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Reciprocity is a fundamental property of wave propagations, and many researchers devoted their efforts to breaking the reciprocity and implementing unidirectional wave propagations. At present, the main method to realize non-reciprocal waves uses aperiodic structure as the wave propagation medium. The non-reciprocal bandgap achieved by this method is narrow and difficult to adjust actively. To improve the controllability of non-reciprocal bandwidth, a one-dimensional (1D) periodic lattice structure based on linkage element is proposed in the work. The linkage element enables the lattice structure to have nonlinear stiffness with respect to the asymmetry of the equilibrium position. This stiffness asymmetry leads to the non-reciprocity of wave propagation, which provides a new idea for the design of non-reciprocal structures. To deal with the strong nonlinearity and high dimensional characteristics of the structure, the improved incremental harmonic balance (IHB) method is used to analyze the dispersion and bandgap characteristics of the structure. The results show that the structure has two bidirectional bandgaps (high and low frequency) and four unidirectional bandgaps, and the position, width and direction of the bandgap can be adjusted by the equilibrium position and mechanical parameters of the structure. The obtained structural properties are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

Summary: The paper is devoted to the prescribed finite time attitude control for quadrotors. A novel prescribed finite time function is introduced, which is independent of initial conditions and design parameters. And a switched prescribed finite time controller is firstly designed, such that the quadrotor can not only converge to the desired attitude in a prescribed time, but also guarantee the stability of the quadrotor after the settling time. Simultaneously, it effectively avoids chattering issues at the controller's switching points. Finally, the simulation comparisons are carried out between the proposed control strategy and infinite time, finite time, traditional prescribed finite time control schemes to demonstrate the superiority of the developed controller. [ABSTRACT FROM AUTHOR]

This article addresses the Bayesian filtering problem for a class of nonlinear systems under multistep randomly delayed and lost measurements. A new measurement model is established that can characterize the random delay and loss of measurement data. First, an augmented Gaussian mixture filter framework is developed in the case of random delay of measurement data; the posterior probability density function after state augmentation is calculated by marginalizing over delay variables to extract accurate information from delayed measurements. The implementation of the filter is transformed into the computation of nonlinear numerical integrals. Second, under the proposed framework, novel expressions of the mean and covariance are generated by propagating the measurement taken at the previous moment in the event of no new measurement being received. Finally, we present two simulation examples for estimating system states, and the results demonstrate the effectiveness and superiority of our proposed filter. [ABSTRACT FROM AUTHOR]

The convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach. [ABSTRACT FROM AUTHOR]

ABSTRACT This article investigates the optimal control problem (OCP) for a class of discrete‐time nonlinear systems with state constraints. First, to overcome the challenge caused by the constraints, the original constrained OCP is transformed into an unconstrained OCP by utilizing the system transformation technique. Second, a new cost function is designed to alleviate the effect of system transformation on the optimality of the original system. Further, a novel off‐policy deterministic approximate dynamic programming (ADP) scheme is developed to obtain a near‐optimal solution for the transformed OCP. Compared to existing off‐policy deterministic ADP schemes, the developed scheme relaxes the requirement on the learning data and saves computing resources from the perspective of training neural networks. Third, considering approximation errors, we analyze the convergence and stability of the developed ADP scheme. Finally, the developed ADP with the designed cost function is tested in two numerical cases, and simulation results confirm its effectiveness. [ABSTRACT FROM AUTHOR]

In this article, the multiplayer hierarchical decision‐making problem for discrete‐time nonlinear networks of service is studied from the perspective of Nash–Stackelberg–Nash games. A novel two‐level value iteration adaptive dynamic programming algorithm is developed to solve the coupled nonlinear Hamilton–Jacobi–Bellman equations associated with the game problem, which neither requires the system drift dynamics to be known as a priori nor requests the initial strategies to be admissible. Moreover, both the value function sequences and the strategy sequences generated by the algorithm converge to their theoretical optimality. An implementation framework for the algorithm is constructed by leveraging the regularized least‐squares method, and a convergence criterion that guarantees the admissibility of the approximated strategies is also proposed. The effectiveness of the proposed algorithm and implementation framework are finally demonstrated through two numerical simulation examples. [ABSTRACT FROM AUTHOR]

This article addresses the identification of unknown nonlinear continuous‐time systems through a linear time‐varying (LTV) approximation as a starting point. The mathematical form of the nonlinear system is unknown and is reconstructed by use of a well‐designed experiment, followed by LTV and linear parameter‐varying (LPV) estimations, and an integration step. The experiment used allows for a linearization of the unknown nonlinear system around a time‐varying operating point (system trajectory), resulting in an LTV approximation. After estimating the LTV model, an LPV model is identified, where the parameter‐varying (PV) coefficients represent partial derivatives of the unknown nonlinear system evaluated at the trajectory. We demonstrate a structural relation in the LPV model structure that ensures that the LPV coefficient vector is the gradient of the unknown nonlinear system. The nonlinear model of the system is then reconstructed through symbolic integration of the PV coefficients. This identification method enables the estimation of the unknown nonlinear system and its mathematical form using input–output measurements. The article concludes by illustrating the method on simulation examples. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive iterative learning control (ILC) scheme for nonlinear systems with iteration-varying trial lengths under external morphologically-similar disturbances, utilising inter-trial iteration and real-time correction. To attenuate external quasi-periodic disturbances and non-repetitive uncertainties, and further achieve better tracking performance along iteration and time axes, the proposed scheme combines the iteration-to-iteration proportional-type (P-type) ILC with the within-iteration P-type scheme. The tracking error with dead zone property and zero filling treatment is constructed. In addition, as opposed to the existing two-dimensional (2D) ILC works, the integrated framework is formed through the connection of adaptive weights, which are calculated by the adaptive weight determination method based on the ideology of the Kalman filter. The convergence of the algorithm is proved based on the contraction mapping principle. Compared with the traditional ILC schemes, illustrative and applicational simulations are provided to demonstrate the effectiveness and the superiority of the proposed framework. [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]

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]

Piezoelectric actuators (PEAs) are extensively used for scanning and positioning in scanning probe microscopy (SPM) due to their high precision, simple construction, and fast response. However, there are significant challenges for instrument designers due to their nonlinear properties. Nonlinear properties make precise and accurate control difficult in cases where position feedback sensors cannot be employed. However, the performance of PEA-driven scanners can be significantly improved without position feedback sensors if an accurate mathematical model with low computational costs is applied to reduce hysteresis and other nonlinear effects. Various methods have been proposed for modeling PEAs, but most of them have limitations in terms of their accuracy and computational efficiencies. In this research, we propose a variant DenseNet-type neural network (NN) model for modeling PEAs in an AFM scanner where position feedback sensors are not available. To improve the performance of this model, the mapping of the forward and backward directions is carried out separately. The experimental results successfully demonstrate the efficacy of the proposed model by reducing the relative root-mean-square (RMS) error to less than 0.1%. [ABSTRACT FROM AUTHOR]

Maximizing the efficiency of photovoltaic (PV) systems relies heavily on employing efficient maximum power point tracking (MPPT) algorithms. This research focuses on the advancement of enhanced MPPT algorithms capable of achieving the maximum power point (MPP) under different climatic profiles. This paper proposes an adapted perturb and observe-based model predictive control (APO-MPC) strategy to validate the effectiveness of PV systems under three climatic situations. The APO algorithm incorporates variable step sizes to compute reference currents to reduce oscillations while maintaining a steady state in output power. The APO-MPC efficiently tracks and stabilizes output power by predicting future states using reference current and minimizing the cost function. This eliminated the necessity for expensive sensing and communication equipment and networks designed for directly measuring variations in solar irradiation. The computational burden of an algorithm is reduced using a simplified mathematical model of a boost converter and a one-step prediction approach. The PV panel and boost converter are modeled to get appropriate parameters for implementing the proposed algorithm. The system undergoes simulations using the MATLAB/Simulink environment, and multiple test cases are conducted under constant, rapid, and linearly changing irradiances. The outcomes demonstrate that the proposed APO-MPC MPPT algorithm outperforms APO, Kalman filter-based MPC (KMF-MPC), and other existing strategies in terms of stability, transient response time, overshoots, steady-state oscillations, and follow of reference trajectory under dynamic weather conditions. [ABSTRACT FROM AUTHOR]

This paper presents an innovative approach for achieving rapid synchronization between two memristor chaotic circuits (MCCs), both with and without noise perturbations. The proposed adaptive control strategy effectively handles the uncertainty in control gains by adhering to predesigned update law. Additionally, this protocol is non-chattering and differentiable, avoiding the use of conventional discontinuous functions such as signum and absolute value functions. This method successfully mitigates the tremors caused by discontinuous functions. We derive two sufficient criteria using finite-time Lyapunov and stochastic finite-time Lyapunov stability methods. Numerical results validate the theoretical analysis and demonstrate the influence of noise intensity on convergence speed. Furthermore, the results have an application in image encryption transmission. [ABSTRACT FROM AUTHOR]

The subject of KCC theory is a second‐order ordinary differential equation, it is sometimes difficult to convert the high dimensional system into an equivalent second‐order system because of the analytical requirements of KCC theory. By means of the Euler‐Lagrange extension of a flow on a Riemannian manifold, this paper gives five geometric invariants of some three‐dimensional systems with great convenience, and focus on the analysis of two of them. The results show that the hyperbolic equilibria corresponding to the seven standard forms of three‐dimensional linear systems are Jacobi unstable. This is completely different from what we got before in two‐dimensional systems, where Jacobi stable and Jacobi unstable correspond to focus and node, respectively. All equilibria of classical Lü chaotic system and Yang‐Chen chaotic system are Jacobi unstable. Meanwhile, in three‐dimensional linear case, the torsion tensors at any point of the trajectory are identically equal to zero, but the two nonlinear systems have nonzero torsion tensors components. [ABSTRACT FROM AUTHOR]

ABSTRACT This article addresses a solution to one of the main challenges of online data‐driven control (DDC) methods: reducing the sensitivity of the model‐free adaptive control (MFAC) method to initial conditions and control parameters with the new control cost function and added the output error rate and integral along with a new anti‐wind up strategy for multi‐input multi‐output (MIMO) systems. The parameters introduced to the new control law have been validated using the boundary‐input boundary‐output (BIBO) approach to design and converge the controller. The simulation findings on a nonlinear auto‐regressive moving average model with exogenous inputs (NARMAX) system with triangular control input demonstrate that the proposed control rule will outperform to prototype MFAC. Furthermore, to analyze the sensitivity of the controller to the initial conditions and the uncertainties of the control parameters, 30 Monte Carlo simulations were performed with random initial conditions in the presence of disturbance in the control input, and output noise, and the results were compared with the prototype MFAC and conventional PID controller using standard criteria such as integral time absolute error, standard deviation, steady‐state error, and mean maximum error, which shows a noticeable superiority of proposed controller relative to the prototype MFAC. [ABSTRACT FROM AUTHOR]

Flexible and lightweight cables are extensively used in engineering structures, which are prone to produce nonlinear deformation and nonlinear vibrations under random excitations. Usually, dampers are installed at certain positions of the cables to reduce the vibration response. The present paper investigates the stochastic responses of the nonlinear inclined cables with an attached damper under Gaussian white noise and wide-band noise excitations. First, the dynamical model of an inclined cable is established and the differential equations for each mode of vibration are derived by using Galerkin's discretization method. Then, the stochastic linearization method is applied to derive the stochastic responses of the generalized displacements. The effectiveness of the truncated order, the effects of the excitation amplitude, damper installation position and damping coefficient are studied by investigating the stochastic responses. Since stochastic linearization is not applicable to systems with strong nonlinearity, stochastic averaging of energy envelope and quasi-Hamiltonian systems are adopted to study the main modal vibration of the inclined cables. The probability density functions of energy and generalized displacement are calculated. The comparisons between the results derived from the theoretical method and those derived from the numerical simulation showed the accuracy of the analytical results. [ABSTRACT FROM AUTHOR]

Many PID (Proportional plus Integral plus Derivative) controller tuning methods are proposed in the control literature based on different closed-loop specifications. Also, tuning techniques, based on the maximum sensitivity specification, have been proposed in the literature. In this paper, a novel PID controller design method, based on maximum sensitivity, has been proposed. In this work, the PID controller is viewed as a gain and dynamic part and tuned separately. The PID controller dynamic part is tuned using one of the existing popular tuning methods. The tuned dynamic part is cascaded with the process. After that, the PID controller gain is tuned for the maximum sensitivity specification. The maximum sensitivity versus controller gain graph can be generated. The user can choose the controller gain for the desired maximum sensitivity specification. The popular Ziegler & Nichols and IMC (Internal Model Control) methods tune the dynamic part of the system in this work. These proposed techniques can achieve the desired maximum sensitivity by tuning the controller gain in the subsequent stage. Many illustrative instances are considered to display the applicability and the proposed technique’s simplicity. [ABSTRACT FROM AUTHOR]

This paper aims to propose a real-time detection method of wheel-rail conditions in a monorail vehicle-track nonlinear system based on vehicle vibration signals. Monorail rubber tires exhibit strong nonlinearity and three-dimensional elasticity, resulting in highly coupled vertical and lateral vibrations. As a result, traditional methods applied in railway system such as transfer function analysis are not suitable for back-calculation of road irregularities for this nonlinear system. Iterative simulation with numerous parameters is time-consuming, thus this paper proposes a parallel simulation approach fused with the genetic algorithm to shorten the calculation time and facilitate big data processing. The multi-rigid body model's simulation result can closely match the test data by intelligently modifying the vehicle parameters. This method overcomes the transfer function's limitations in nonlinear systems and the significant errors introduced by the simplified mathematical derivation method. It also overcomes the shortcoming of significant errors in the mathematical derivation method and disperses errors caused by simplifying the multi-rigid body dynamics and ensures calculation accuracy. Additionally, this paper highlights the application of artificial intelligence techniques in intelligent wheel eccentricity detection. It improves the traditional algorithm to shorten the calculation time and benefit big data processing. [ABSTRACT FROM AUTHOR]

This paper investigates the group consensus of hybrid‐order heterogeneous multi‐agent systems (MASs) consisting of first‐order linear agents and second‐order nonlinear agents with and without input saturation. First, group consensus algorithms are introduced. Then, by using various mathematical methods, including the graph theory, LaSalle invariant set principle, and Lyapunov stability theory, it is shown that hybrid‐order heterogeneous MASs can reach group consensus if sufficient conditions are satisfied. Further, the simulations are conducted to verify the theoretical results. Finally, the simulation results demonstrate that hybrid‐order heterogeneous MASs with and without input saturation can achieve the group consensus. [ABSTRACT FROM AUTHOR]

Since the Leibniz rule for integer-order derivatives of the product of functions, which includes a finite number of terms, is not true for fractional-order (FO) derivatives of that, all sliding mode control (SMC) methods introduced in the literature involved a very limited class of FO nonlinear systems. This article presents a solution for the unsolved problem of SMC of a class of FO nonstrict-feedback nonlinear systems with uncertainties. Using the Leibniz rule for the FO derivative of the product of two functions, which includes an infinite number of terms, it is shown that only one of these terms is needed to design a SMC law. Using this point, an algorithm is given to design the controller for reference tracking, that significantly reduces the number of design parameters, compared to the literature. Then, it is proved that the algorithm has a closed-form solution which presents a straightforward tool to the designer to obtain the controller. The solution is applicable to the systems with a mixture of integer-order and FO dynamics. Stability and finite-time convergence of the offered control law are also demonstrated. In the end, the availability of the suggested SMC is illustrated through a numerical example arising from a real system. [ABSTRACT FROM AUTHOR]

A higher-order iterative learning control (ILC) is developed for nonlinear continuous-time systems with input saturation, the process of which consists of input-driven part and the free part. In the time interval of the input-driven part, the controlled system operates according to the imposed control input. Then, it executes autonomously in the rest of the time interval, which is regarded as the free part. Thus, the developed higher-order ILC law pursues the desired trajectory tracking within the time interval affected by control input. Based on the assumption that the initial state is variable around the desired one within a bound, the ILC tracking errors can be driven into a range whose bound is proportional to the initial state vibration. As a special case, when the initial state equals the desired initial state, the ILC tracking errors are controlled to zero as the iteration number tends to infinity. Robustness and convergence analysis of the proposed higher-order ILC law are provided against the initial states vibration. Simulation results are given to illustrate the effectiveness of the presented higher-order ILC scheme. [ABSTRACT FROM AUTHOR]

We address the prescribed-time stability of a class of nonlinear system with uncertainty/disturbance. With the help of the parametric Lyapunov equation (PLE), we designed a state feedback control to regulate the full-state of a controlled system within prescribed time, independent of initial conditions. The result illustrated that the controlled state converges to zero as t approaches the settling time and remains zero thereafter. It was further proved that the controller is bounded by a constant that depends on the system state. A numerical example is presented to verify the validity of the theoretical results [ABSTRACT FROM AUTHOR]

An adaptive control method based on immersion and invariance (I&I) is presented in a class of nonlinear systems with time-varying uncertain parameters. A parameter estimation law based on reference models using I&I is designed to accelerate the convergence of estimated parameters to the true value, enabling the closed-loop system to reach the predefined target system on the manifold more quickly and reducing the energy consumption of the system. The inherent integrability obstacles in I&I are overcome by using dynamic scaling techniques, reducing the complexity of controller design. Stability analysis of the closed-loop system demonstrates that the proposed control method can achieve asymptotic stability control of the target system, and verified the robustness of the closed-loop system in the face of external disturbances. Finally, simulations of attitude tracking control demonstrate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of data-driven control of nonlinear systems, focusing on the limitations and capabilities of model reference Gaussian process regression (MR-GPR) and its evolved counterpart, model reference neural networks (MR-NN). MR-GPR, based on Gaussian processes renowned for their adaptability to diverse data structures, encounters scalability issues especially when handling large datasets. To address these limitations, this paper introduces MR-NN, an extension of MR-GPR, leveraging neural networks (NN) to manage large datasets and capture complex nonlinear dynamics effectively. We present a comprehensive evaluation of both methods through a classical control problem of the inverted pendulum, a system well-recognized for its nonlinear behavior. Numerical experiments are conducted to compare the methods in terms of control performance, computational efficiency, and reliability. [ABSTRACT FROM AUTHOR]

An interesting field of studying nonlinear systems is their sensitivity study. With sensitivity study the most influential parameters on a system can be obtained and then the simplification and improvement of the model will be possible. In this paper the global sensitivity study of a Duffing-type vibration system is carried out with Sobol’s variance-based method taking the root mean square of acceleration and the maximum acceleration as output variables. With the sensitivity study it was observed that the parameters of the excitation signal like the amplitude and the angular velocity are the most influential. It was also found that a single parameter has less influence on the system than the parameter combinations. The aim of the research is to carry out the global sensitivity study of a relatively simple nonlinear system. The study is the basis for further research tasks in order to perform the sensitivity study of more complex systems.

A new control algorithm for nonlinear plants is proposed, ensuring the controlled variable stays within a given set under conditions of parametric uncertainties, external disturbances and high-frequency noises in measurements. The problem is solved in two stages. In the first stage, a low-pass filter is applied to eliminate high-frequency components in the measured controlled signal. In the second stage, a coordinate transformation represents the initial problem with given restrictions as an input-state stability analysis problem of a new system without constraints. An output feedback algorithm has been developed for uncertain nonlinear systems under conditions of parametric uncertainties, external disturbances, and high-frequency noise in measurements. Simulations in MATLAB/Simulink are given. The simulation results show the efficiency of the proposed algorithm. The proposed algorithm can effectively solve control problems for power systems or electromechanical systems in the presence of measurement noises.

This article proposes a novel approach to design a robust estimator that is able to keep its consistency in system state estimation when system process model mismatch occurs. To successfully develop such an estimator, not only the estimation strategy proposed but also the designer's knowledge and experience about the system behavior are crucial and determining. To assess the performance of the resultant estimator, its performance is compared with that of three well‐known estimators, that is, the unscented Kalman filter, the cubature Kalman filter, and the extended Kalman filter on the IEEE 5‐generator 14‐bus system. The results indicate that the proposed method has led to an estimator outperforming its rivals under the presence of model errors. [ABSTRACT FROM AUTHOR]

The primary focus of this research paper is to explore the realm of dynamic learning in sampled‐data strict‐feedback nonlinear systems (SFNSs) by leveraging the capabilities of radial basis function (RBF) neural networks (NNs) under the framework of adaptive control. First, the exact discrete‐time model of the continuous‐time system is expressed as an Euler strict‐feedback model with a sampling approximation error. We provide the consistency condition that establishes the relationship between the exact model and the Euler model with meticulous detail. Meanwhile, a novel lemma is derived to show the stability condition of a digital first‐order filter. To address the non‐causality issues of SFNSs with sampling approximation error and the input data dimension explosion of NNs, the auxiliary digital first‐order filter and backstepping technology are combined to propose an adaptive neural dynamic surface control (ANDSC) scheme. Such a scheme avoids the n$$ n $$‐step time delays associated with the existing NN updating laws derived by the common n$$ n $$‐step predictor technology. A rigorous recursion method is employed to provide a comprehensive verification of the stability, guaranteeing its overall performance and dependability. Following that, the NN weight error systems are systematically decomposed into a sequence of linear time‐varying subsystems, allowing for a more detailed analysis and understanding. In order to ensure the recurrent nature of the input variables, a recursive design is employed, thereby satisfying the partial persistent excitation condition specifically designed for the RBF NNs. Meanwhile, it can verify that the NN estimated weights converge to their ideal values. Compared with the common n$$ n $$‐step predictor technology, there is no need to redesign the learning rules due to the designed NN weight updating laws without time delays. Subsequently, after capturing and storing the convergence weights, a novel neural learning dynamic surface control (NLDSC) scheme is specifically formulated by leveraging the acquired knowledge. The introduced methodology reduces computational complexity and facilitates practical implementation. Finally, empirical evidence obtained from simulation experiments validates the efficacy and viability of the proposed methodology. [ABSTRACT FROM AUTHOR]

The operation of multi‐agent systems (MAS) in space necessitates considerations for obstacle avoidance, collision prevention, and connectivity among agents. This coupling conflict, stemming from spatial resource utilization, poses a significant and non‐negligible threat to the safe operation of MAS. This article proposes a consensus control scheme for the time‐varying formation of MAS, incorporating functions for maintaining connectivity, collision avoidance, and obstacle dodging. This scheme effectively constrains the time‐varying formation tracking error within an arbitrarily small range. The considered system model takes a high‐order nonlinear form, with uncertainties and disturbances present in each order. This grants the control scheme with high generality and practicability. By employing barrier Lyapunov function to delineate the safe operational space of MAS, conflicts in spatial resource utilization are avoided. This approach simultaneously fulfills the requirements for connectivity maintenance, collision avoidance, and obstacle dodging in the safe operation of MAS. An additional rotation operator is integrated into the controller to smoothly address the "minima" problem, eliminating the need for external intervention. Gaussian radial basis function is used to estimate the nonlinear terms, uncertainties, and unknown perturbation online in the system. The stability of the MAS under the proposed control scheme is analyzed through Lyapunov function. Finally, numerical simulation results are demonstrated to explain the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This paper deals with the discrete-time antiwindup compensator (AWC) synthesis for nonlinear discrete-time systems under input saturation. The proposed method considers the objective of an optimal AWC design for fast convergence and for improved performance against the saturation nonlinearity. A discrete-time full-order AWC architecture is presented for nonlinear discrete-time systems to achieve an improved performance against the saturation nonlinearity. Additionally, an equivalent decoupled AWC architecture for nonlinear discrete-time system is derived through algebraic analysis and transformation of saturation to dead-zone function. To achieve fast convergence, a more generic Lyapunov function has been applied for the AWC design by incorporating an exponential term in the Lyapunov function. Then, new conditions for the AWC synthesis are revealed by application of the resultant decoupled discrete-time architecture, nonlinearity condition, a modified quadratic-exponential Lyapunov function, optimally exponential L 2 approach, and input saturation properties. The design conditions are provided for both global and local design scenarios, which can be applied to both stable and unstable plants. Compared with the conventional methods, the proposed approach deals with nonlinear systems, can be more practical due to discrete-time scenario, provides an optimal design for both fast convergence and performance, and applicable to both stable and unstable plants. A simulation example has been provided to demonstrate the efficacy of the proposed nonlinear AWC design. [ABSTRACT FROM AUTHOR]

In this paper, the cascade architecture of spline adaptive filtering (CSAF) for nonlinear systems is presented with the normalized version of orthogonal gradient adaptive (NOGA) algorithm. Spline adaptive filtering comprises a sandwich of the first linear adaptive filtering (LAF) and nonlinear adaptive look-up table. In this cascading architecture, SAF is connected to the second LAF. NOGA is considered as the fast convergence applied by stochastic gradient-based approach. Convergence properties of the proposed NOGACSAF algorithm in terms of instantaneous errors can be derived by using Taylor series expansion. Experimental results demonstrate the effectiveness of proposed NOGA-CSAF algorithm using the mean square error scheme. It clearly outperforms the traditional least mean square algorithm on CSAF model in the nonlinear identification system. [ABSTRACT FROM AUTHOR]

Abstract This research introduces a new technique to control constrained nonlinear systems, named Lyapunov-based neural network model predictive control using a metaheuristic optimization approach. This controller utilizes a feedforward neural network model as a prediction model and employs the driving training based optimization algorithm to resolve the related constrained optimization problem. The proposed controller relies on the simplicity and accuracy of the feedforward neural network model and the convergence speed of the driving training based optimization algorithm. The closed-loop stability of the developed controller is ensured by including the Lyapunov function as a constraint in the cost function. The efficiency of the suggested controller is illustrated by controlling the angular speed of three-phase squirrel cage induction motor. The reached results are contrasted to those of other methods, specifically the fuzzy logic controller optimized by teaching learning-based optimization algorithm, the optimized PID with particle swarm optimization algorithm, the neural network model predictive controller based on particle swarm optimization algorithm, and the neural network model predictive controller using driving training based optimization algorithm. This comparative study showcase that the suggested controller provides good accuracy, quickness and robustness due to the obtained values of the mean absolute error, mean square error root mean square error, enhancement percentage, and computing time in the different simulation cases, and it can be efficiently utilized to control constrained nonlinear systems with fast dynamics.

In this paper we study the well-posedness for the periodic Cauchy problem and the internal controllability of a one-dimensional system that describes the propagation of long water waves with small amplitude in the presence of surface tension. The well-posedness is proved by using the Fourier transform restriction method and the controllability is proved by using the moment method.

Nowadays, cars have become the mainstream means of transportation, and traffic accidents caused by cars often occur on the road. Therefore, its safety is very important and has also attracted the attention of the general public. The braking system of a car is a very important part of its composition and structure, which determines the smoothness and safety of the car. The automobile braking system is a complex nonlinear system, which has multiple inputs, multiple outputs, uncertainties and multiple interference sources. Due to the complex relationship between input, interference, and output, the uncertainty of internal and external parameters in automobiles makes it very difficult to maintain appropriate braking. In order to improve the stability and safety of automobiles, this article conducts research on artificial intelligence technology, collaborative control algorithms, and automobile braking systems. The aim is to strengthen automobile braking systems through artificial intelligence technology and design an intelligent braking system to ensure smooth and safe driving of automobiles. Experiments have shown that the intelligent braking system can maintain a constant speed and maintain relative stability during emergency braking. The intelligent braking system can automatically detect accident prone road sections for reminders and speed reduction, and also automatically detect the situation around the car to give a warning. The experimental results show that when the car's speed reaches 25m/s or above (90km/h), the warning distance of the system is nearly 150 meters, which can fully ensure the safety of the driver; when driving at low speeds, the warning distance would not be too long to avoid affecting the driver's driving experience. [ABSTRACT FROM AUTHOR]

This paper describes using phase plane analysis to investigate the short-period longitudinal stability of a general aviation aircraft during take-off and landing phases. Firstly, the aerodynamic coefficients and characteristics of the aircraft in take-off and landing configurations are analyzed. What is more, considering the effects of deploying flaps during take-off and landing, a second-order short-period modal equation is constructed to evaluate the pitch stability of the aircraft. The stability criterion for the system is also provided. Finally, phase plane analysis is performed on 3 Cases, and the phase trajectory and equilibrium points of the system under 8 different combinations of flight surfaces are obtained. The results show that the deployment of flaps during take-off and landing affects the longitudinal stability of the aircraft, and also some unstable regions that could affect flight safety are predicted. [ABSTRACT FROM AUTHOR]

Metaheuristic algorithms are computational techniques based on the collective behavior of swarms and the study of organisms acting in communities. These algorithms involve different types of organisms. Finding controller values for nonlinear systems is a challenging task using classical approaches. Hence, using metaheuristics to find the controller values of a twin rotor multi-input multi-output system (TRMS), one of the nonlinear systems studied in the literature, seems to be more appropriate than using classical methods. In this study, different types of metaheuristic algorithms were used to find the PID controller values for a TRMS, including a genetic algorithm (GA), a dragonfly algorithm, a cuckoo algorithm, a particle swarm optimization (PSO) algorithm, and a coronavirus optimization algorithm (COVIDOA). The obtained graphs were analyzed based on certain criteria for the main rotor and tail rotor angles to reach the reference value in the TRMS. The experimental results show that when the rise and settlement times of the TRMS are compared in terms of performance, the GA took 1.5040 s (seconds) and the COVIDOA took 9.59 s to increase the pitch angle to the reference value, with the GA taking 0.7845 s and the COVIDOA taking 2.4950 s to increase the yaw angle to the reference value. For the settling time, the GA took 11.67 s and the COVIDOA took 28.01 s for the pitch angle, while the GA took 14.97 s and the COVIDOA took 26.69 s for the yaw angle. With these values, the GA and COVIDOA emerge as the foremost algorithms in this context. [ABSTRACT FROM AUTHOR]

This research introduces a new technique to control constrained nonlinear systems, named Lyapunov-based neural network model predictive control using a metaheuristic optimization approach. This controller utilizes a feedforward neural network model as a prediction model and employs the driving training based optimization algorithm to resolve the related constrained optimization problem. The proposed controller relies on the simplicity and accuracy of the feedforward neural network model and the convergence speed of the driving training based optimization algorithm. The closed-loop stability of the developed controller is ensured by including the Lyapunov function as a constraint in the cost function. The efficiency of the suggested controller is illustrated by controlling the angular speed of three-phase squirrel cage induction motor. The reached results are contrasted to those of other methods, specifically the fuzzy logic controller optimized by teaching learning-based optimization algorithm, the optimized PID with particle swarm optimization algorithm, the neural network model predictive controller based on particle swarm optimization algorithm, and the neural network model predictive controller using driving training based optimization algorithm. This comparative study showcase that the suggested controller provides good accuracy, quickness and robustness due to the obtained values of the mean absolute error, mean square error root mean square error, enhancement percentage, and computing time in the different simulation cases, and it can be efficiently utilized to control constrained nonlinear systems with fast dynamics. [ABSTRACT FROM AUTHOR]

Malicious attack is a potential threat to collision‐free and connectivity‐preserving formation. In this article, a predictor‐based collision‐free and connectivity‐preserving resilient formation control strategy is proposed for a class of multi‐agent systems under sensor deception attacks. The predictor states are constructed to replace original states in the control strategy, and a novel attack compensator is constructed to suppress sensor deception attacks. Prediction errors, instead of compromised errors, are introduced to update weights of radial basis function neural networks (RBFNNs). To achieve collision avoidance and connectivity preservation, a transformation function in logarithmic form is introduced. To avoid static and dynamic obstacles, an improved artificial potential function (APF) combined with their velocity information is constructed. Furthermore, to solve the local minimum problem in the combining of transformation function and APF, a virtual force is added. Based on the Lyapunov function, all closed‐loop signals are bounded and collision‐free and connectivity‐preserving formation is achieved. The simulation related to a group of quadrotors verifies the effectiveness of the proposed resilient control strategy. [ABSTRACT FROM AUTHOR]

For regulating the Synchronous Generator (SG) output voltage, the Automatic Voltage Regulator (AVR) system is a significant device. This work propounds a survey on Optimization Algorithms (OAs) utilized for tuning the controller parameters on the AVR system. A device wielded for adjusting the SG's Terminal Voltage (TV) is named AVR. A Controller is utilized for improving stability and getting a superior response by mitigating maximum Over Shoot (OS), reducing Rise Time (RT), reducing Settling Time (ST), and enhancing Steady State Error (SSE) since output voltage has a slower response and instability. The controllers utilized here are Proportional-Integral-Derivative (PID), Intelligent Controller (IC), along with Fraction Order PID (FOPID). Owing to the occurrence of time delays, nonlinear loads, variable operating points, and others, OAs are wielded for tuning the controller. (a) Particle Swarm Optimization (PSO), (b) Genetic Algorithm (GA), (c) Gray Wolf Optimizer (GWO), (d) Harmony Search Algorithm (HSA), (e) Artificial Bee Colony (ABC), (f) Teaching Learned Based Optimization (TLBO), et cetera are the various sorts of OA. For enhancing the TV response along with stability, various OAs were tried by researchers. [ABSTRACT FROM AUTHOR]

Summary: In this article, the problem of global adaptive practical tracking for high‐order uncertain nonstrict feedback nonlinear systems with unknown control coefficients is studied. To avoid the algebraic loop problem associated with the nonstrict feedback condition and guarantee the controllability of the tracking error, a novel dual dynamic gain scaling method is introduced to compensate nonlinearities and the tracking error simultaneously. Besides, by incorporating the sign functions into the design of adding a power integrator, a general approach for the handing of unknown control coefficients and the direction design of the controller is developed. The presented control scheme can ensure that all system states are globally bounded without constraints on state variables while the reference signal is tracked with expected precision. Three simulation examples, including a practical application, are provided to illustrate the validity of the control scheme. [ABSTRACT FROM AUTHOR]

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

In this article, predictive cloud control is investigated for nonlinear networked multiagent system (NMAS) with quantizers via extended state observer (ESO). Considering the network‐induced delays in NMAS, the cloud control scheme is designed. Then, arbitrary region quantizers are used to decrease the quantity of data packets. Moreover, the ESO that can estimate the state and uncertainty of nonlinear NMAS is used to obtain the prediction of data packets. Input‐to‐state stability (ISS) can guarantee the validity of ESO. Sufficient conditions that can achieve stability and consistency for NMAS are given by the zoom strategy. The significance of the scheme is verified by simulation results. [ABSTRACT FROM AUTHOR]

Currently, the focus of stochastic resonance (SR) research is primarily on bistable systems, and classical bistable SR systems have the problems of low dimension, inconvenient parameter adjustment, and high threshold for SR effects. In this paper, based on the classic bistable system, a class of multi-dimensional single potential well SR systems without transition threshold is proposed and applied to signal processing. Firstly, the mechanism of double potential well SR and single potential well SR is studied. On this basis, a kind of multi-dimensional single potential well SR system is defined and its theoretical conditions are analyzed. Then a specific four-dimensional single potential well SR system is constructed, and the dynamics of the system is analyzed. The gain range and the approximate relationship between the system input and the four-dimensional output are derived. Finally, the four-dimensional single potential well SR system is applied to the processing of various signals. The experimental results show that the constructed system has good noise reduction and feature amplification effects on noisy signals through the advantages of multi-dimensional output, and can be used to highlight the fault feature frequency in bearing fault signals. [ABSTRACT FROM AUTHOR]

We present a proportional–integral–derivative-based controller plus an adaptive slide surface to solve the trajectory tracking control problem for a fully actuated vessel with unknown parameters perturbed by slowly varying external unknown dynamics. The controller design assumes that the vessel moves at low speed and frequency, its physical parameters are unknown, and its state is measurable. The control approach ensures error tracking convergence toward a small vicinity at the origin. We conduct the corresponding stability analysis using the Lyapunov theory and saturation functions. We tested the controller through two numerical experiments—a turning ellipse maneuver and a rest-to-rest maneuver—where the vessel parameters were unknown, and we obtained satisfactory results. [ABSTRACT FROM AUTHOR]

To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach to state estimation called nonlinear observer-unscented Kalman filter (NLO-UKF). The proposed method is designed to improve the accuracy of state estimation in complex systems that are subject to nonlinearity and uncertainty. The key idea of the NLO-UKF is to use a nonlinear observer to correct the projected sigma points based on a measurement, and then update the mean and covariance using the UKF. The paper provides a detailed description of the NLO-UKF algorithm and demonstrates its boundedness. The use of NLO-UKF for pose estimation is presented to compare the effectiveness of the proposed method with other state estimation methods in the simulation of an autonomous truck–trailer system and experimentation with a container truck system. The NLO-UKF demonstrates improved accuracy during steady-state estimation. [ABSTRACT FROM AUTHOR]

To improve the dynamic performances of nonlinear magnetorheological (MR) semi-active suspension, a hybrid damping control (HDC) based on Kalman observer of nonlinear suspension system is proposed. Firstly, the mechanical test of MR damper is carried out, and the mechanical model of MR damper and suspension system model are established. On this basis, a feedback linearization Kalman observer (FLKO) based on differential geometry theory is designed. Then, the working modes of the MR suspension system are divided according to different driving roads. HDC is proposed to achieve the dynamic control objectives under different working modes, and genetic algorithm is used to optimize the coefficients of skyhook, groundhook and distribution. The simulation results show that the estimation accuracy of FLKO is more than 85%. Compared with passive suspension, the tire dynamic load is optimized by 15.53% on A class road, improving the road holding. On B class road, the body acceleration, suspension deflection and tire dynamic load are optimized by 2.22%, 23.76% and 1.47% respectively, optimizing the dynamic performances comprehensively. On C class road, the body acceleration is optimized by 17.69%, improving the ride comfort effectively. Finally, a test bench is built, and the test results are basically consistent with simulation, which verifies the effectiveness of the designed FLKO and HDC. [ABSTRACT FROM AUTHOR]

We prove partial regularity of solutions u of the nonlinear quasimonotone system div A x , u , D u + B x , u , D u = 0 under natural polynomial growth of its coefficient functions A and B. We propose a new direct method based on an L p estimate with low exponent p > 1 for a linear elliptic system with constant coefficient. [ABSTRACT FROM AUTHOR]

Purpose. Solution of the three-dimensional nonlinear problem of external ballistics and development of an approximate mathematical model of the dynamic process for cargo falling from low-speed aircraft, which makes it possible to obtain an analytical solution, which is possible in combination with a geometric representation of the dynamic process using computer algebra. Methodology. Utilizing a blend of analytical and numerical research algorithms, an innovative model was devised, grounded in a nonlinear system of differential equations characterized by time-varying coefficients. The applied three-dimensional approach to the dynamic problem with an initial velocity from a UAV, in the presence of frontal and side wind loading, made it possible to use the nonlinear theory of external ballistics. This streamlining of the problem involved solving a related system of differential equations with variable coefficients along corresponding coordinates, leveraging an asymptotic approach. Furthermore, the formulation of the problem incorporated applied mathematical analysis and modeling, accommodating various pertinent environmental parameters. Findings. The creation of mathematical models and algorithms for calculating the parameters of the dynamic process of falling loads from low-speed aircraft within the framework of the theory of nonlinear external ballistics is an urgent problem both from the point of view of the development of the dynamic theory of the specified class of systems, and the creation of effective calculation algorithms with the possibility of practical application. As a result of the research, characteristic valuations of the influence of variable coefficients on the results of estimated accuracy of landing as a derivative of time were obtained. The obtained analytical and graphical dependences with the provision of appropriate assessments of the applied approach make it possible to establish the correlation of methods and results. Originality. The relevance of scientific research in the field of nonlinear external ballistics is based both on the internal trends of the development of this science and on the urgent needs of modern industry. In this paper, an approximate analytical solution of the nonlinear problem of external ballistics is proposed, which is subject to the applied conditions of motion. The resulting dependencies made it possible to establish the relationship between the parameters and find the degree of their influence on the landing time function. Practical value. The derived analytical findings and solution methodology can be integrated into practical applications within the realms of mathematical physics and engineering computations. This is particularly pertinent in the advancement of control algorithms for ballistic systems. [ABSTRACT FROM AUTHOR]

Summary: In the practical application of adaptive control methods, a windup phenomenon for the systems with input saturation may occur because there exists an input restriction such as saturation of actuator in most actual systems due to physical reasons. In this paper, to alleviate the influence of the windup phenomenon by input saturation, we propose an output feedback exponentially passive (OFEP)‐based adaptive model recovery anti‐windup (AMRAW) control strategy for the stable nonlinear systems with input saturation. Moreover, in order to realize an augmented OFEP system for non‐OFEP nonlinear systems that do not satisfy the OFEP properties, a parallel feedforward compensator (PFC) is introduced, and a radial basis function (RBF) neural network (NN)‐based adaptive feedforward input is designed to attain accurate tracking performance for systems with the PFC. Furthermore, the detailed stability analysis of the proposed AMRAW control system is provided, and the performance of the proposed method is validated through appropriate numerical simulations. [ABSTRACT FROM AUTHOR]