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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.

Vehicle states estimation (e.g., vehicle sideslip angle and tire force) is a key factor for vehicle stability control. However, the accurate values of these parameters could not be obtained directly. In this paper, an interacting multiple model-cubature Kalman filter (IMM-CKF) is used to estimate the vehicle state parameters. And improvements about estimation method are achieved in this paper. Firstly, the accuracy of the reference model is improved by building two different models: one is 7-degree-of-freedom (7 DOF) vehicle model with linear tire model, and the other is 7 DOF vehicle model with nonlinear Dugoff tire model. Secondly, the different models are switched by IMM-CKF to match different driving condition. Thirdly, the lateral acceleration correction for sideslip angle estimation is considered, because the sensor of lateral acceleration is easy to be influenced by the gravity on banked road. Then, to compare cubature Kalman filter (CKF) estimation method and IMM-CKF estimation method Hardware-In-Loop (HIL) tests are carried out in the paper. And simulation results show that IMM-CKF methodology can provide accurate estimation values of vehicle states parameters.

In this paper, post-buckling and free nonlinear vibration of microbeams resting on nonlinear elastic foundation subjected to axial force are investigated. The equations of motion of microbeams are derived by using the modified couple stress theory. Using Galerkin’s method, the equation of motion of microbeams is reduced to the nonlinear ordinary differential equation. By using the equivalent linearization in which the averaging value is calculated in a new way called the weighted averaging value, approximate analytical expressions for the nonlinear frequency of microbeams with pinned–pinned and clamped–clamped end conditions are obtained in closed-forms. Comparisons with previous solutions are showed accuracy of the present solutions. Effects of the material length scale parameter and the axial compressive force on the frequency ratios of microbeams; and effect of the material length scale parameter on the buckling load ratios of microbeams are investigated in this paper.

In this paper, relying on the Volterra series nonlinear system model and the high-order kernel Hilbert’s reconstructed kernel fast solved algorithm, a fault feature frequency domain identification method based on Volterra high-order kernel generalized frequency response graph analysis is proposed. Firstly, the method uses the system input and output vibration signals to determine the Volterra model. Then, the Volterra high-order kernel function is solved quickly by reproducing kernel Hilbert space method, and the generalized frequency response function is used to identify the model. Finally, multidimensional high-order spectral pattern analysis is used to separate and extract the fault and degree characteristic information implied by frequency and phase coupling in the third-order kernel function. Following the theoretical approach, in the experimental part, this paper uses the planetary gearbox fault loading test rig to complete the data collection and establishes the Volterra experimental model through the measured data. The generalized frequency responses of each order kernel function are compared and analyzed and the capability of distinguishing and the adaptability of different order kernel functions for the degree of crack failure are discussed. The effects of changing the memory length of the Volterra model and the order of the kernel function on the recognition result are verified. The final experimental results show that the use of reproducing kernel Hilbert space can effectively avoid the dimension disaster problem that occurs in the high-order kernel solution process. Moreover, the third-order kernel can describe more intuitively the nonlinear system model under multifactor coupling than the second-order kernel. Finally, Volterra series model the third-order kernel’s generalized frequency response can effectively distinguish between nondefective and faulty gears, and its resolution is enough to distinguish the degree of failure of gear cracks.

The adaptive fuzzy output feedback control problem for a class of pure feedback systems with partial state constraints is addressed in this paper. The fuzzy state observers are designed to estimate the unmeasured state while the fuzzy logic systems are used to approximate the unknown nonlinear functions. The proposed adaptive fuzzy output feedback controller can guarantee that the partial state constraints are not violated, and all closed-loop signals remain bounded by use of Barrier Lyapunov Functions (BLFs). A numerical example is presented to illustrate the effectiveness of the results in this paper.

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.

The Magic Formula tire model can describe the mechanical properties of tire accurately and thus is applied in the research field of vehicle dynamics widely. The Magic Formula tire model has the characteristics of a great number of parameters and the high nonlinearity, so it is hard to identify parameters. Researchers generally use different intelligent optimization algorithms for parameter identification. However, in the process of parameter identification, with a few experimental data, parameter identification results generally have the low accuracy, while, in the case of a large number of experimental data, the amount of work done in the experiment will increase and there will be many experimental errors. To solve these problems, this paper researches the longitudinal force of tire and proposes an interpolation method and a method based on the nonlinear research of the tire force. The results of parameter identification experiments on the two kinds of tire data show that both of the two methods can be used for the parameter identification of Magic Formula tire model fast and accurately with only a few experimental data. In addition, this paper proposes a method estimating the maximum longitudinal force and corresponding slip rate.

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 deals with the hybrid particle swarm optimization-Cuckoo Search (PSO-CS) algorithm which is capable of solving complicated nonlinear optimization problems. It combines the iterative scheme of the particle swarm optimization (PSO) algorithm and the searching strategy of the Cuckoo Search (CS) algorithm. Details of the PSO-CS algorithm are introduced; furthermore its effectiveness is validated by several mathematical test functions. It is shown that Lévy flight significantly influences the algorithm’s convergence process. In the second part of this paper, the proposed PSO-CS algorithm is applied to two different engineering problems. The first application is nonlinear parameter identification for the motor drive servo system. As a result, a precise nonlinear Hammerstein model is obtained. The second one is reactive power optimization for power systems, where the total loss of the researched IEEE 14-bus system is minimized using PSO-CS approach. Simulation and experimental results demonstrate that the hybrid optimal algorithm is capable of handling nonlinear optimization problems with multiconstraints and local optimal with better performance than PSO and CS algorithms.

Based on the plastic upper bound theorem, a three-dimensional kinematically admissible velocity field is constructed for the collapse of the soil masses above a shallow tunnel. In this field, this paper considers the influences of the roof stratification, pore water pressure, ground overload, and support pressure. This study deduced the upper bound solutions of the weight of the collapsed soil masses and the corresponding collapse surfaces by utilizing the nonlinear failure criterion, associated flow rule, and variation principle. Furthermore, we verified the validity of the proposed method in this paper by comparing this research with the existing work and numerical simulation results. This study obtains the influence laws of varying parameters on the area and weight of the collapsed soil masses. The results reveal that the area and weight of the collapsed soil masses increase with increasing support pressure and soil cohesion, but decrease with increasing thickness of the upper soil layer, nonlinear coefficient, pore water pressure, and ground overload. Among them, the roof stratification, pore water pressure, soil cohesion, and nonlinear coefficient have a significant influence on tunnel collapse, which should be given special consideration in engineering design.

This paper is concerned with the nonlinear static behavior of a cantilever functionally graded material (FGM) microbeam with the influence of thermal stress and the intermolecular force. A significant extension of the recent works of constructing analytical approximate solutions to a clamped-clamped FGM MEMS/NEMS beam is formed in the paper. Based on the modified couple stress theory and an internal material length-scale parameter, the governing equations account for the microbeam size dependency. Note that the thermal force and moment in boundary condition make procedure of solution more complex. The combinations of Galerkin method and the assumption of deflection function are used to establish analytical approximate solutions which have brief expressions. Good agreements of approximate results are found for large range of free-end deflection of cantilever FGM microbeam through comparing them with numerical solutions and other existing results. The influence of various physical parameters, such as the material attributes (Young modulus, Poisson ratio, etc.), the electrostatic gap, and microsize of the beam on mechanical behavior, or Pull-In voltage of electrostatically actuated microbeams, could also be investigated with these analytical expressions.

This paper presents mega-sub isolation system. Shaking table test of the mega-sub isolation system is carried out in this paper. Three test models have been developed. One is called aseismic model, in which all the substructures are fixedly connected with the megastructures. The second one is known as isolated model, where the substructures are connected with the megastructures with isolators, and the last one is called the lower substructure consolidated (LSC) model, in which all the substructures except for the substructures at the lowest level, in other words, substructures at the second mega floor, are isolated from the megastructures. Nonlinear dynamic time analysis of the test models is conducted by SAP2000. Acceleration responses of the megastructure, story drift responses of the megastructure and the substructure, and the deformations of the isolation layer are compared between experimental and numerical simulation results. The results show that the experimental results and numerical simulation results agree well with each other, and the isolated model and LSC model perform better than the counterpart aseismic model. The structures with isolation devices can reduce the structural responses effectively and are much safer than the structure without isolation devices.

Pressure regulator is a common device used to regulate the working pressure for plants and machines. In aerospace propulsion systems, it is used to pressurize liquid propellant rocket tanks at specified pressure for obtaining the required propellant mass flow rate. In this paper, a generalized model is developed to perform dynamic analysis of a pressure regulator so that constant pressure at outlet can be attained. A nonlinear mathematical model of pressure regulator is developed that consists of dynamic equation of pressure, temperature, equation of mass flow rate, and moving shaft inside regulator. The system of nonlinear and coupled differential equations is numerically simulated and computation of pressure and temperature is carried out for required conditions and given design parameters. Valve opening and mass flow rate are also found as a function of given inlet pressure and time. In the end, an analytical solution based on constant mass flow rate assumption is compared with nonlinear formulation. The results demonstrate a high degree of confidence in the nonlinear modeling framework proposed in this paper. The proposed model solves a real problem of liquid rocket propulsion system. For the real system under consideration, inlet pressure of regulator is decreased linearly from 150 bar to 60 bar and outlet pressure of nearly 15 bar is required from pressure regulator for the complete operating time of 19 s.

This paper presents a novel way of controlling the bouncing phenomenon commonly present in the Radio Frequency Microelectromechanical Systems (RF MEMS) switches using a double-electrode configuration. The paper discusses modeling bouncing using both lumped parameter and beam models. The simulations of bouncing and its control are discussed. Comparison between the new proposed method and other available control techniques is also made. The Galerkin method is applied on the beam model accounting for the nonlinear electrostatic force, squeeze film damping, and surface contact effect. The results indicate that it is possible to reduce bouncing and hence beam degradation, by the use of double electrodes.

This paper is concerned with consensus of heterogeneous nonlinear multiagent systems via distributed control. Both the cases of leaderless and leader-following are systematically investigated. Different from some existing results, completed consensus can be reached in this paper among heterogeneous multiagent network instead of bounded-consensus. First, a novel distributed control protocol is proposed, and some general consensus criterions are derived for multiagent systems without leader. Second, a leader with unknown but bounded input for the heterogeneous multiagent network is considered; aperiodically intermittent communications among followers are considered to avoid channel blocking in this case. Finally, two simulation examples are presented to verify the effectiveness of the main results.

Flexible photoelectric film is an anisotropic material. The slight change of equipment performance during processing is prone to cause deformation of the material. Therefore, it is important to predict the degradation of processing equipment performance. Since the performance degradation of flexible photoelectric film material Roll-to-Roll (R2R) processing equipment is a nonlinear process, this paper introduces an adaptive fuzzy clustering method to construct a fuzzy membership function model for calculating the performance degradation index of R2R processing equipment and studies the parameter solving method such as the AFCM division of the roller vibration data, the category center value of the fuzzy membership function, and the input data division area width. Finally, the performance degradation index calculation algorithm is designed. The roller shaft accelerated life test was carried out using self-made equipment. The test data were 1000 sets. The results showed that the root mean square eigenvalues and the kurtosis eigenvalues of the roller vibration data are sensitive to the performance degradation. The equipment performance curve described by the first and second types of performance degradation indicators was very stable in the early stage. After the 800th group, the curve continued to decrease, and the change was more severe, indicating that the performance degradation of the equipment is more serious. In the 980th group, the longer-lasting roller shaft was damaged, and the performance index value was about zero, which proved the correctness of the performance degradation prediction method proposed in this paper in calculating the performance degradation value of the equipment.

This paper investigates the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems of a class of nonlinear descriptor systems via dissipative matrix method. Firstly, under an output feedback law, two nonlinear descriptor systems are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two resulting closed-loop systems. Then, the two systems are combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique. Based on the dissipative system, an adaptive parallel simultaneous stabilization controller and a robust adaptive parallel simultaneous stabilization controller are designed for the two systems. Furthermore, the case of more than two nonlinear descriptor systems is investigated. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the adaptive parallel simultaneous stabilization controllers obtained in this paper work very well.

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 investigates a tracking problem for flexible air-breathing hypersonic vehicles (FAHVs) with composite disturbance. The composite disturbance produced by flexible effects, parameter uncertainties, and external interferences is modeled as a kind of unknown derivative-bounded disturbance in this paper. Then a novel composite control strategy is presented for the nonlinear FAHV model with the composite disturbance, which combines a nonlinear disturbance-observer-based compensator (NDOBC) and a dynamic-inversion-based sliding mode controller (DIBSMC). Specifically, the NDOBC is constructed to estimate and compensate for the composite disturbance, and the DIBSMC is designed to track desired trajectories of velocity and flight path angle. Moreover, the uniformly ultimate boundedness of the composite system can be guaranteed by using Lyapunov theory. Finally, simulation results on a full nonlinear model of FAHVs demonstrate that the proposed nonlinear disturbance-observer-based sliding mode controller is more effective than the traditional DIBSMC. Specifically, it is shown that the chattering of traditional DIBSMC in presence of composite disturbances can be attenuated with the NDOBC.

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.

In order to further provide theoretical support for the stability of an auxiliary inverter parallel system, a new model which covers most of control parameters needs to be established. However, the ability of the small-signal model established by the traditional method is extremely limited, so this paper proposes a new small-signal modeling method for the parallel system. The new small-signal model not only can analyze the influence of the droop parameters on the system performance, but also can analyze the influence of the output impedance of the inverter, the unbalanced and nonlinear loads, and the power calculation method and cut-off frequency of the low-pass filter on the system performance and stability. Based on this method, this paper carries out a comprehensive analysis on the performance of a parallel inverter system. And the correctness of the modeling method and analysis process of the system performance and stability are verified by the consistency of the simulation and experimental results.

There have been many approaches for achieving the trajectory tracking control of parallel manipulator. However, these approaches are complex for calculating Lagrangian multipliers. In this paper, unlike the former approaches, a new approach of trajectory tracking control which is based on Udwadia-Kalaba approach is presented. Using this methodology, we can obtain a concise and explicit equation of motion and consider holonomic and nonholonomic constraint whether it is ideal or nonideal simultaneously. The most important difference is that we divide constraints into structural constraints and performance constraints in this paper. Structural constraints are used to establish dynamic model without regard for trajectory control. And performance constraints are used to represent the desired trajectory. For the parallel manipulator, a nonlinear dynamics system, its constraint forces are obtained by second-order constraints. And the numerical simulation in MATLAB shows the parallel manipulator’s movement meets the requirement; tracking trajectory is exact and perfect. Through this paper, we can see that the method can simplify calculation availably.

When applied to solving the data modeling and optimal control problems of complex systems, the dual heuristic dynamic programming (DHP) technique, which is based on the BP neural network algorithm (BP-DHP), has difficulty in prediction accuracy, slow convergence speed, poor stability, and so forth. In this paper, a dual DHP technique based on Extreme Learning Machine (ELM) algorithm (ELM-DHP) was proposed. Through constructing three kinds of network structures, the paper gives the detailed realization process of the DHP technique in the ELM. The controller designed upon the ELM-DHP algorithm controlled a molecular distillation system with complex features, such as multivariability, strong coupling, and nonlinearity. Finally, the effectiveness of the algorithm is verified by the simulation that compares DHP and HDP algorithms based on ELM and BP neural network. The algorithm can also be applied to solve the data modeling and optimal control problems of similar complex systems.

The robust nonlinear dynamic inversion (RNDI) control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI). NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC). SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.

On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear forceQ1and the displacement componentw. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.

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 presented an inverse optimal neural controller with speed gradient (SG) for discrete-time unknown nonlinear systems in the presence of external disturbances and parameter uncertainties, for a power electric system with different types of faults in the transmission lines including load variations. It is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF) based algorithm. It is well known that electric power grids are considered as complex systems due to their interconections and number of state variables; then, in this paper, a reduced neural model for synchronous machine is proposed for the stabilization of nine bus system in the presence of a fault in three different cases in the lines of transmission.

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.

In order to calculate negative skin friction (NSF) of pile group embedded in a consolidating soil, the dragload calculating formulas of single pile were established by considering Davis one-dimensional nonlinear consolidation soils settlement and hyperbolic load-transfer of pile-soil interface. Based on effective influence area theory, a simple semiempirical mathematical model of analysis for predicting the group effect of pile group under dragload was described. The accuracy and reliability of mathematical models built in this paper were verified by practical engineering comparative analysis. Case studies were studied, and the prediction values were found to be in good agreement with those of measured values. Then, the influences factors, such as, soil consolidation degree, the initial volume compressibility coefficient, and the stiffness of bearing soil, were analyzed and discussed. The results show that the mathematical models considering nonlinear soil consolidation and group effect can reflect the practical NSF of pile group effectively and accurately. The results of this paper can provide reference for practical pile group embedded in consolidating soil under NSF design and calculation.

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.

The efficiency and reliability of pumps are highly related to their operation conditions. The concept of the optimization pump operation conditions is to adjust the operation point of the pump to obtain higher reliability at the cost of lower system efficiency using a joint regulation of valve and frequency convertor. This paper realizes the control of the fluid conveying system based on the optimization results. The system is a nonlinear Multi-Input Multioutput (MIMO) system with time delays. In this paper, the time delays are separated from the system. The delay-free system is linearized using input-output linearization and controlled using a sliding mode method. A modified Smith predictor is used to compensate time delays of the system. The control strategy is validated to be effective on the test bench. The comparison of energy consumption and operation point deviation between conventional speed regulation and the new method is presented.

The goal of this special issue of Mathematical Problems in Engineering MPE is to present papers, containing complete reviews on modern dynamics models, available in the current literature, classify them, and discuss their applications and limitations. It was assumed to consider papers containing a discussion on appropriate models and control criteria and on various applications on Engineering and Sciences and suggest directions for further works. The critical reviews, a description of open problems, and future developments were hailed. 93 papers were presented for this issue, and 21 of them were accepted. There are 9 review papers and 12 research articles. In particular, there are reviews on the feedback designs for linear descriptors, modeling of ship dynamics, continuous models for discrete media, applications of fractional calculus in engineering, nonlinear fault tolerant control, simulation of a target tracking system with backlash compensation, dynamics of furuta’s pendulum, and identification approaches for discrete event systems. One review is devoted to advances in structural control of civil engineering in China. There are 8 articles which are devoted to investigations in nonlinear dynamics; 8 articles are devoted to the control problems; 4 articles treat numerical approaches and problems of simulation. The majority of accepted articles contains modeling, as well as analytical and/or numerical investigations. The contents of the 9 reviews papers are briefly summarized in the following.

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 model of a target tracking system assembled in a moving body. The system is modeled in time domain as a nonlinear system, which includes dry friction, backlash in gear transmission, control input tensions saturation, and armature current saturation. Time delays usually present in digital controllers are also included, and independent control channels are used for each motor. Their inputs are the targets angular errors with respect to the system axial axis and the outputs are control tensions for the motors. Since backlash in gear transmission may reduce the systems accuracy, its effects should be compensated. For that, backlash compensation blocks are added in the controllers. Each section of this paper contains a literature survey of recent works dealing with the issues discussed in this article.

Fault tolerant control (FTC) is the branch of control theory, dealing with the control of systems that become faulty during their operating life. Following the systems classification, as linear and nonlinear models, FTC can be classified in two different groups, linear FTC (LFTC) dealing with linear models, and the one of interest to us in this paper, nonlinear FTC (NFTC), which deals with nonlinear models. We present in this paper a survey of some of the results obtained in these last years on NFTC.

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.

This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

In order to solve the influence of load uncertainty on hydrothermal power system operation and achieve the optimal objectives of system power generation consumption, pollutant emissions, and first-stage hydropower station storage capacity, this paper introduced CVaR method and built a multiobjective optimization model and its solving method. In the optimization model, load demand’s actual values and deviation values are regarded as random variables, scheduling objective is redefined to meet confidence level requirement and system operation constraints and loss function constraints are taken into consideration. To solve the proposed model, this paper linearized nonlinear constraints, applied fuzzy satisfaction, fuzzy entropy, and weighted multiobjective function theories to build a fuzzy entropy multiobjective CVaR model. The model is a mixed integer linear programming problem. Then, six thermal power plants and three cascade hydropower stations are taken as the hydrothermal system for numerical simulation. The results verified that multiobjective CVaR method is applicable to solve hydrothermal scheduling problems. It can better reflect risk level of the scheduling result. The fuzzy entropy satisfaction degree solving algorithm can simplify solving difficulty and get the optimum operation scheduling scheme.

This paper focuses on the problems of short-term traffic flow forecasting. The main goal is to put forward traffic correlation model and real-time correction algorithm for traffic flow forecasting. Traffic correlation model is established based on the temporal-spatial-historical correlation characteristic of traffic big data. In order to simplify the traffic correlation model, this paper presents correction coefficients optimization algorithm. Considering multistate characteristic of traffic big data, a dynamic part is added to traffic correlation model. Real-time correction algorithm based on Fuzzy Neural Network is presented to overcome the nonlinear mapping problems. A case study based on a real-world road network in Beijing, China, is implemented to test the efficiency and applicability of the proposed modeling methods.

This paper presents a sensorless speed control strategy for a permanent-magnet synchronous motor (PMSM) based on an adaptive nonlinear extended state observer (ANLESO). In this paper, an extended state observer (ESO), which takes back-EMF (back electromotive force) as an extended state, is used to estimate the rotor position and the rotor speed because of its simpler structure and higher accuracy. Both linear ESO (LESO) and nonlinear ESO (NLESO) are considered to estimate the back-EMF of PMSM, and NLESO is finally implemented due to its obvious advantage in convergence. The convergence characteristics of the estimation error of the observer are analyzed by the Lyapunov theory. In order to take both stability and steady-state error into consideration, an adaptive NLESO is proposed, which adaptively adjusts the parameters of NLESO to a compromised value. The performance of the proposed method was demonstrated by simulations and experiments.

There are many practical systems which can be modelled by dynamical equations. Increasing requirements on system performance mean that within control system analysis and design it is necessary to deal with the increasingly complex dynamical systems that are used to model reality. The complexity stems from nonlinearity, uncertainty, time delay, system singularity, stochastic effects, the presence of interconnections, and so forth. Advances in both technology and control theory have provided the potential to investigate complex dynamical systems. Study on complex systems is becoming increasingly important and this has provided renewed impetus for the development of novel techniques and skills for complex control systems. This provides the motivation for this special issue. The purpose of this special issue is to provide an opportunity for scientists and control engineers to publish their latest, novel, and original contributions to the development of complex control systems. The special issue focusses on recent achievements and applications in the field of control and analysis for complex systems with a special emphasis on how to solve various control design and/or observer design problems for nonlinear systems and interconnected systems. The considered systems typically involve at least two features such as nonlinearity, disturbances/uncertainty, faults, time delay, interconnections between subsystems, system singularity, stochastic processes, and comparison between simulation and experiments. The special issue focuses on results in theoretical research and practical applications with emphasis on novel methodologies for analysis, design, synthesis, and/or applications. The topics within the special issue include interconnected/networked systems, variable structure control, singular system control, time delay systems, fuzzy control and impulsive control, robust observer design and parameter identification, fault detection and fault tolerant control, analysis and control of stochastic systems, and applications of advanced control systems. A total of 109 papers were submitted to the special issue for possible publication and 38 of them were accepted and published following a fair and rigorous review process organised by the guest editorial team with the help of the editorial office. The acceptance rate is less than 35%. The accepted papers have been grouped in the following six clusters.

The first sliding mode control application may be found in the papers back in the 1930s in Russia. With its versatile yet simple design procedure the methodology is proven to be one of the most powerful solutions for many practical control designs. For the sake of demonstration this paper is oriented towards application aspects of sliding mode control methodology. First the design approach based on the regularization is generalized for mechanical systems. It is shown that stability of zero dynamics should be taken into account when the regular form consists of blocks of second-order equations. Majority of applications in the paper are related to control and estimation methods of automotive industry. New theoretical methods are developed in the context of these studies: sliding made nonlinear observers, observers with binary measurements, parameter estimation in systems with sliding mode control.

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.