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The paper delves into an in-depth analysis of the intrinsic resistance of the inverted pendulum system which causes the modeling of the system to differ from the actual system. Our primary objective revolves around the implementation and subsequent optimization of fuzzy logic controllers (FLC), drawing inspiration from human perceptual assessments. The processing comprises comprehensive mathematical system modeling, intrinsic resistance examination, and improved fuzzy logic control with detailed membership function and rule design. In addition, we conduct a comparative analysis with the widely recognized linear quadratic regulator (LQR) algorithm, which is considered the conventional control algorithm. The result demonstrates that the improved FLC outperforms the conventional LQR algorithm overshoot mitigation, thereby underscoring its superior efficacy and optimality. [ABSTRACT FROM AUTHOR]

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]

Purpose: This study presents a novel optimization algorithm which optimize the controller parameters of a nonlinear ball balancer system. Proposed approach is successfully balancing a ball over a rectangular plate under the presence of continuous vibrations. Method: To develop the proposed computational technique, Giza pyramid construction algorithm is improved by introducing “Command Phase” and “Co-operate Phase”. This improvement is responsible for the development of proposed HGPCTLBO (Hybrid Giza Pyramid Construction Teaching Learning Based Optimization) algorithm. The developed algorithm is optimizing the unconstrained parameters of proportional integral and derivative controller, which controls the nonlinear vibrations of rectangular plate and achieves proper balancing of ball over this rectangular plate. This scheme is capable of handling the unknown but bounded disturbances/vibrations with comfort. Initially, the mathematical modelling of balancer system is obtained using a two degree of freedom ball balancer system under the presence of unknown but bounded disturbances. Results: Integral Square Error (ISE), Integral of Absolute Error (IAE) and Integral of the Time weighted Absolute Error (ITAE) are used as control fitness functions. MATLAB/Simulink platform is used to demonstrate the simulation as well as real time results while proving the dominance of proposed work over the work available in literature. [ABSTRACT FROM AUTHOR]

Image encryption is an effective method for protecting the security of image information, and chaotic maps are generally applied to realize some random operations. Inspired by the nonlinear characteristic of optimization test functions, a chaotic map called drop-wave map developed from the two-dimensional (2D) drop-wave function is proposed in this paper. The drop-wave map has a wide range of parameters and uniform phase trajectories. Utilizing the generated pseudo-random sequences with the proposed drop-wave map, a novel multi-layer image encryption algorithm is presented through processing bit-planes using bit circle-shift, bit-plane permutation using Baker map, intra-layer permutation, and multi-direction diffusion. First, the bit circle-shift operation is performed on each pixel to change values initially, where the shifted digits are determined with one pseudo-random sequence. Second, the Baker map is used to scramble the bit positions in each bit-plane and the timestamp is regarded as an extra key. Furthermore, the intra-layer permutation operation with another pseudo-random sequence is performed to permutate the bit positions completely. Finally, the ciphertext image is obtained by using multi-direction diffusion to change pixel values. The main contributions of this work lie in the design of a 2D drop-wave map and a combination of multi-layer operations to enhance the security of image encryption. Simulation results and security analysis verify the validity and feasibility of the proposed algorithm through statistical analysis and robustness analysis. [ABSTRACT FROM AUTHOR]

For the nonlinear systems with input delay, an adaptive fixed-time tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for the first time. First, to address the main challenge brought by input delay, an auxiliary system is constructed, which transforms the input delay systems into non-delay systems. Second, the MTNs are introduced into the backstepping design process, which reduce the design difficulty by approximating unknown nonlinear functions. Thus, a control scheme subject to low complexity is obtained. Third, aside from ensuring that the tracking error converges within a small neighbourhood of the origin within a fixed-time, the designed control scheme not only makes all signals in the closed-loop system remain bounded, but also avoids the problem of finite-time control relying on initial state. Finally, three simulations are given to prove the feasibility and superiority of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the identification problem of feedback nonlinear system with time delay (FNTD). A data-driven identification method for the FNTD system based on bidirectional long short-term memory (BiLSTM) networks is proposed. First, considering the long input and output data sequence and the existence of bidirectional features, the BiLSTM network is chosen for identification. In addition, in order to mine the complex nonlinear mapping relationship between input and output, the attention mechanism is introduced into the BiLSTM algorithm to highlight the influence of key factors. The Gaussian kernel function selects the optimal complexity model to enhance the extrapolation performance, and further improves the identification accuracy. Then, the attention-BiLSTM algorithm is proposed. In the simulation, a numerical example and two application examples are implemented. The results show that the attention-BiLSTM method can effectively identify the FNTD system, and is superior to LSTM and BiLSTM in terms of identification accuracy and speed. The proposed attention-BiLSTM method has the highest identification accuracy, and the RMSE is 5.57 % and 1.05 % lower than the LSTM and BiLSTM models, respectively. The R 2 value reaches 0.9997, which is 16.17 % and 0.77 % higher than LSTM and BiLSTM, respectively. [ABSTRACT FROM AUTHOR]

Spherical tanks have been predominantly used in process industries due to their large storage capability. The fundamental challenges in process industries require a very efficient controller to control the various process parameters owing to their nonlinear behavior. The current research work in this paper aims to propose the Approximate Generalized Time Moments (AGTM) optimization technique for designing Fractional-Order PI (FOPI) and Fractional-Order PID (FOPID) controllers for the nonlinear Single Spherical Tank Liquid Level System (SSTLLS). This system features a large dead time, and its real-time modeling generally represents a Single Input Single Output (SISO) model. However, in practice, the derived SISO model is often a First Order Plus Dead Time (FOPDT) model, necessitating an effective controller to maintain the tank's steady-state level. In this research, the proposed AGTM method, based on the conventional Proportional Integral (PI) and Proportional Integral Derivative (PID) controllers, is compared with the FOPI and FOPID controllers for the nonlinear SSTLLS. The performance of these controllers is contrasted using metrics such as Integral Squared Error (ISE) and Integral Absolute Error (IAE), as well as time-domain characteristics containing Rise time, Peak time, Settling time, Peak overshoot, and Steady-state error. The implementation of the aforementioned controllers is done in simulation and real-time employing the MATLAB software environment and the Data Acquisition (DAQ) device National Instrument NI-DAQmx 6211. The simulation and experimental results demonstrate the exceptional performance of the designed Fractional-Order controllers based on the proposed method which offers an increased degree of freedom despite the more complex design process. [ABSTRACT FROM AUTHOR]

ABSTRACT This study proposes a filtering based maximum likelihood generalized extended gradient algorithm for multivariable nonlinear systems with autoregressive moving average noises. The parameter estimates are obtained by minimizing the half squared residual measurement which can approach the true values. An auxiliary model is also established with the measurable information of the system, and the output of the auxiliary model is used to replace the unmeasurable variables of the system, so that the output of the auxiliary model approximates these unmeasurable variables, so as to obtain the consistent estimation of the system parameters. A maximum likelihood generalized extended gradient algorithm is derived for comparison and a numerical example is provided to show the effectiveness of the proposed method and the estimates converge to the actual values quickly. [ABSTRACT FROM AUTHOR]

Tensegrity structures are geometric nonlinear systems and statically and kinematically indeterminate structures that require an initial shape-finding procedure to establish a self-equilibrium state. This paper presents a shape-finding algorithm requiring structure topology, strut force, cable force density, and a random initial estimate of node coordinates as input. The equilibrium of the structure is achieved by zeroing the nonlinear static equilibrium in which the generalized nodal coordinates are chosen as variables. The modified Newton-Raphson method is used to solve the nonlinear equilibrium system by decreasing the nonlinear least square function to ensure global convergence. The stability of the self-balancing structure was evaluated using the properties of the geometric and tangent stiffness matrix. Various numerical examples are presented to illustrate the method's effectiveness for 2-d and 3-d tensegrity structures with multiple states of self-stress. [ABSTRACT FROM AUTHOR]

As a result of this study, an improved direct torque control (DTC) method based on sliding mode control (SMC) was used to control the sensorless three-phase asynchronous motor, as well as a third-order cascade inverter has a frequency-modulated carrier (FM—Frequency Modulation) to reduce total harmonic distortion (THD) in torque and current, in order to achieve the best possible result. The rapid change in current and voltage on the load caused oscillations around the sliding surface (chattering) that damaged the actuators by means of rapid changes and large amplitudes of current and voltage. This study, therefore, proposed the use of nonlinear Tansig functions rather than classical sign functions as the control algorithm. Additionally, due to the fact that direct torque control (DTC) had the advantage that it was not sensitive to motor parameters, thereby ensuring that, even when nonlinear parameters change with time, they did not affect the whole closed system as a whole. Hence, radial basis function networks (RBFNs) were used to approximate magnetic fluxes and torques. A simulation and experiment were conducted by OPAL-RT equipment on Matlab/Simulink for a squirrel-cage rotor motor 1 hp, 150 rad/s with third-order cascade inverter that has a frequency-modulated carrier. In spite of the change in torque in the presence of noise, the system remained stable regardless of the set value from the lowest velocity 3 rad/s to the highest velocity 150 rad/s. This algorithm was simple, required little memory, and had high-order harmonic components of torque and low current (THD-Total Harmonic Distortion). The algorithm had been proven to be stable by Lyaponov. [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]

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]

The proper orthogonal decomposition (POD) method is used to model the shell-motor-rotor coupled system with bearing nonlinearities to reduce the computational cost. The rotor system with 192 degrees of freedom is modeled by the finite element method for the coupled shell-motor-rotor structure. The basic principle of the POD method and its specific expression in the shell-motor-rotor coupled system are introduced. By using the POD method, the shell-motor-rotor coupled system is reduced to 20, 18 and 15 degrees of freedom, and the computation time is reduced by more than 94%. The time course curves and spectra of the simplified system and the original system are compared, which verifies the efficiency and accuracy of the POD method. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive filtering algorithm based on the symmetry Kernel Hyperbolic Tangent Mixed Error Criterion (KHTMC), aimed at addressing the identification of nonlinear systems under non-Gaussian noise environments. The algorithm optimizes signal processing by constructing a mixed cost function that combines the symmetry logarithmic square error and the hyperbolic tangent function and integrates it with the kernel adaptive filtering method. Simulation results show that, compared to existing kernel adaptive filtering algorithms, the KHTMC algorithm exhibits significant advantages in terms of convergence speed and steady-state mean square error. It demonstrates strong robustness and tracking performance, especially when dealing with mixed non-Gaussian noise. Therefore, this algorithm shows great potential in signal processing applications under complex noise conditions, offering a more reliable and efficient solution. [ABSTRACT FROM AUTHOR]

Previous works have analyzed finite/fixed-time tracking control for nonlinear systems. In these works, achieving the accurate time convergence of errors must be under the premise of known initial values and careful design of control parameters. Then, how to break through the constraints of initial values and design parameters for this issue is an unsolved problem. Motivated by this, we successfully studied prescribed-time tracking control for single-input single-output nonlinear systems with uncertainties. Specifically, we designed a state feedback controller on [ 0 , T p) , based on the backstepping method, to make the tracking error (TE) tend to zero at T p , in which T p is the arbitrarily selected prescribed-time. Furthermore, on [ T p , ∞) , another controller, similarly to that on [ 0 , T p) , was designed to keep TE within a precision after T p , while TE may not stay at zero. Therefore, on [ T p , ∞) , another new controller, based on sliding mode control, was built to ensure that TE stays at zero after T p. [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]

The replacement of mechanical planetary gears with magnetic gears (MGs) is an emerging transmission solution for electric vehicles that reduce shock and vibration. This article proposes magnetic two-speed transmission and examines the influence of the noncontact torque of MGs, the meshing stiffness of mechanical gears, and the system load on the vibration of magneto-mechanical combined transmission systems. First, the noncontact torque of an MG is analysed on the basis of the magnetic field modulation principle. A set of dynamic equations was subsequently constructed on the basis of the centralized parameter method. Thereafter, with the principle of harmonic balance, a rapid method for constructing a nonlinear vibration harmonic balance solution for a magneto-mechanical combined vibration system in matrix form is obtained. Finally, simulations and prototype tests were conducted. The results show that noncontact torque consists of stable torque and ripple torque. They also interact with mechanical gears to affect system vibration. he vibration amplitude of the inner rotor is sensitive to the pulsating torque, whereas the vibration of the ferromagnetic pole-pieces is sensitive to the meshing stiffness. The stable torque and load dynamic balance affect the natural frequency of the system. The system demonstrates "load‒stiffness adaptive" characteristics compared with those of pure mechanical gearing. The proposed Harmonic Balance Method can quickly calculate this characteristic, and it offers a theoretical basis for dynamic analysis and vibration reduction in magnetic two-speed transmissions. [ABSTRACT FROM AUTHOR]

This article presents a compact magnetic levitation energy harvester (MLEH) with tunable resonant frequency. Unlike many of the reported tunable harvesters with unknown tuning results, the proposed MLEH can be tuned toward designated resonant frequency values within its tuning range. The targeted tuning processes is realized by a nonlinear magnet repulsive force exerted on a Halbach magnet array, combined with a calibrated scaling system. At a sinusoidal acceleration of ±0.15 g, the maximum frequency tuning range of the proposed MLEH is 6.3 Hz (8.1–14.4 Hz), which is 77.8% of its resonant MLEH (8.1 Hz). At a frequency of 9.7 Hz, the output power is 462.1 μW and the calculated normalized power density is 496 μW cm−3 g−2. HIGHLIGHTS: • A magnetic levitation energy harvester (MLEH) with tunable resonant frequency based on a Halbach magnet array is proposed. • The MLEH has the advantages of low resonant frequency, wide tuning range, and simple tuning procedure. • It can be precisely tuned toward a specific target frequency in a one-off manner without the need for repeated frequency scanning. [ABSTRACT FROM AUTHOR]

This paper presents an extension of the Vector Fitting algorithm with the purpose of constructing compact behavioral models of weakly nonlinear circuits starting from frequency-domain input-output data. Using the concept of generalized transfer function provided by Volterra series theory for nonlinear systems, the algorithm approximates a given dataset of generalized transfer function samples with a black-box multivariate rational model. The fitted model can then be recast into a bilinear state-space form for time-domain analysis. Practical extraction of the required data samples can be carried out by measurement or harmonic balance analysis available in commercial solvers. Examples demonstrating the accuracy and efficiency of the behavioral models include a Low-Dropout Regulator and a Low Noise Amplifier.

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.

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]

The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-equation method, not yet explored in the literature, to derive new solutions for the governing model. Second, it analyzes the complex dynamical structure of the governing model using bifurcation, chaos, and sensitivity analyses. To provide a more accurate depiction of the underlying dynamics, they use quantum mechanics to explain the intricate behavior of the system. To illustrate the physical behavior of the obtained solutions, 2D and 3D plots, along with a phase plane analysis, are presented using appropriate parameter values. These results validate the effectiveness of the employed method, providing thorough and consistent solutions with significant computational efficiency. The investigated soliton solutions will be valuable in understanding complex physical structures in various scientific fields, including ferromagnetic dynamics, nonlinear optics, soliton wave theory, and fiber optics. This approach proves highly effective in handling the complexities inherent in engineering and mathematical problems, especially those involving fractional-order systems. [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]

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

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 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]

The present study proposes an approximate analytical solution to a nonlinear system of time-fractional partial differential equations. The Sadik residual power series method, which integrates the two-part Sadik integral transform with the residual power series technique, is employed to solve the fractional differential equation in the Caputo sense. Nonlinear problems with known and unknown solutions are examined to demonstrate the capacity of the technique. Numerical simulations and 3D visualizations are conducted for various values of the fractional order to further understand the solution's behavior. Additionally, the results are validated against exact solutions or existing methodologies to ensure their reliability and accuracy. A key advantage of the proposed method is its ability to generate results without the need for Adomian polynomials, perturbation techniques, discretization, or linearization, enabling a more efficient. [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]