-KdV system with M-fractional derivatives. The fractional complex transformation is used to convert the system into a traditional differential system, and the semi-inverse method is further applied to establish a needed variational principle. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is formulated, suitable to explain the evolution of income distribution over a population in the presence of production. The model is conceived from the perspective of complexity. Indeed, the income distribution emerges as the result of a myriad of economic exchanges taking place between individuals. In fact, the aim of the paper is to provide a framework and mathematical tools for the construction and the investigation of models having an exploratory character. The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. Numerical solutions of these systems are constructed under different assumptions on the law of production and in the presence of different fiscal systems, which provides an example of the versatility of the method. [ABSTRACT FROM AUTHOR]

Neural network models are often used to analyse non-linear systems; here, in cases of small datasets, we review our complementary approach to deep learning with the purpose of highlighting the importance and roles (linear, non-linear or threshold) of certain variables (assumed as causal) in determining the behaviour of a target variable; this also allows us to make predictions for future scenarios of these causal variables. We present a neural tool endowed with an ensemble strategy and its applications to influence analyses in terms of pruning, attribution and future predictions (free code issued). We describe some case studies on climatic applications which show reliable results and the potentialities of our method for medical studies. The discovery of the importance and role (linear, non-linear or threshold) of causal variables and the possibility of applying the relationships found to future scenarios could lead to very interesting applications in medical research and the study and treatment of cancer, which are proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory within a unified perspective. We demonstrate that the closed-loop nonlinear system's asymptotic stability in probability is ensured through a Lyapunov function, identified as the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation. This dual assurance guarantees both stochastic stability and optimality. Additionally, optimal feedback controllers for affine nonlinear systems are developed using an inverse optimality framework tailored to the stochastic stabilization problem. Furthermore, the paper derives stability margins for optimal and inverse optimal stochastic feedback regulators. Gain, sector, and disk margin guarantees are established for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton–Jacobi–Bellman controllers. [ABSTRACT FROM AUTHOR]

The paper aims to design a high-gain observer for nonlinear systems with nonlinear and discontinuous sensor signal. The ultimate boundedness and exponential stability of the estimation error of high-gain observer are presented. The performance recovery property of output feedback control using high-gain observer is demonstrated. Simulation examples are illustrated to validate the proposed results of this paper. [ABSTRACT FROM AUTHOR]

This paper gives a fault-tolerant control scheme concerning with the optimal and near-optimal system performance for a class of nonlinear systems with time-varying actuator faults, time-varying disturbances, and identification errors of the neural network-based identifier. In this paper, the adaptive dynamic programming method is directly used to design the optimal sliding surface, so that the designer can design the target dynamics of the sliding mode in advance. In addition, the barrier function-based sliding-mode control is used to cope with the bounded but boundary-unknown estimation errors of the identifier, and the method ensures that the sliding-mode variable converges to the designer's predefined neighborhood of zero in finite time and the control gain is not overestimated. Specifically, first, by adaptive dynamic programming, near-optimal sliding surface is designed in the sense of the quadratic optimal criterion. Second, a neural network identifier is designed to model the lumped uncertainties including actuator faults and disturbances. Third, a barrier function-based adaptive sliding-mode control is used to cope with the identification errors of the neural network identifier and has no control gain overestimation, which can guarantee to confine the sliding variable to a predefined vicinity of the proposed sliding surface. For this system with faults and disturbances, it is shown that near-optimal property is achieved by this scheme, the chattering phenomenon is effectively suppressed, and the reconstruction error of the neural network identifier with unknown boundary is effectively handled by the adaptive sliding-mode control based on the barrier function. The proof of stability is given by Lyapunov's direct method and the effectiveness of this control scheme is verified by applying it to the spacecraft attitude system. [ABSTRACT FROM AUTHOR]

This paper presents a novel input channel gain adaptive active disturbance rejection control (ICGA‐ADRC) framework for the nonlinear control system with large load variation. This paper first introduces the design of ICGA‐ADRC and proves its stability through the rigorous Lyapunov approach. Subsequently, the proposed controller is simulated by subjecting it to a nonlinear mass‐spring‐damping system characterized by significant load variations. Furthermore, the position‐tracking performance of the controller is tested experimentally by using a motor‐driven pendulum system with various loads. Finally, the results of both simulations and experiments show that the ICGA‐ADRC is capable of compensating for system model uncertainty and external perturbation while accurately estimating the system input channel gain in real‐time. The innovation of this paper is that the robustness of active disturbance rejection control (ADRC) to the system load variation is significantly strengthened by integrating robust adaptive finite‐time parameter estimation method into the conventional ADRC control architecture. [ABSTRACT FROM AUTHOR]

This paper begins by exploring the challenge of event-triggered state estimations in nonlinear systems, grappling with packet dropout and correlated noise. A communication mechanism is introduced that determines whether to transmit measurement values based on whether event-triggered conditions are violated, thereby minimizing redundant communication data. In designing the filter, noise decorrelation is initially conducted, followed by the integration of the event-triggered mechanism and the unreliable network transmission system for state estimator development. Subsequently, by combining the three-degree spherical–radial cubature rule, the numerical implementation steps of the proposed state estimation framework are outlined. The performance estimation analysis highlights that by adjusting the event-triggered threshold appropriately, the estimation performance and transmission rate can be effectively balanced. It is established that when there is a lower bound on the packet dropout rate, the covariance matrix of the state estimation error remains bounded, and the stochastic stability of the state estimation error is also confirmed. Ultimately, the algorithm and conclusions that are proposed in this paper are validated through a simulation example of a target tracking system. [ABSTRACT FROM AUTHOR]

An application of moving-horizon strategy for nonlinear systems with possible outliers in measurements is addressed. With the increased success of movinghorizon strategy in the state estimation for linear systems with outliers acting on the measurement, investigating the nonlinear approach is highly required. In this paper we applied the nonlinear version which has been presented in the literature in term of discrete-time linear time-invariant systems, where the applied strategy considers minimizing a least-squares functions in which each measure possibly contaminated by outlier is left out in turn and the lowest cost is propagated. The moving horizon filter effectiveness as compared with the extended Kalman filter is shown by means of simulation example and estimation error comparison. The moving horizon filter shows the feature of resisting outliers with robust estimation. [ABSTRACT FROM AUTHOR]

Hybrid test is a new seismic test method combining numerical simulation with physical test. It is an advanced test method to evaluate the performance of nonlinear structures and systems. This paper proposes a novel hybrid test control system based on MATLAB-STM32. The system uses the STM32 microcontroller as the main controller and electrodynamic vibrator as excitation source of system. Furthermore, a complete set of hybrid test control system which includes physical hardware test and numerical software simulation is established by using MATLAB-STM32 communication technology, PID control method, displacement sensors, force sensors, etc. It provides a test platform for nonlinear test structures, components that are difficult to model, or components that require performance testing. This system realizes the function of real-time two-way communication between MATLAB and STM32 microcontroller. It uses the finite element software OpenSees to establish the numerical substructure, which solves the problem of the collaborative work between the numerical simulation test and the physical test of the experimental substructure, and can simulate the hybrid dynamic seismic test of the damping structure. To test the control performance of the designed system, this paper selects the viscoelastic dampers as the test substructure, and the performance detection and test analysis are completed for the hybrid test of single-layer frame structure with a viscoelastic damper. The test results show that the data communication between the upper and lower computers is stable and the whole control system performs well on both dynamic and static behaviors. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method for isolating real roots of a bivariate nonlinear system. It is a subdivision method based on analyzing the local geometrical properties of the given system. We propose the concept of opposite monotone system in a box and use it to determine the existence and the uniqueness of a simple real zero of the system in the box. We have implemented our method and the experiments show the effectivity and efficiency of our approach, especially for high degree sparse polynomial systems. This paper is an extended version of the ISSAC'19 conference paper (Cheng and Wen (2019)). [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]

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]

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]

This paper addresses the control of a nonlinear system affected by deadzone effects, using a constrained actuator. The system itself incorporates a second-order oscillatory dynamic actuator, with an unknown nonlinear input-output relationship. The proposed algorithm not only accommodates the deadzone constraints on control inputs but also considers the actuator's saturation limits in control input calculations. It introduces a trajectory tracking mechanism that, instead of directly following the primary trajectory, adheres to an alternative trajectory capable of stable tracking, gradually converging to the main trajectory while accounting for operational constraints. In practical control systems, the actuator's input-output relationship is often nonlinear and unknown, requiring inversion for model-based control. This paper employs an offline-trained neural network trained on synthetic data to identify and approximate the actuator's behavior. To optimize the control system's performance and ensure stability during sudden error changes, the control input operates in two modes: position and velocity control. This dual-mode control allows for continuous switching between the two, facilitated by an innovative optimization technique based on the gradient descent method with a variable step size. Simulation results validate the effectiveness of the proposed algorithm in controlling systems constrained by hard limits and featuring nonlinear oscillatory actuators, providing a valuable contribution to the field of control systems. • Developing a dual mode non-predictive control algorithm based on discrete-time system equations. • Utilizing an offline-trained neural network for estimating the inverse of the nonlinear actuator relationship. • Stable desired trajectory mapping based on inherent and actuation constraints while maintaining asymptotic stability. • Substituting the trajectory within a fixed range outside of the constant deadzone and inside the variable saturation. • Optimized balancing position and velocity control modes through a weighted average of two control forces. [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]

Modern power systems are high-dimensional, strongly coupled nonlinear systems with complex and diverse dynamic characteristics. The polynomial model of the power system is a key focus in stability research. Therefore, this paper presents a study on the approximate transient stability solution targeting the fault process in power systems. Firstly, based on the inherent sinusoidal coupling characteristics of the power system swing equations, a generalized polynomial matrix description in perturbation form is presented using the Taylor expansion formula. Secondly, considering the staged characteristics of the stability process in power systems, the approximate solutions of the polynomial model during and after the fault are provided using coordinate transformation and regular perturbation techniques. Then, the structural characteristics of the approximate solutions are analyzed, revealing the mathematical basis of the stable motion patterns of the power grid, and a monotonicity rule of the system's power angle oscillation amplitude is discovered. Finally, the effectiveness of the proposed methods and analyses is further validated by numerical examples of the IEEE 3-machine 9-bus system and IEEE 10-machine 39-bus system. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fixed-time event-triggered consensus control for a class of multi-agent systems with disturbed and non-linear dynamics. A fixed-time consensus protocol based on an event-triggered strategy is proposed, which can ensure a fixed-time event-triggered consensus, reduce energy consumption, and decrease the frequency of controller updates. The control protocol can also be applied to the case when the systems are free of disturbances; it solves the problem of high convergence time of the systems and reduces energy consumption of the systems. Sufficient conditions are proposed for the multi-agent systems with disturbed and non-linear dynamics to achieve the fixed-time event-triggered consensus by using algebraic graph theory, inequalities, fixed-time stability theory, and Lyapunov stability theory. Finally, simulation results show that the proposed control protocol has the advantages of both event-triggered and fixed-time convergence; compared to previous work, the convergence time of the new control protocol is greatly reduced (about 1.5 s) and the update times are also greatly reduced (less than 50 times), which is consistent with the theoretical results. [ABSTRACT FROM AUTHOR]

In recent years, the simplified computation of position and velocity changes in nonlinear systems using Lie groups and Lie algebra has been widely used in the study of robot localization systems. The unscented Kalman filter (UKF) can effectively deal with nonlinear systems through the unscented transformation, and in order to more accurately describe the robot localization system, the UKF method based on Lie groups has been studied successively. The computational complexity of the UKF on Lie groups is high, and in order to simplify its computation, the Lie groups are applied to the manifold, which efficiently handles the state and uncertainty and ensures that the system maintains the geometric constraints and computational simplicity during the updating process. In this paper, a multi-sensor fusion localization method based on an unscented Kalman filter on manifolds (UKF-M) is investigated. Firstly, a system model and a multi-sensor model are established based on an Autonomous Underwater Vehicle (AUV), and a corresponding UKF-M is designed for the system. Secondly, the multi-sensor fusion method is designed, and the fusion method is applied to the UKF-M. Finally, the proposed method is validated using an underwater cave dataset. The experiments demonstrate that the proposed method is suitable for underwater environments and can significantly correct the cumulative error in the trajectory estimation to achieve accurate underwater localization. [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]

One of the main difficulties for application of sliding mode control is the presence of chattering. It is a well known fact that the amplitude of chattering is proportional to the magnitude of discontinuous control. The problem can be alleviated by making the magnitude as small as possible while still ensuring the existence of the sliding mode. In this paper, a novel predefined-time single layer adaptive scheme based on equivalent concept with a relaxed assumption about unknown dynamics is proposed for dynamically tuning the gain associated with the control magnitude, and applying this scheme in sliding mode control algorithms enables decreasing the control action magnitude to the minimum possible value remaining the characteristic of finite-time convergence. Simulation results are shown to verify the effectiveness of the designed scheme. [ABSTRACT FROM AUTHOR]

Designing a full-state observer for nonlinear systems has always been accompanied by challenges and restrictive constraints. Mainly, applying a state observer in nonlinear systems with non-minimum phase characteristics is more challenging when the limiting constraints are not satisfied due to diverging internal dynamics. In this paper, a robust sliding-mode observer approach has been successfully employed to estimate the states of nonlinear systems with unbounded and diverging dynamics. The design principles of this observer are based on applying a classifying algorithm in single-input single-output and multiple-input multiple-output nonlinear systems. It is noteworthy that this observer is highly robust against disturbance, uncertainty and measurement noise, and its conditions are less conservative compared to previous nonlinear sliding-mode observers. One novel feature of the proposed observer is that while the system's state gets unbounded and diverged in fault-occurring scenarios or critical circumstances, this observer retains accuracy. The efficiency of the proposed observer is verified in the simulation results for two nonlinear industrial systems, including a hydro-turbine power generation plant and a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

A central processing unit receives data from all agents and transmits control commands in a Networked Control System (NCS) which is centralised. Centralised NCSs have numerous applications in industrial settings due to their efficiency, simplicity and cost-effective design. However, centralised NCSs are vulnerable to false data injection (FDI) attacks. Despite the fact that researchers have developed detection and mitigation defense mechanisms during past several years, most of these methods have focused on systems with linear dynamics. Furthermore, the existing literature only assumes the injection of FDI attacks on measurement signals. In this paper, we assume that an adversary has injected the FDI attack into both state measurements and control signals with nonlinear dynamics while considering communication noises and disturbances. We propose a secure nonlinear control design that mitigates FDI attacks in real time by combining learning and model-based approaches. We used Lyapunov stability analysis to design the controller, estimator and updating laws of the neural network (NN). In addition, we selected a network of two robots with Euler–Lagrange dynamics to illustrate the robustness of the proposed controller and estimator. [ABSTRACT FROM AUTHOR]

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results. [ABSTRACT FROM AUTHOR]

For switched under-actuated systems subject to bouc-wen hysteresis, an adaptive neural predefined-time control scheme is presented first time in this paper. To improve the robustness and response rate of the system under consideration, a hierarchical sliding mode control technique is introduced. Based on a predefined-time stability criterion, the stabilization time of the system can be directly preset under the designed controller. Besides, the convergence time depends only on the preset value and is independent of all other parameters. The projection algorithm is introduced to avoid the singularity problem in the controller design process. Meanwhile, it is proved that all signals of the closed-loop system are bounded after a preset time through the Lyapunov stability theory. Finally, a simulation example and a comparison example are given to further illustrate the effectiveness and superiority of developed control approach. [ABSTRACT FROM AUTHOR]

In this paper, an output feedback controller using iterative learning algorithm is proposed for stabilising a class of uncertain nonlinear single-input single-output (SISO) systems with unknown bounded disturbances. By dividing the time interval into equal iteration periods, iterative learning algorithm is integrated into output feedback control and is carried out under alignment condition. Using the output signal, control input and estimates of uncertain parameters, adaptive state observers are established to generate state estimates which will be employed to design the control law. Based on the backstepping technique, the output feedback controller is developed consisting of the ILC part and robust control part. Different from the traditional ILC update laws of uncertain parameters with constant gains, a novel type of parameter update law is developed where the ILC gain is variable and determined by the real-time state estimates such that system stability can be guaranteed. By virtue of the composite energy function, it is proved that all the signals of the closed-loop system are bounded and the output will uniformly converge to zero along the iteration axis, which indicates the stabilisation of the output signal over the time domain. Simulation verification is conducted to apply the proposed controller to a one-degree-of-freedom suspension system to validate the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we mainly concern with the system of the coupled nonlinear Schrödinger equation with initial data in critical spaces in dimension 3. We first obtain the global well-posedness of the solution to the coupled nonlinear Schrödinger equation with initial data in a critical space $ W^{\frac {11}{7}, \frac 76}({\mathbb {R}}^3) $ W 11 7 , 7 6 ( R 3). The key is to derive a uniform bound of a modified energy $ \mathcal {E}(t) $ E (t) based on a decomposition for the solution as in Dodson [Global well-posedness for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space. Rev Mat Iberoam. 2022;38:1087–1100]. In addition, inspired by Dodson [Scattering for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space. International mathematics research notices; 2023], we make a new decomposition for the solution and show the scattering to the coupled nonlinear Schrödinger equation with radially symmetric initial data in a critical Besov space $ B_{1,1}^2({\mathbb {R}}^3) $ B 1 , 1 2 ( R 3). [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]

This paper addresses the problem of transforming a single-input single-output discrete-time system into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the input, output and their forward shifts up to a finite order. The necessary and sufficient conditions for the existence of the extended observer form are provided in terms of vector fields. The algorithm is presented to find a parametrised state transformation necessary to transform the system into the extended observer form. The obtained results are applicable also in case of non-reversible systems. [ABSTRACT FROM AUTHOR]

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a systematic deterministic learning-based rapid sensor fault detection, isolation and accommodation (SFDIA) scheme for a class of nonlinear systems with unmodeled output dynamics. First, locally accurate approximations of sensor faults and unmodeled output dynamics are achieved by using a deterministic learning-based neural network observer. Second, a sensor fault pattern bank which stores the knowledge of sensor faults and unmodeled output dynamics is established. A set of observers utilising the learned knowledge are constructed to generate residuals for rapid SFDIA. The contributions are: (1) the fault detectability and isolability conditions are rigorously analysed and verified in the simulation; (2) using the proposed fault accommodation approach, compared with online parameter adaptation techniques, better tracking performance can be achieved in the presence of sensor faults. Simulation results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Autonomous vehicles that can reliably operate outside the stable handling limits would have access to a wider range of maneuvers in emergencies, improving overall safety. To that end, this paper presents a novel Nonlinear MPC approach for vehicle control with deeply saturated rear tires. Longitudinal slip management is elevated from the chassis control layer into the optimisation problem by using a coupled-slip tire model, and explicitly including wheelspeed dynamics. Terminal costs on sideslip stability help compensate for the finite horizon, while road bounds and static obstacles are encoded using slack constraints. Experiments on a racetrack with a modified Toyota GR Supra validate the controller's ability to smoothly transition from dynamic, non-equilibrium drifting to grip driving. Further experiments demonstrate robustness to significant longitudinal force and wheelspeed disturbances, and showcase the controller flexibly transitioning in and out of the sliding tire regime to balance slack constraints with tracking objectives. [ABSTRACT FROM AUTHOR]

Motivated by the fully actuated system (FAS) approach, this paper proposes a direct robust control method for a type of uncertain multi‐order sub‐fully actuated systems (MOSFASs). Unlike numerous previous results, this paper broadens to a more general multi‐order model and the more challenging sub‐fully actuated case with the presence of singular problems. Firstly, a general uncertain MOSFAS model is presented, where the uncertainty merely needs to satisfy a common assumption. Secondly, a direct robust control method is proposed, giving a robust controller which only needs to satisfy very loose and basic requirements to ensure that the states ultimately converge into an arbitrarily small region. Simultaneously, by constraining the initial values of the states, it is perfectly guaranteed that the states always remain in a "safe" zone free of singular points, thus preserving the realizability of the controller. Finally, under certain conditions, a less conservative robust control scheme is introduced, which can relax the constraint of initial values easily. A simulation for a coarse‐fine angle system demonstrates the validity and value of the proposed robust control method. [ABSTRACT FROM AUTHOR]

To cope with the well-known peaking phenomenon and noise sensitivity in the application of the High-Gain observer, a parameter tuning method based on the LPV/LMI approach for a 2nd-order cascade observer structure is proposed in this paper. Compared to other high-gain observer methods, this method can significantly reduce the infimum of gain in the observer, thereby reducing the peak phenomenon of state estimation and the influence of measurement output noise. By transforming the observer structure into a Luenberger-like structure, the parameters of the observer can be solved by one linear matrix inequality (LMI) with a high-gain effect or a 2n of LMI sets (LMIs) without a high-gain effect. Then by decomposing the nonlinear part of the system dynamics into high-dimensional and low-dimensional parts, we could solve the adjustable number 2js of LMIs can be solved to obtain the result with limited high-gain effect. Stability analysis based on the Lyapunov method proves the convergence of this method, and the effectiveness of this method is verified through applications to one single-link mechanical arm model and a vehicle trajectory estimation application. [ABSTRACT FROM AUTHOR]

This paper investigates the control problem of spacecraft rendezvous with obstacle constraint, considering the external disturbance forces caused by orbit perturbation. Firstly, the translational dynamic model of spacecraft rendezvous is given and then rewritten into a second‐order fully‐actuated system form. Then, by employing the prescribed performance control method, the performance function and error transformation are determined, pre‐defining the prescribed performance bounds. Moreover, the fully‐actuated system approach is used to linearize the original nonlinear system, which simplifies the processes of control law design and ensures model accuracy. After that, to ensure that the spacecraft could avoid the dangerous zone during its manoeuvre, the artificial potential function is introduced, based on which a sliding mode surface is designed. Finally, the prescribed performance control–artificial potential function‐based control law is derived, further adopting the neuro‐adaptive method to deal with external interferences. The stability of the close‐loop control system is analysed through the Lyapunov approach and the effectiveness of the proposed control scheme is verified by carrying out a numerical simulation. [ABSTRACT FROM AUTHOR]

The paper proposes a low-pass filter adaptive iterative learning control (LPF-AILC) strategy for unmatched, uncertain, time-varying, non-parameterized nonlinear systems (NPNL systems). To address the difficulty of nonlinear parameterization terms in system models, a new function approximator (FSE-RBFNN), which combines the radial basis function neural network (RBFNN) and Fourier series expansion (FSE), is introduced to model each time-varying nonlinear parameterized function. The adaptive backstepping method is used to design control laws and parameter adaptive laws. In the process of controller design, we may encounter the problem of too many derivatives, which can cause parameter explosions after derivatives. Therefore, we introduce a first-order low-pass filter to solve this problem and simplify the structure of the controller. As the number of iterations increases, the maximum tracking error gradually decreases until it converges to the nearby region, approaching zero within the entire given interval [0, T], according to the Lyapunov-like synthesis. To mitigate the impact of initial state errors, a dynamically changing boundary layer is introduced, along with a series to deal with the unknown error upper bounds. Finally, two simulation examples prove the correctness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered prescribed-time control problem for a class of high-order nonlinear systems based on finite time-varying gain. Due to the existence of unknown gain functions and system uncertainties, the resultant control with prescribed-time convergence performance becomes nontrivial. The problem becomes even more complex due to the use of event-based communication instead of continuous communication. To tackle the aforementioned challenges, this paper proposes an event-triggered prescribed-time stabilization approach with the following key steps. Firstly, we establish a new prescribed-time stability lemma to overcome the technical difficulty arising from the prescribed-time controller design, and stability analysis. Secondly, we give the controller design procedure upon using the backstepping technique. Thirdly, we redesign the event-triggering threshold condition based on time-varying functions, which allows the controller terminal jitter to be mitigated and the controller to be implemented straightforwardly in practice. Furthermore, the proposed control scheme avoids Zeno behavior. The numerical simulation confirms the effectiveness of the proposed control scheme. • Development of a new prescribed-time stability lemma for complex nonlinear system. • Utilization of finite time-varying gain in the prescribed-time control strategy. • The proposed event-triggering condition, significantly reducing controller jitter. • Successful avoidance of Zeno behavior in the prescribed-time control scheme. [ABSTRACT FROM AUTHOR]

In this paper, we deal with initial value problems for coupled systems of nonlinear fractional differential equations, subject to coupled nonlocal initial and impulsive conditions on the half line. Global existence-uniqueness results are obtained under weak conditions allowing the reaction part of the problem to increase indefinitely with time. Our approach relies mainly to some fixed point theorem of Perov's type in generalized gauge spaces. The obtained results improve, generalize and complement many existing results in the literature. An example illustrating our main finding is also given. [ABSTRACT FROM AUTHOR]

Computational models of turbofans that are oriented to assist the design and testing of innovative components are of fundamental importance in order to reduce their environmental impact. In this paper, we present an effective method for developing numerical turbofan models that allows reliable steady-state turbofan performance calculations. The main difference between the proposed method and those used in various commercial algorithms, such as GasTurb, GSP 12 and NPSS, is the use of neural networks as a multidimensional interpolation method for rotational component maps instead of classical β parameter. An additional aspect of fundamental importance lies in the simplicity of implementing this method in Matlab and the high degree of customization of the turbofan components without performing any manipulation of variables for the purpose of reducing the dimensionality of the problem, which would normally lead to a high condition number of the Jacobian matrix associated with the nonlinear turbofan system (and, thus, to significant error). In the proposed methodology, the component behavior can be modeled by analytical relationships and through the use of neural networks trained from component bench test data or data obtained from CFD simulations. Generalization of rotational component maps by feedforward neural networks leads to an average interpolation error up to around 1 % , for all variables. The resulting nonlinear system is solved by a combined genetic algorithm and least squares algorithm approach, instead of the standard Newton's method. The turbofan numerical model turns out to be convergent, and results suggest that the trend in overall turbofan performance, as flight conditions change, is in agreement with the outputs of the GSP 12 software. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative. Given the growing interest in fractional-order systems for their ability to capture complex dynamics, ensuring their practical stability remains a significant challenge. We propose a novel concept of practical stability tailored to nonlinear Hadamard fractional-order systems, which guarantees that the system solutions converge to a small ball containing the origin, thereby enhancing their robustness against perturbations. Furthermore, we introduce a practical observer design that extends the classical observer framework to fractional-order systems under an enhanced One-Sided Lipschitz (OSL) condition. This extended OSL condition ensures the convergence of the proposed practical observer, even in the presence of significant nonlinearities and disturbances. Notably, the novelty of our approach lies in the extension of both the practical observer and the stability criteria, which are innovative even in the integer-order case. Theoretical results are substantiated through numerical examples, demonstrating the feasibility of the proposed method in real-world control applications. Our contributions pave the way for the development of robust observers in fractional-order systems, with potential applications across various engineering domains. [ABSTRACT FROM AUTHOR]

We extend two KdVSKR models to fractional KdVSKR models with the Caputo derivative. The KdVSKR equation in (2+1)-dimension, which is a recent extension of the KdVSKR equation in (1+1)-dimension, can model the soliton resonances in shallow water. Applying the Hirota bilinear method, finite symmetry group method, and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton and elliptical function interplaying solution for the fractional KdVSKR model in (1+1)-dimension has been derived for the first time. For the fractional KdVSKR model in (2+1)-dimension, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. The effect of the order γ on the dynamical behaviors of the solutions has been illustrated by figures. The three-wave interaction solution has not been studied in the current references. The novelty of this paper is that the finite symmetry group method is adopted to construct interaction solutions of fractional nonlinear systems. This research idea can be applied to other fractional differential equations. [ABSTRACT FROM AUTHOR]

A set of planar motion mechanism experiments of the Duisburg Test Case Post-Panamax container model executed in a towing tank with shallow depth is applied to train a neural network to analyse the ability of the proposed model to learn the effects of different depth conditions on ship's manoeuvring capabilities. The motivation of the work presented in this paper is to contribute an alternative and effective approach to model non-linear systems through artificial neural networks that address the manoeuvring simulation of ships in shallow water. The system is developed using the Levenberg–Marquardt backpropagation training algorithm and the resilient backpropagation scheme to demonstrate the correlation between the vessel forces and the respective trajectories and velocities. Sensitivity analyses were performed to identify the number of layers necessary for the proposed model to predict the vessel manoeuvring characteristics in two different depths. The outcomes achieved with the proposed system have shown excellent accuracy and ability in predicting ship manoeuvring with varying depths of shallow water. [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for a class of coupled system of the four-dimensional cubic focusing nonlinear Schrödinger equations was investigated. By exploiting the double Duhamel method and the long-time Strichartz estimate, the global well-posedness and scattering were proven for the system below the ground state. In our proof, we first established the variational characterization of the ground state, and obtained the threshold of the global well-posedness and scattering. Second, we showed that the non-scattering is equivalent to the existence of an almost periodic solution by following the concentration-compactness/rigidity arguments of Kenig and Merle [17] (Invent. Math., 166 (2006), 645–675). Then, we obtained the global well-posedness and scattering below the threshold by excluding the almost periodic solution. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the nonlinear vibration characteristics and time-delay feedback controllability of a fractional horizontal roll system, which is described by a fractional Duffing-van der Pol oscillator under an external harmonic excitation. We focused on the resonance of fractional roller systems and conducted corresponding vibration control. The amplitude-frequency equations of primary resonance and superharmonic resonance were obtained using the multiple scale method. The amplitude-frequency characteristic curves of the system with different parameters were presented, and the influence of system parameters on the curves was analyzed. In addition, the timedelay feedback controller was designed to control the parameter excitation vibration. The numerical simulation results have verified the effectiveness of the time-delay controller in eliminating the jumping and hysteresis phenomena of the rolling system. The comparisons of approximate analytical solution and numerical solution was fulfilled, and the result certifies the correctness and satisfactory precision of the approximately analytical solution. The analysis results provide certain theoretical guidance for the vibration reduction of the horizontal nonlinear roller system. [ABSTRACT FROM AUTHOR]

In view of the worse dynamic performance and steady-state accuracy caused by nonlinear friction in turntable servo systems, challenges are posed in precise positioning tasks. However, most of the existing research ignores the effect of friction on system performance. Therefore, it is of great significance to analyze the nonlinear characteristics of the transmission mechanism and study compensation strategies for improving the control quality of non-direct drive turntable servo systems. Therefore, an improved active disturbance rejection control (ADRC) based on state feedback compensation is proposed in this paper to optimize the accuracy of the turntable servo system and improve the robustness of the system under nonlinear friction conditions. Firstly, friction is modeled and analyzed through offline identification, which is the basis for nonlinear friction compensation. Subsequently, the two methods of friction compensation are compared. Since feedforward compensation is prone to under-compensation and over-compensation, it is highly dependent on the parameters, while the traditional ADRC compensation method has poor dynamic performance under gap conditions. Therefore, the advantages of ADRC and state feedback are combined together to reduce the steady-state error and optimize the control performance of the system. Lastly, the effectiveness of the proposed compensation method is verified and compared through simulations and experiments. The method is able to comprehensively compensate the gap and friction nonlinearities, and the experimental steady-state error is reduced from 0.55° to 1/3 (0.19°), which improves the load-side positioning accuracy. Finally, a conclusion can be drawn that the new compensation method can improve the parameter adjustability, speed estimation precision, and system robustness. [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]

Due to variable and complex work environments, nonlinearities, uncertainty and disturbances are inevitable in multi‐agent systems. Approximation‐free control can address these issues without involving approximators, such as fuzzy logic systems and neural networks. However, some issues like the singularity problem caused by the signals exceeding the preset boundary in changing work conditions still remain. This paper proposes an adaptive and reliable approximation‐free control, which comprises a novel singularity compensator and a modified transforming function. The proposed control scheme performs better in terms of convergence rate and overshoot, avoids issues relating to singularity, and has added flexibility in terms of parameter choice. The proposed control law adapts to changes in operating conditions and nonlinearities—the efficacy of which is demonstrated using simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive stabilisation of output-constrained high-order nonlinear systems with more general high-order and low-order nonlinearities. By skilfully introducing nonlinear mappings, a key coordinate transformation, integral Lyapunov functions and the sign function into the adding a power integrator technique, and combining a novel analysis method, a continuous adaptive state-feedback controller is constructed. When the initial value of system states lies in the constrained set, it is rigorously proved that all the closed-loop signals are uniformly bounded, the asymmetric output constraint isn't transgressed, and the equilibrium point of the closed-loop system is uniformly asymptotically stable. A simulation example shows the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]