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In this paper, an antidisturbance controller is presented for helicopter stochastic systems under disturbances. To enhance the antidisturbance abilities, the nonlinear disturbance observer method is applied to reject the time-varying disturbances. Then, the antidisturbance nonlinear controller is designed by combining the backstepping control scheme. And the stochastic theory is used to guarantee that the closed-loop system is asymptotically bounded in mean square while the proposed control method is shown via some traditional nonlinear control techniques, which still show some common issues such as “dimension explosion” or others. The result of this paper can be regarded as a typical case of the nonlinear control method to help and promote the generation of advanced methods.

The cable-stayed bridge is widely used due to its strong spanning capacity and navigability. However, flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis. Based on the nonlinear distributed model, two modal governing equations of the cable are established via the Galerkin method. A certain working condition, when the external excitation frequency is close to the second-order natural frequency of the stay cable while nearly twice the first-order natural frequency, is theoretically and experimentally investigated. Specifically, the frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. Theoretical and experimental results show that bridge deck vibration can induce not only the primary and superharmonic resonance of the cable but also the principal parametric resonance. Parametric resonance-induced bifurcations are also observed in the system. Particularly, the energy exchange from second-order primary resonance to first-order principal parametric resonance is found, which can induce the parametric resonance with the response amplitude one to three times higher than that of the primary resonance. This paper also validates the superiority of the present modal interaction model over the traditional single-mode model in practical engineering applications.

This paper discusses the finite-time stable and finite-time H ∞ control problems of affine nonlinear singular systems subject to actuator saturation. Some sufficient conditions, to guarantee the system is finite-time stable, are established for the affine nonlinear singular systems subject to actuator saturation. First, the finite-time stable problem is investigated by the state undecomposed method, and then the finite-time robust H ∞ control law is presented for the system. Finally, the effectiveness of the designed controllers is shown by an example of a nonlinear singular circuit system in this paper.

In this paper, a disturbance observer-based complementary fractional-order sliding mode control (CFOSMC) scheme is proposed for the permanent magnet synchronous motor (PMSM) drive system. First, to reconstruct the load disturbance and parameter variations, a nonlinear disturbance observer is designed. Next, a disturbance observer-based fractional-order sliding mode with a saturation function control law is designed to reduce the chattering problem in the existing fractional-order sliding mode control (FOSMC) method. Furthermore, to reduce the thickness of the boundary layer, a CFOSMC scheme is designed. By using the fractional-order Lyapunov stability theorem, the existence condition and the chattering problem are analyzed. Compared with the existing FOSMC, the obtained CFOSMC law does not contain any high-order derivatives of tracking error, which is easier to implement. Finally, the numerical simulations and experimental results are provided to show the superiority of the proposed method. To improve the performance of the permanent magnet synchronous motor (PMSM) drive system in terms of tracking rapidity, accuracy, and robustness, a complementary fractional-order sliding mode control (CFOSMC) scheme with disturbance observer is proposed in this paper.

The optimal amount of fertilizer application which was needed by the trees and the factors that influence the fertilization have an intricated nonlinear relationship. According to the problems that the traditional fertilization prediction model has, such as lacking of the scalability and practicality, this paper initiates an accurate fertilization prediction model that was based on the GRA-PSO-BP neural network which can make the accurate fertilization come true and improve the economic benefits of forest industry. This paper uses the GRA method to determine the input of the neural network as the site index and make the forest age, nutrient content of the advantage trees, biomass of the advantage trees, biomass of average trees, and target yield as the output numbers of the Actual amount of fertilizer applied. During the calculation process, the global particle swarm optimization algorithm is used to optimize the initial numbers and threshold numbers of BP neural network which build a phased GRA-PSO-BP accurate fertilization model. Compared with the prediction algorithm of full input variate that is based on the single BP neural network and the prediction algorithm of full input variate that is based on PSO-BP Neural Network, the GRA method can determine the key factors that influence the amount of fertilizer applied in different forest areas and modify the prediction model to improve the scalability and accuracy of the prediction and finally achieve the precision fertilization as the data of different forests updated, so we can see that the prediction result of this paper is more accurate. The result demonstrates that the GRA-PSO-BP neural network Segment fertilization model is more accurate than the traditional BP neural network and BP Neural Network that was optimized by the PSO algorithm, and specifically, the error of the predicted amount of fertilizer application and the actual amount of fertilizer application is less than 5%, which can effectively guide the fertilization in stages.

Linearized model of the system is often used in control design. It is generally believed that we can obtain the linearized model as long as the Taylor expansion method is used for the nonlinear model. This paper points out that the Taylor expansion method is only applicable to the linearization of the original nonlinear function. If the Taylor expansion is used for the derived nonlinear equation, wrong results are often obtained. Taking the linearization model of the maglev system as an example, it is shown that the linearization should be carried out with the process of equation derivation. The model is verified by nonlinear system simulation in Simulink. The method in this paper is helpful to write the linearized equation of the control system correctly.

An adaptive high-order difference solution about a 2D nonlinear degenerate singular reaction-diffusion equation with a convection term is initially proposed in the paper. After the first and the second central difference operator approximating the first-order and the second-order spatial derivative, respectively, the higher-order spatial derivatives are discretized by applying the Taylor series rule and the temporal derivative is discretized by using the Crank–Nicolson (CN) difference scheme. An alternating direction implicit (ADI) scheme with a nonuniform grid is built in this way. Meanwhile, accuracy analysis declares the second order in time and the fourth order in space under certain conditions. Sequentially, the high-order scheme is performed on an adaptive mesh to demonstrate quenching behaviors of the singular parabolic equation and analyse the influence of combustion chamber size on quenching. The paper displays rationally that the proposed scheme is practicable for solving the 2D quenching-type problem.

This paper is focused on a kind of distributed optimal control design for a class of switched nonlinear systems with the state time delay which have a prescribed switching sequence. Firstly, we design a bounded controller to make the system stable for each mode of the nominal system. Then, a distributed optimal controller which can satisfy input constraint is designed based on the bounded stabilization controller. A sufficient condition to guarantee ultimate boundedness of the system is given based on appropriate assumption. The significance of this paper is that distributed optimal control method is applied to switched nonlinear systems with the state time delay. Finally, a simulation example is given to verify the effectiveness of the proposed method.

This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampère equation with Dirichlet boundary. We discuss and study the performance of the three kinds of multiscale methods. The first method is the cascadic meshfree method, which was proposed by Liu and He (2013). The second method is the stationary multilevel method, which was proposed by Floater and Iske (1996), and is used to solve the fully nonlinear partial differential equation in the paper for the first time. The third is the hierarchical radial basis function method, which is constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii. Compared with the first two methods, the hierarchical radial basis function method can not only solve the present problem on a single level with higher accuracy and lower computational cost but also produce highly sparse nonlinear discrete system. These observations are obtained by taking the direct approach of numerical experimentation.

The nonlinear time-delay dynamic absorber has a good control effect on the main system under harmonic excitation, but the control effect on the main system under complicated excitation is not obvious. In the previous study, they do not have an effective method to obtain the time-delay control parameters under different external excitations. Because of the above problems, this paper proposed an innovative method to obtain the control parameters of time-delay dynamic absorbers. For the vibration system including the nonlinear time-delay dynamic absorber, the transient time-integration method was used to solve the nonlinear delay dynamic differential equation of the system under the specific excitation. Then, the quantitative relationship was established between the time-domain responses of the vibration system, the external excitation, and time-delay control parameters. The time-delay control parameters would be obtained when the time-domain response of the main system is minimized under specific excitation using an algorithm that continuously compares the objective function that is related to the time-domain response of the main system. This paper took the two-degree-of-freedom vibration system with a nonlinear time-delay dynamic absorber as the target system to simulate the time-domain response of the main system. The simulation results show that the time-delay control parameters calculated by the new method can obtain significant vibration reduction effects for both harmonic excitation and multiharmonic excitation. The suppression performance of the nonlinear time-delay dynamic absorber is significantly improved.

This research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. The Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana–Baleanu and Katugampola. The existence of solution has been proven by two main fixed-point theorems: O’Regan’s fixed-point theorem and Krasnoselskii’s fixed-point theorem. By applying Banach’s fixed-point theorem, we proved the uniqueness result for the concerned problem. This research paper highlights the examples related with theorems that have already been proven.

The traditional predictive method cannot fully reflect the complex nonlinear characteristics and regularities of automobile and parts sales data, so the prediction precision is not high. The purpose of this paper is to propose the gray GM(1,1) nonlinear periodic predictive model by introducing the seasonal variation index to improve predictive accuracy of the single GM(1,1) model. Firstly, the paper analyzes concept of GM(1,1) and then proposes the gray GM(1,1) nonlinear periodic predictive model to forecast automobile parts sales. The model algorithm used gray theory and accumulated technology to generate new data and set up unified differential equations to find the fitting curve of automobile parts sales prediction by the seasonal variation index to remove random elements. Lastly, the gray GM(1,1) nonlinear periodic predictive model is used for empirical analysis; the result of example shows that the model proposed in the paper is feasible. The superiority of the proposed predictive model compared with the single gray GM(1,1) model is demonstrated. The reliability of this model is experienced by the accuracy test, which provides a theoretical guidance for the prediction of automobile part sales. And the average relative error is reduced by 8.52% compared with the single GM(1,1) model.

This paper examined the three-dimensional steady thin film flow of tangent hyperbolic fluid with nonlinear mixed convection flow and entropy generation past a stretching surface under the influence of magnetic field. For the flow problem, the Cattaneo–Christov heat and mass diffusion model was employed to examine heat and mass transfer characteristics and impacts of the normally directed magnetic field. To transform nonlinear PDEs into ODEs, the variable transformation technique was used. The bvp4c algorithm was implemented to solve these ODEs. The behavior of every leading parameter on the velocities, temperature, concentration profile, entropy generation, and Bejan number was reported with tabular and figurative form. The results show that as the values of Br increase, the entropy generation enhances, but the Bejan number decreases. Moreover, as the values of B increase, the opposite characteristics are observed in entropy generation and Bejan number graphs. Furthermore, the skin friction coefficient number, local Nusselt number, and Sherwood number are graphically discussed for the active involved parameters. The best agreement is recorded when we compare this paper with the previous literature for various values of M .

Solving nonlinear equation systems for engineering applications is one of the broadest and most essential numerical studies. Several methods and combinations were developed to solve such problems by either finding their roots mathematically or formalizing such problems as an optimization task to obtain the optimal solution using a predetermined objective function. This paper proposes a new algorithm for solving square and nonsquare nonlinear systems combining the genetic algorithm (GA) and the homotopy analysis method (HAM). First, the GA is applied to find out the solution. If it is realized, the algorithm is terminated at this stage as the target solution is determined. Otherwise, the HAM is initiated based on the GA stage’s computed initial guess and linear operator. Moreover, the GA is utilized to calculate the optimum value of the convergence control parameter (h) algebraically without plotting the h-curves or identifying the valid region. Four test functions are examined in this paper to verify the proposed algorithm’s accuracy and efficiency. The results are compared to the Newton HAM (NHAM) and Newton homotopy differential equation (NHDE). The results corroborated the superiority of the proposed algorithm in solving nonlinear equation systems efficiently.

This paper studies and analyzes a model describing the flow of contaminated brines through the porous media under severe thermal conditions caused by the radioactive contaminants. The problem is approximated based on combining the mixed finite element method with the modified method of characteristics. In order to solve the resulting algebraic nonlinear equations efficiently, a two-grid method is presented and discussed in this paper. This approach includes a small nonlinear system on a coarse grid with size H and a linear system on a fine grid with size h . It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy H = O h 1 / 3 .

The objective of this paper is to establish an accurate nonlinear mathematical model of the hydraulic damper during the orifice-working stage. A new mathematical model including the submodels of the orifices, hydraulic fluids, pressure chambers, and reservoir chambers is established based on theories of the fluid mechanics, hydropneumatics, and mechanics. Subsequently, a force element based on the established model of the hydraulic damper which contains 56 inputs, 6 force states, and 47 outputs is developed with the FORTRAN language in the secondary development environment of the multibody dynamics software SIMPACK. Using the force element, the damping characteristics of the modified yaw damper with different diameters of the base orifice are calculated under different amplitudes and frequencies of the sine excitation, and then the simulation results are compared with the experimental results which are obtained under the same conditions. Results show that during the orifice-working stage, the new established mathematical model can accurately reproduce the nonlinear static and dynamic characteristics of hydraulic dampers such as the force-displacement characteristic, force-velocity characteristic, fluid shortage, hysteresis effect, and pressure limited effect. Furthermore, it also shows that the nonlinear characteristics of the orifice, air release, cavitation, leakage for high frequencies, and dynamic characteristics of fluid (i.e., the density, bulk modulus, and air/gas content) should be taken seriously during the modelling of the hydraulic damper at the orifice-working stage. The mathematical model proposed in this paper is more applicable to the railway vehicle system dynamics and individual system description of the hydraulic damper.

Synthetic aperture imaging (SAI) technology gets the light field information of the scene through the camera array. With the large virtual aperture, it can effectively acquire the information of the partially occluded object in the scene, and then we can focus on the arbitrary target plane corresponding to the reference perspective through the refocus algorithm. Meanwhile, objects that deviate from the plane will be blurred to varying degrees. However, when the object to be reconstructed in the scene is occluded by the complex foreground, the optical field information of the target cannot be effectively detected due to the limitation of the linear array. In order to deal with these problems, this paper proposes a nonlinear SAI method. This method can obtain the occluded object’s light field information reliably by using the nonlinear array. Experiments are designed for the nonlinear SAI, and refocusing is performed for the occluded objects with different camera arrays, different depths, and different distribution intervals. The results demonstrate that the method proposed in this paper is advanced than the traditional SAI method based on linear array.

In this paper, one unscented Kalman filter with adjustable scaling parameters is proposed to estimate the state of charge (SOC) for lithium-ion batteries, as SOC is most important in monitoring the latter battery management system. After the equivalent circuit model is applied to describe the lithium-ion battery charging and discharging properties, a state space equation is constructed to regard SOC as its first state variable. Based on this state space model about SOC, one state estimation problem corresponding to the nonlinear system is established. In implementing the unscented Kalman filter, state estimation is influenced by the scaling parameter. Then, one criterion function is constructed to choose the scaling parameter adaptively by minimizing this criterion function. To extend one single unscented Kalman filter with adjustable scaling parameters to multiple module estimation, one improved unscented Kalman filter is advised based on iterative multiple models. Generally, the main contributions of this paper consist in two folds: one is to introduce a selection strategy for the scaling parameter adaptively, and the other is to combine iterative multiple models and a single unscented Kalman filter with adjustable scaling parameters. Finally, two simulation examples confirm that our unscented Kalman filter with adjustable scaling parameters and its improved iterative form are better than the classical Kalman filter; i.e., our obtained SOC estimation error converges to zero.

Reconstruction of realistic economic data often causes social economists to analyze the underlying driving factors in time-series data or to study volatility. The intrinsic complexity of time-series data interests and attracts social economists. This paper proposes the bilateral permutation entropy (BPE) index method to solve the problem based on partly ensemble empirical mode decomposition (PEEMD), which was proposed as a novel data analysis method for nonlinear and nonstationary time series compared with the T-test method. First, PEEMD is extended to the case of gold price analysis in this paper for decomposition into several independent intrinsic mode functions (IMFs), from high to low frequency. Second, IMFs comprise three parts, including a high-frequency part, low-frequency part, and the whole trend based on a fine-to-coarse reconstruction by the BPE index method and the T-test method. Then, this paper conducts a correlation analysis on the basis of the reconstructed data and the related affected macroeconomic factors, including global gold production, world crude oil prices, and world inflation. Finally, the BPE index method is evidently a vitally significant technique for time-series data analysis in terms of reconstructed IMFs to obtain realistic data.

One of the most popular statistical models is a low-order polynomial response surface model, i.e., a polynomial of first order or second order. These polynomials can be used for global metamodels in weakly nonlinear simulation to approximate their global tendency and local metamodels in response surface methodology (RSM), which has been studied in various applications in engineering design and analysis. The order of the selected polynomial determines the number of sampling points (input combinations) and the resulting accuracy (validity, adequacy). This paper derives a novel method to obtain an accurate high-order polynomial while requiring fewer sampling points. This method uses a two-stage procedure such that the second stage modifies the low-order polynomial estimated in the first stage; this second stage does not require new points. This paper evaluates the performance of the method numerically by using several test functions. These numerical results show that the proposed method can provide more accurate predictions than the traditional method.

This paper presents a new solubility optimal system to improve the efficiency of supercritical fluid extraction (SFE). The major contribution is a nonlinear temperature-pressure decoupling model constructed with unequal-interval grey optimal models (UEIGOMs) and Peng-Robinson models (PRMs). The linear parts of temperature and pressure process can be constructed with UEIGOM, respectively. The nonlinear parts of temperature and pressure process can be described by PRMs, respectively. The whole nonlinear model cannot be input-output decoupled resulting from the singularity of decoupling matrix for PRM. This problem on input-output nondecoupling can be transformed to the problem on disturbance decoupling for a class of MIMO nonlinear systems. Therefore, the whole nonlinear coupling model can be disturbance decoupled. Furthermore, solubility optimal method is presented in the paper; it can calculate the optimal pressure according to the given temperature, namely, optimal working points, to maximize solubility for SFE process. The feasibility, effectiveness, and practicality of the proposed nonlinear temperature-pressure decoupling model constructed with UEIGOMs and PRMs are verified by SFE experiments in biphenyl. Experiments using the designed solubility optimal system are carried out to demonstrate the effectiveness in control scheme, simplicity in structure, and flexibility in implementation for the proposed solubility optimal system based on a new nonlinear temperature-pressure coupling model constructed with UEIGOMs and PRMs.

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method.

Methods of utilizing independent component analysis (ICA) give little guidance about practical considerations for separating single-channel real-world data, in which most of them are nonlinear, nonstationary, and even chaotic in many fields. To solve this problem, a three-step method is provided in this paper. In the first step, the measured signal which is assumed to be piecewise higher order stationary time series is introduced and divided into a series of higher order stationary segments by applying a modified segmentation algorithm. Then the state space is reconstructed and the single-channel signal is transformed into a pseudo multiple input multiple output (MIMO) mode using a method of nonlinear analysis based on the high order statistics (HOS). In the last step, ICA is performed on the pseudo MIMO data to decompose the single channel recording into its underlying independent components (ICs) and the interested ICs are then extracted. Finally, the effectiveness and excellence of the higher order single-channel ICA (SCICA) method are validated with measured data throughout experiments. Also, the proposed method in this paper is proved to be more robust under different SNR and/or embedding dimension via explicit formulae and simulations.

This paper presentsH∞excitation control design problem for power systems with input time delay and disturbances by using nonlinear Hamiltonian system theory. The impact of time delays introduced by remote signal transmission and processing in wide-area measurement system (WAMS) is well considered. Meanwhile, the systems under investigation are disturbed by random fluctuation. First, under prefeedback technique, the power systems are described as a nonlinear Hamiltonian system. Then theH∞excitation controller of generators connected to distant power systems with time delay and stochasticity is designed. Based on Lyapunov functional method, some sufficient conditions are proposed to guarantee the rationality and validity of the proposed control law. The closed-loop systems under the control law are asymptotically stable in mean square independent of the time delay. And we through a simulation of a two-machine power system prove the effectiveness of the results proposed in this paper.

This paper focuses on the filtering problems of nonlinear discrete-time stochastic dynamic systems, such as the model simplification, noise characteristics uncertainty, initial conditions uncertainty, or system parametric variation. Under these circumstances, the measurements of system have one sampling time random delay. A new method, that is, strong tracking filtering algorithm of randomly delayed measurements (STF/RDM) for nonlinear systems based on recursive operating by analytical computation and first-order linear approximations, is proposed; a principle of extended orthogonality is presented as a criterion of designing the STF/RDM, and through the residuals between available and predicted measurements, the formula of fading factor is obtained. Under the premise of using the extended orthogonality principle, STF/RDM proposed in this paper can adjust the fading factor online via calculating the covariance of residuals, and then the gain matrices of the STF/RDM adjust in real time to enhance the performance of the proposed method. Lastly, in order to prove that the performance of STF/RDM precedes existing EKF method, the experiment of tracking maneuvering aircraft is carried out.

The one-dimensional continuous genetic algorithm (CGA) previously developed by the principal author is extended and enhanced to deal with two-dimensional spaces in this paper. The enhanced CGA converts the partial differential equations into algebraic equations by replacing the derivatives appearing in the differential equation with their proper finite difference formula in 2D spaces. This optimization methodology is then applied for the solution of steady-state two-dimensional Stokes and nonlinear Navier Stokes problems. The main advantage of using CGA for the solution of partial differential equations is that the algorithm can be applied to linear and nonlinear equations without any modification in its structure. A comparison between the results obtained using the 2D CGA and the known Galerkin finite element method using COMSOL is presented in this paper. The results showed that CGA has an excellent accuracy as compared to other numerical solvers.

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods.

Spheroid disturbance of input data brings great challenges to support vector regression; thus it is essential to study the robust regression model. This paper is dedicated to establish a robust regression model which makes the regression function robust against disturbance of data and system parameter. Firstly, two theorems have been given to show that the robust linearε-support vector regression problem could be settled by solving the dual problems. Secondly, it has been focused on the development of robust support vector regression algorithm which is extended from linear domain to nonlinear domain. Finally, the numerical experiments result demonstrates the effectiveness of the models and algorithms proposed in this paper.

This paper considers controller parameterization method ofH∞control for polynomial Hamiltonian systems (PHSs), which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems areH∞stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimizeH∞control by adjusting parameters. All these results are expected to be of use in the study ofH∞control for nonlinear systems with perturbations.

The dissipative delay-feedback control problems for nonlinear stochastic delay systems (NSDSs) based on dissipativity analysis are studied in this paper. Based on the Lyapunov stability theory and stochastic analysis technique, both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequalities- (LMIs-) based feasibility tests. The obtained results in this paper for the nominal systems include the available results onH∞approach and passivity for stochastic delay systems as special cases. The delay-dependent feedback controller is designed by considering the relationship among the time-varying delay, its lower and upper bound, and its differential without ignoring any terms, which effectively reduces the conservative. A numerical example is given to illustrate the theoretical developments.

This paper studies the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Based on the sliding mode control theory, we present a new method for the sliding mode controller design and the control law algorithm for such systems. In order to achieve the goal of stabilization unified chaotic systems, the presented controller can make the movement starting from any point in the state space reach the sliding mode in limited time and asymptotically reach the origin along the switching surface. Compared with the existing literature, the controller designed in this paper has many advantages, such as small chattering, good stability, and less conservative. The analysis of the motion equation and the simulation results all demonstrate that the method is effective.

This paper presents a method determining neighborhoods of the image pixels automatically in adaptive denoising. The neighborhood is named stationary neighborhood (SN). In this method, the noisy image is considered as an observation of a nonlinear time series (NTS). Image denoising must recover the true state of the NTS from the observation. At first, the false neighbors (FNs) in a neighborhood for each pixel are removed according to the context. After moving the FNs, we obtain an SN, where the NTS is stationary and the real state can be estimated using the theory of stationary time series (STS). Since each SN of an image pixel consists of elements with similar context and nearby locations, the method proposed in this paper can not only adaptively find neighbors and determine size of the SN according to the characteristics of a pixel, but also be able to denoise while effectively preserving edges. Finally, in order to show the superiority of this algorithm, we compare this method with the existing universal denoising algorithms.

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.

To a large extent, the efficiency and durability of the proton exchange membrane fuel cell (PEMFC) depend on the effective control of air supply system. However, dynamic load scenarios, internal and external disturbances, and the characteristics of strong nonlinearity make the control of complex air supply systems challenging. This paper mainly studies the modeling of PEMFC air supply system and the design of a nonlinear controller for oxygen excess ratio tracking control. First, we analyze and calibrate the system’s optimal oxygen excess ratio control target and explore how the system temperature and humidity impact it, respectively; second, a second-order affine oriented control model which can represent the static and dynamic characteristics of the air supply system is derived, and a disturbance observer is designed to estimate and compensate the “lumped error” online. Then, aiming at the problem of unmeasurable cathode pressure, a state observer based on Kalman optimal estimation algorithm is proposed to realize the real-time estimation of cathode pressure; finally, a dynamic output feedback control system based on observer and backstepping nonlinear controller is proposed, and the comparison and evaluation of two control strategies based on constant oxygen excess ratio tracking and optimal oxygen excess ratio tracking are carried out. The simulation results show the effectiveness and superiority of the designed control system compared with the reference controller.

This paper investigates the input-to-state stable in the mean (ISSiM) property of the switched stochastic nonlinear (SSN) systems with an improved average dwell time (ADT) method in two cases: (i) all of the constituent subsystems are ISSiM and (ii) parts of the constituent subsystems are ISSiM. First, an improved ADT method for stability of SSN systems is introduced. Then, based on that not only a new ISSiM result for SSN systems whose subsystems are ISSiM is presented, but also a new ISSiM result for such systems in which parts of subsystems are ISSiM is established. In comparison with the existing ones, the main results obtained in this paper have some advantages. Finally, an illustrative example with numerical simulation is verified the correctness and validity of the proposed results.

Although polynomial NARX models have been intensively used in nonlinear system identification, few papers discussed how to relate the inner nonlinearities to specific types of clusters and regressors. The objective of this paper is to discuss this relationship for a class of systems that contain even or odd nonlinearities. This class covers block-structured models (Hammerstein, Wiener, and others) and systems with dynamic nonlinearities. To achieve the paper’s aim, a deep frequency-domain analysis is performed. For each type of nonlinearity, all the NARX clusters are investigated and the results show that each regressor type provides specific nonlinear contribution. The investigation is based on an output power spectra analysis when a specific multisinusoidal excitation is applied. According to the spectral contributions in some of the frequency lines, the nonlinearity classification is possible. By applying the same procedure to the clusters, one interprets how these clusters can (or not) contribute to explain the system nonlinearity. The paper findings have two major impacts: (i) one gains deep knowledge on how the nonlinearities are coded by the clusters, and (ii) this information can be used, for instance, to aid a structure selection procedure (ERR, term clustering, etc.) during the discarding of the clusters which are not able to explain the system nonlinear behavior. Some practical and experimental aspects are discussed, while numerical examples are presented to show the validity of the theoretical analysis.

This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

This paper outlines a methodology to study the stability of Takagi-Sugeno's (TS) fuzzy models. The stability analysis of the TS model is performed using a quadratic Liapunov candidate function. This paper proposes a relaxation of Tanaka's stability condition: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them. The coefficients of this sums depend on the membership functions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among which the Parallel Distributed Compensation (PDC). An application to the inverted pendulum is proposed here.

In this paper, the generic uniqueness of Pareto weakly efficient solutions, especially Pareto-efficient solutions, of vector optimization problems is studied by using the nonlinear and linear scalarization methods, and some further results on the generic uniqueness are proved. These results present that, for most of the vector optimization problems in the sense of the Baire category, the Pareto weakly efficient solution, especially the Pareto-efficient solution, is unique. Furthermore, based on these results, the generic Tykhonov well-posedness of vector optimization problems is given.

This paper considers the characterization and computation of invariant sets for discrete-time, time-invariant, linear systems with disturbance inputs whose values are confined to a specified compact set but are otherwise unknown. The emphasis is on determining maximal disturbance-invariant sets X that belong to a specified subset Γ of the state space. Such d-invariant sets have important applications in control problems where there are pointwise-in-time state constraints of the form χ ( t ) ∈ Γ . One purpose of the paper is to unite and extend in a rigorous way disparate results from the prior literature. In addition there are entirely new results. Specific contributions include: exploitation of the Pontryagin set difference to clarify conceptual matters and simplify mathematical developments, special properties of maximal invariant sets and conditions for their finite determination, algorithms for generating concrete representations of maximal invariant sets, practical computational questions, extension of the main results to general Lyapunov stable systems, applications of the computational techniques to the bounding of state and output response. Results on Lyapunov stable systems are applied to the implementation of a logic-based, nonlinear multimode regulator. For plants with disturbance inputs and state-control constraints it enlarges the constraint-admissible domain of attraction. Numerical examples illustrate the various theoretical and computational results.

The paper proposes a procedure for design of PI controllers for hydraulic systems with long transmission lines which are described by models of high order. Design is based on the combination of the IE criterion and engineering specifications (settling time and relative stability) as well as on the application ofD-decomposition. In comparison with some known results, the method is of graphical character, and it is very simple (solving nonlinear algebraic equations is eliminated). The paper presents the algorithm of software procedure for design of the controller. The method is compared with other methods at the level of simulation, and its superiority is shown. By applying the Nyquist criterion, it is shown that the method possesses robustness in relation to non modelled dynamics.

Continuous-time recurrent neural networks (RNNs) play an important part in practical applications. Recently, due to the ability of assuring the convergence of the equilibriums on the boundary line between stable and unstable, the study on the critical dynamics behaviors of RNNs has drawn especial attentions. In this paper, a new asymptotical stable theorem and two corollaries are presented for the unified RNNs, that is, the UPPAM RNNs. The analysis results given in this paper are under the generallyP-critical conditions, which improve substantially upon the existing relevant critical convergence and stability results, and most important, the compulsory requirement of diagonally nonlinear activation mapping in most recent researches is removed. As a result, the theory in this paper can be applied more generally.

This paper is concerned with an integral terminal sliding mode tracking control for a class of uncertain nonaffine nonlinear systems. Firstly, the nonaffine nonlinear systems is approximated to facilitate the desired control design via a novel dynamic modeling technique. Next, for the unmeasured disturbance of nonlinear systems, integral terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to zero in the finite time. Subsequently, based on approximated nonlinear model and the designed disturbance observer, the integral terminal sliding mode tracking control is presented for nonaffine nonlinear systems with uncertainty. Different from traditional terminal sliding-mode control, this paper accomplishes finite convergence time for nonaffine nonlinear systems and avoids the singular problem in the controller design. Furthermore, the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated. Finally, two numerical simulation results are given to illustrate the effectiveness of the proposed method.

The aim of this paper is to study the controllability of fractional systems involving the Atangana–Baleanu fractional derivative using the Caputo approach. In the first step, the solution of a linear fractional system is obtained. Then, based on the obtained solution, some necessary and sufficient conditions for the controllability of such a system will be presented. Afterwards, the controllability of a nonlinear fractional system will be analyzed, based on these results. Our tool for the presentation of the sufficient conditions of controllability in this part is Schauder fixed point theorem. In the last step, the analytical results are illustrated by numerical examples.

Chaotic oscillation will occur in power system when there exist periodic load disturbances. In order to analyze the chaotic oscillation characteristics and suppression method, this paper establishes the simplified mathematical model of the interconnected two-machine power system and analyzes the nonlinear dynamic behaviors, such as phase diagram, dissipation, bifurcation map, power spectrum, and Lyapunov exponents. Based on fractional calculus and sliding mode control theory, the fractional-order hyperbolic tangent sliding mode control is proposed to realize the chaotic oscillation control of the power system. Numerical simulation results show that the proposed method can not only suppresses the chaotic oscillation but also reduce the convergence time and suppress the chattering phenomenon and has strong robustness.

In order to mitigate the seismic response of a cable-stayed bridge, a new type damping device named asymmetric pounding tuned mass damper (APTMD) is developed in this paper on the basis of the traditional symmetric pounding tuned mass damper. The novel APTMD has three parameters to be determined: the left-side gap, the right-side gap, and the frequency ratio. A numerical model of the APTMD damping system is established with consideration of both the computational efficiency and accuracy to enable the parametric optimization of the damper. The numerical model is based on a simplified model of the cable-stayed bridge and a nonlinear pounding force model. The genetic algorithm is utilized for the optimization of the damper. Afterwards, the cable-stayed bridge is subjected to 20 recorded ground motions to evaluate the vibration control effectiveness of the APTMD. Four systems are considered: (1) without dampers; (2) with a TMD; (3) with a PTMD; and (4) with an APTMD. Time history analysis reveals the following: (1) those dampers can all effectively suppress the vibration of the bridge and (2) the vibration control effectiveness of the APTMD is slightly better than the TMD and the PTMD.

This paper addresses the problem of composite curve path following for an underactuated autonomous underwater vehicle by utilizing an adaptive integral line-of-sight (AILOS) guidance and nonlinear iterative sliding mode (NISM) controller. First, the composite curve path is parametrized by a common scalar variable in a continuous way. Then, the kinematics error of an underactuated vehicle is described based on the nonprojection Frenet–Serret frame with a virtual point, which can be eliminated by the virtual point control and AILOS guidance. Meanwhile, the subpath switching algorithm is studied to realize the global path following for the composite curve path. Besides, the NISM controller is cascaded with the AILOS guidance law, and the cascade structure proved to be globally κ -exponentially stable under the influence of slow time-varying currents. Finally, simulations are considered to demonstrate the effectiveness of the proposed composite curve path following control scheme.

Firstly, this paper puts forward two new types of suspension vibration reduction systems (SVRSs) with geometric nonlinear damping based on general SVRS (GSVRS), which only has geometric nonlinear stiffness. Secondly, it derives the motion differential equations for the two new types of SVRS, respectively, and discusses the similarities and differences among the two types and GSVRS through the comparison of motion differential equations. Then, it conducts dimensionless processing of the motion differential equations for the two new types of SVRS and carries out a comparative study on the vibration isolation performance of the two types of SVRS under impact excitation and random excitation, respectively. At last, it performs the optimal computation of the chosen new type of SVRS through the ergodic optimization method and studies the influence rule of SVRS parameters on vibration isolation performance so as to realize the optimization of vibration isolation performance.