Search

This paper presents stress influence functions for uniformly distributed, time-harmonic rectangular loads within a three-dimensional, viscoelastic, isotropic full-space. The coupled differential equations relating displacements and stresses in the full-space are solved through double Fourier integral transforms in the wave number domain, in which they can be solved algebraically. The final stress fields are expressed in terms of double indefinite integrals arising from the Fourier transforms. The paper presents numerical schemes with which to integrate these functions accurately. The article presents numerical validation of the synthesized stress kernels and their behavior for high frequencies and large distances from the excitation source. The influence of damping ratio on the dynamic results is also investigated. This article is complementary to previous results of the authors in which the corresponding displacement solutions were derived. Stress influence functions, together with their displacement counterparts, are a fundamental part of many numerical methods of discretization such the boundary element method.

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.

Finite mixture model (FMM) is being increasingly used for unsupervised image segmentation. In this paper, a new finite mixture model based on a combination of generalized Gamma and Gaussian distributions using a trimmed likelihood estimator (GGMM-TLE) is proposed. GGMM-TLE combines the effectiveness of Gaussian distribution with the asymmetric capability of generalized Gamma distribution to provide superior flexibility for describing different shapes of observation data. Another advantage is that we consider the spatial information among neighbouring pixels by introducing Markov random field (MRF); thus, the proposed mixture model remains sufficiently robust with respect to different types and levels of noise. Moreover, this paper presents a new component-based confidence level ordering trimmed likelihood estimator, with a simple form, allowing GGMM-TLE to estimate the parameters after discarding the outliers. Thus, the proposed algorithm can effectively eliminate the disturbance of outliers. Furthermore, the paper proves the identifiability of the proposed mixture model in theory to guarantee that the parameter estimation procedures are well defined. Finally, an expectation maximization (EM) algorithm is included to estimate the parameters of GGMM-TLE by maximizing the log-likelihood function. Experiments on multiple public datasets demonstrate that GGMM-TLE achieves a superior performance compared with several existing methods in image segmentation tasks.

Considering the fact that transboundary pollution control calls for the cooperation between interested parties, this paper studies a cooperative stochastic differential game of transboundary industrial pollution between two asymmetric nations in infinite-horizon level. In this paper, we model two ways of transboundary pollution: one is an accumulative global pollutant with an uncertain evolutionary dynamic and the other is a regional nonaccumulative pollutant. In our model, firms and governments are separated entities and they play a Stackelberg game, while the governments of the two nations can cooperate in pollution reduction. We discuss the feedback Nash equilibrium strategies of governments and industrial firms, and it is found that the governments being cooperative in transboundary pollution control will set a higher pollution tax rate and make more pollution abatement effort than when they are noncooperative. Additionally, a payment distribution mechanism that supports the subgame consistent solution is proposed.

Optimized torque-distribution control method (OTCM) is a critical technology for front/rear axle electric wheel loader (FREWL) to improve the operation performance and energy efficiency. In the paper, a longitudinal dynamics model of FREWL is created. Based on the model, the objective functions are that the weighted sum of variance and mean of tire workload is minimal and the total motor efficiency is maximal. Four nonlinear constraint optimization algorithms, quasi-newton Lagrangian multiplier method, sequential quadratic programming, adaptive genetic algorithms, and particle swarm optimization with random weighting and natural selection, which have fast convergent rate and quick calculating speed, are used as solving solutions for objective function. The simulation results show that compared to no-control FREWL, controlled FREWL utilizes the adhesion ability better and slips less. It is obvious that controlled FREWL gains better operation performance and higher energy efficiency. The energy efficiency of FREWL in equipment transferring condition is increased by 13–29%. In addition, this paper discussed the applicability of OTCM and analyzed the reason for different simulation results of four algorithms.

This paper introduces a game theory approach to implement power flow distribution mission for a fuel cell/battery hybrid system considering uncertain power information. To fully describe the vying interaction relationship between the fuel cell and the battery, we design the power distribution problem as a noncooperative game problem, in which the fuel cell and the battery are deemed to be two interactional players, and each one chooses proper amount of power supply to maximize its own optimization function relying on the other chosen. Different from all previous research work in the published papers, the power demand information of the adopted driving cycle is assumed to be absolutely known. In this paper, we discuss the case that when the power demand is uncertain how the players act and the Nash Equilibrium can be effectively achieved. Three original contributions are made. First, we develop the utility function for each player taking into account the uncertain behavior of the power demand due to inaccurate prediction of driving cycle. Second, an iterative algorithm with a fuzzy logical controller for correction is proposed to reduce the influence of uncertain power demand information on the decisions of the players. Finally, the effectiveness is validated by a comparison simulation test.

The traditional spectral analysis method is used to study the characteristics of bearing fault signals in frequency domain, which is reasonable and effective in general cases. However, it is proved that the fault signals have heavy tails in this paper, which are α stable distribution, and 1<α<2, and even the noises belong to α stable distribution. Then the conventional spectral analysis methods degenerate and even fail under α stable distribution environment. Several improved frequency spectral analysis methods are proposed employing fractional lower order covariation or fractional lower order covariance in this paper, including fractional lower order Blackman-Tukey covariation spectrum (FLOBTCS), fractional lower order periodogram covariation spectrum (FLOPCS), and fractional lower order welch covariation spectrum (FLOWCS). In order to suppress side lobe and improve resolution, we present novel fractional lower order autoregression (FLO-AR) and fractional lower order autoregressive moving average (FLO-ARMA) parameter model frequency spectrum methods, and the calculation steps are summarized. The proposed spectrum methods are compared with the existing methods based on second-order statistics under Gaussian and SαS distribution environments, and the results show that the new algorithms have better performance than the traditional methods. Finally, the improved methods are applied to estimate frequency spectrums of the normal and outer race fault signals, and it is demonstrated that they are effective for fault diagnosis.

Selectively completed horizontal wells (SCHWs) can significantly reduce cost of completing wells and delay water breakthrough and prevent wellbore collapse in weak formations. Thus, SCHWs have been widely used in petroleum development industry. SCHWs can shorten the effective length of horizontal wells and thus have a vital effect on production. It is significant for SCHWs to study their rate decline and flux distribution in naturally fractured reservoirs. In this paper, by employing motion equation, state equation, and mass conservation equation, three-dimension seepage differential equation is established and corresponding analytical solution is obtained by Laplace transform and finite cosine Fourier transform. According to the relationship of constant production and wellbore pressure in Laplace domain, dimensionless rate solution is gotten under constant wellbore pressure in Laplace domain. Dimensionless pressure and pressure derivate curves and rate decline curves are drawn in log-log plot and seven flow regimes are identified by Stehfest numerical inversion. We compared the simplified results of this paper with the results calculated by Saphir for horizontal wells in naturally fractured reservoirs. The results showed excellent agreement. Some parameters, such as outer boundary radius, storativity ratio, cross-flow coefficient, number and length of open segments, can obviously affect the rate integral and rate integral derivative log-log curves of the SCHWs. The proposed model in this paper can help better understand the flow regime characteristics of the SCHWs and provide more accurate rate decline analysis of the SCHWs data to evaluate formation.

This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.

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.

In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.

First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.

In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.

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 deals with the classic problem of the synthesis of planar linkages for path generation. Based on the Fourier theory, the task curve and the synthesized four-bar coupler curve are regarded as the same curve if their Fourier descriptors match. Using Fourier analysis, a curve must be given as a function of time, termed a parametrization. In practical applications, different parametrizations can be associated with the same task and coupler curve, respectively; however, these parametrizations are Fourier analyzed to different Fourier descriptors, thus resulting in the mismatch of the task and coupler curve. In this paper, we present a parametrization-invariant method to eliminate the influence of parametrization on the values of Fourier descriptors by unifying given parametrizations to the arc length parametrization; meanwhile, a new design space decoupling scheme is introduced to separate the shape, size, orientation, and location matching of the task and four-bar curve, which leads naturally to an efficient synthesis approach.

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.

The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

This paper investigates a hybrid structure based synchronous control strategy for multimotor system of shaftless-driven printing press. Many existing algorithms can obtain a stable synchronous system; however, the obtained stable system may encounter a large enough disturbance that can destroy the synchronization. Focusing on this challenging technological problem about how to receive more robust synchronization during steady-state process, this paper first proposes a state-dependent-switching based leader-following control approach, in which synchronization includes two parts, one associated with tracking control for all members, and the other one associated with consensus maintained among followers in the case that one follower loses synchronization with the leader during steady-state motion. By employing the algebra graph theory, matrix theory, and Lyapunov analysis, the convergence and stability of the given multimotor system are proved. Finally, simulation examples are presented to demonstrate the effectiveness and robustness of the theoretical results.

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbation and Markovian switching. The complex dynamical networks consist ofκmodes, and the networks switch from one mode to another according to a Markovian chain with known transition probability. Based on the Lyapunov function method and stochastic analysis, by employingM-matrix approach, some sufficient conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbation and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, two numerical examples are included to show the effectiveness of our results.

This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper.

This paper presents a fault diagnosis algorithm to estimate the fault for a class of linear discrete systems based on an adaptive fault estimation observer. And observer gain matrix and adaptive adjusting rule of the fault estimator are designed. Furthermore, the adaptive regulating algorithm can guarantee the first-order difference of a Lyapunov discrete function to be negative, so that the observer is ensured to be stable and fault estimation errors are convergent. Finally, simulation results of an aircraft F-16 illustrate the advantages of the theoretic results that are obtained in this paper.

Recently, distributed coordination control of the unmanned aerial vehicle (UAV) swarms has been a particularly active topic in intelligent system field. In this paper, through understanding the emergent mechanism of the complex system, further research on the flocking and the dynamic characteristic of UAV swarms will be given. Firstly, this paper analyzes the current researches and existent problems of UAV swarms. Afterwards, by the theory of stochastic process and supplemented variables, a differential-integral model is established, converting the system model into Volterra integral equation. The existence and uniqueness of the solution of the system are discussed. Then the flocking control law is given based on artificial potential with system consensus. At last, we analyze the stability of the proposed flocking control algorithm based on the Lyapunov approach and prove that the system in a limited time can converge to the consensus direction of the velocity. Simulation results are provided to verify the conclusion.

A quantitative analysis to identify the key geometric error elements and their coupling is the prerequisite and foundation for improving the precision of machine tools. The purpose of this paper is to identify key geometric error elements and compensate for geometric errors accordingly. The geometric error model of three-axis machine tool is built on the basis of multibody system theory; and the quantitative global sensitivity analysis (GSA) model of geometric error elements is constructed by using extended Fourier amplitude sensitivity test method. The crucial geometric errors are identified; and stochastic characteristics of geometric errors are taken into consideration in the formulation of building up the compensation strategy. The validity of geometric error compensation based on sensitivity analysis is verified on a high-precision three-axis machine tool with open CNC system. The experimental results show that the average compensation rates along theX,Y, andZdirections are 59.8%, 65.5%, and 73.5%, respectively. The methods of sensitivity analysis and geometric errors compensation presented in this paper are suitable for identifying the key geometric errors and improving the precision of CNC machine tools effectively.

This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real-life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry.

Sea level fluctuation gains increasing interests in several fields, such as geoscience and ocean dynamics. Recently, the long-range dependence (LRD) or long memory, which is measured by the Hurst parameter, denoted byH, of sea level was reported by Barbosa et al. (2006). However, reports regarding the local roughness of sea level, which is characterized by fractal dimension, denoted byD, of sea level, are rarely seen. Note that a common model describing a random function with LRD is fractional Gaussian noise (fGn), which is the increment process of fractional Brownian motion (fBm) (Beran (1994)). If using the model of fGn,Dof a random function is greater than 1 and less than 2 becauseDis restricted byHwith the restrictionD=2−H. In this paper, we introduce the concept of one-dimensional random functions with LRD based on a specific class of processes called the Cauchy-class (CC) process, towards separately characterizing the local roughness and the long-range persistence of sea level. In order to achieve this goal, we present the power spectrum density (PSD) function of the CC process in the closed form. The case study for modeling real data of sea level collected by the National Data Buoy Center (NDBC) at six stations in the Florida and Eastern Gulf of Mexico demonstrates that the sea level may be one-dimensional but LRD. The case study also implies that the CC process might be a possible model of sea level. In addition to these, this paper also exhibits the yearly multiscale phenomenon of sea level.

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes' problems. Traditionally, exact solutions to the Stokes' problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and initial conditions. However, it fails to solve the extended Stokes' problems by using the integral-transform method only. The reason for this difficulty is that the inverse transform cannot be reduced to a simpler form. To this end, several crucial mathematical techniques have to be involved together with the integral transforms to acquire the exact solutions. Moreover, new dimensionless parameters are defined to describe the flow phenomena more clearly. On the basis of the exact solutions derived in this paper, it is found that the mass influx on the boundary hastens the development of the flow, and the mass efflux retards the energy transferred from the plate to the far-field fluid.

An instrumental matrix approach to design output feedback passive controller for switched singular systems is proposed in this paper. The nonlinear inequality condition including Lyapunov inverse matrix and controller gain matrix is decoupled by introducing additional instrumental matrix variable. Combined with multiple Lyapunov function method, the nonlinear inequality is transformed into linear matrix inequality (LMI). An LMI condition is presented for switched singular system to be stable and passive via static output feedback under designed switching signal. Moreover, the conditions proposed do not require the decomposition of Lyapunov matrix and its inverse matrix or fixing to a special structure. The theoretical results are verified by means of an example. The method introduced in the paper can be effectively extended to a single singular system and normal switched system.

This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.

This paper analyses the dynamics of dual-channel energy supply chain model with heterogeneous retailers (as regards the type of expectations’ formation). On the basis of analyzing the stabilities of four fixed points in the three-dimensional dynamic system, local stable regions of Nash equilibrium are obtained. Effects ofSon the stable regions and profit are studied. Simulation results show that the adjustment of price speed has an obvious impact on the complexity of competition. The performances of the model in different period are measured by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of parameters control method when the model is in chaos and then allows the oligarchs to eliminate the negative effects.

The paper focuses on studying the Noether theorem for nonholonomic systems with time delay. Firstly, the differential equations of motion for nonholonomic systems with time delay are established, which is based on the Hamilton principle with time delay and the Lagrange multiplier rules. Secondly, based upon the generalized quasi-symmetric transformations for nonconservative systems with time delay, the Noether theorem for corresponding holonomic systems is given. Finally, we obtain the Noether theorem for the nonholonomic nonconservative systems with time delay. At the end of the paper, an example is given to illustrate the application of the results.

Due to the spectrum congestion of current navigation signals in L-band, C-band has been taken into consideration as a candidate frequency band for global navigation satellite system (GNSS). As is known, modulation scheme is the core part of signal structure, and how to design a modulation waveform that could make full use of narrow bandwidth 20 MHz and satisfy the constraint condition of frequency compatibility in C-band is the main research content of this paper. In view of transmission characteristics and constraint condition of compatibility in C-band, multi-hcontinuous phase modulation (CPM) is proposed as a candidate modulation scheme. Then the classical channel capacity estimation and a comprehensive evaluation criterion for GNSS modulation signals are employed to assess the proposed scheme in the aspects of the capacity over additive white Gaussian noise (AWGN), tracking accuracy, multipath mitigation, antijamming, and so on. Simulation results reveal that, through optimizing the number and size of modulation indexes, the flexible scheme could offer better performance in terms of code tracking, multipath mitigation, and antijamming compared with other candidates such as MSK and GMSK while maintaining high band efficiency and moderate implementation complexity of receiver. Moreover, this paper also provides a reference for next generation modulation signals in C-band.

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.

The neurophysiological studies of animals locomotion have verified that the fundamental rhythmic movements of animals are generated by the central pattern generator (CPG). Many CPG models have been proposed by scientific researchers. In this paper, a modified CPG model whose output function issin(x)is presented. The paper proves that the modified model has stable periodic solution and characteristics of the rhythmic movement using the Lyapunov judgement theorem and the phase diagram. A modified locomotion model is established in which the credit-assignment cerebellar model articulation controller (CA-CMAC) algorithm is used to realize the pattern mapping between the CPG output and the musculoskeletal system. And a seven-link biped robot is employed to simulate cyclic walking gait in order to test the validity of the locomotion model. The main findings include the following. (1) The modified CPG model can generate spontaneous oscillations which correspond to biological signals. (2) The analysis of the modified locomotion model reveals that the CA-CMAC algorithm can be used to realize the pattern mapping between the CPG output and the musculoskeletal system.

This paper presents the representation of the fractional Riemann-Liouville integral by using the Mikusinski operators. The Mikusinski operators discussed in the paper may yet provide a new view to describe and study the fractional Riemann-Liouville integral operator. The present result may be useful for applying the Mikusinski operational calculus to the study of fractional calculus in mathematics and to the theory of filters of fractional order in engineering.

A number of acceleration schemes for speeding up the time-consuming bilateral filter have been proposed in the literature. Among these techniques, the histogram-based bilateral filter trades the flexibility for achievingO(1) computational complexity using box spatial kernel. A recent study shows that this technique can be leveraged forO(1) bilateral filter with arbitrary spatial and range kernels by linearly combining the results of multiple-box bilateral filters. However, this method requires many box bilateral filters to obtain sufficient accuracy when approximating the bilateral filter with a large spatial kernel. In this paper, we propose approximating arbitrary spatial kernel using a fixed number of boxes. It turns out that the multiple-box spatial kernel can be applied in manyO(1) acceleration schemes in addition to the histogram-based one. Experiments on the application to the histogram-based acceleration are presented in this paper. Results show that the proposed method has better accuracy in approximating the bilateral filter with Gaussian spatial kernel, compared with the previous histogram-based methods. Furthermore, the performance of the proposed histogram-based bilateral filter is robust with respect to the parameters of the filter kernel.

Based on the moving least-squares (MLS) approximation, an improved interpolating moving least-squares (IIMLS) method based on nonsingular weight functions is presented in this paper. Then combining the IIMLS method and the Galerkin weak form, an improved interpolating element-free Galerkin (IIEFG) method is presented for two-dimensional potential problems. In the IIMLS method, the shape function of the IIMLS method satisfies the property of Kroneckerδfunction, and there is no difficulty caused by singularity of the weight function. Then in the IIEFG method presented in this paper, the essential boundary conditions are applied naturally and directly. Moreover, the number of unknown coefficients in the trial function of the IIMLS method is less than that of the MLS approximation; then under the same node distribution, the IIEFG method has higher computational precision than element-free Galerkin (EFG) method and interpolating element-free Galerkin (IEFG) method. Four selected numerical examples are presented to show the advantages of the IIMLS and IIEFG methods.

This paper aims to efficiently implement the maximum likelihood estimator (MLE) for Hurst exponent, a vital parameter embedded in the process of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN), via a combination of the Levinson algorithm and Cholesky decomposition. Many natural and biomedical signals can often be modeled as one of these two processes. It is necessary for users to estimate the Hurst exponent to differentiate one physical signal from another. Among all estimators for estimating the Hurst exponent, the maximum likelihood estimator (MLE) is optimal, whereas its computational cost is also the highest. Consequently, a faster but slightly less accurate estimator is often adopted. Analysis discovers that the combination of the Levinson algorithm and Cholesky decomposition can avoid storing any matrix and performing any matrix multiplication and thus save a great deal of computer memory and computational time. In addition, the first proposed MLE for the Hurst exponent was based on the assumptions that the mean is known as zero and the variance is unknown. In this paper, all four possible situations are considered: known mean, unknown mean, known variance, and unknown variance. Experimental results show that the MLE through efficiently implementing numerical computation can greatly enhance the computational performance.

Network-based control systems have been emerging technologies in control and computer communication fields over the past decade. This paper focuses on the analysis and design of network-based control systems with binary modulation. First, it is shown that different modulations can result in different delays which are inevitable in network-based control systems. The delay can be seen as constant delay when the transmission time is the main consideration. Second, channel noise can result in bit error while bit error is seen as active packet loss in this paper, in this context, the conditions of signal-to-noise ratio (SNR) for binary modulation that can guarantee the stability of systems are obtained according to the proposed algorithm. Third, the system with delay and noisy communication can be modeled as an asynchronous dynamic system (ADS); in addition, the stability is analyzed and controller is designed in terms of Lyapunov function and linear matrix inequality (LMI) scheme. Finally, without loss of generality, numerical simulation demonstrates the effectiveness of the proposed scheme and designed controller based on binary amplitude shift keying (2ASK) modulation.

Purpose.The purpose of this paper is to study a class of the natural languages called the lattice-valued phrase structure languages, which can be generated by the lattice-valued type 0 grammars and recognized by the lattice-valued Turing machines.Design/Methodology/Approach.From the characteristic of natural language, this paper puts forward a new concept of the l-valued Turing machine. It can be used to characterize recognition, natural language processing, and dynamic characteristics.Findings.The mechanisms of both the generation of grammars for the lattice-valued type 0 grammar and the dynamic transformation of the lattice-valued Turing machines were given.Originality/Value.This paper gives a new approach to study a class of natural languages by using lattice-valued logic theory.

Formal methods can strongly contribute to improve dependability of controllers during design, by providing means to avoid flaws due to designers' omissions or specifications misinterpretations. This paper presents a synthesis method dedicated to logic controllers. Its goal is to obtain the control laws from specifications given in natural language by symbolic computation. The formal framework that underlies this method is the Boolean algebra ofn-variable switching functions. In this algebra, thanks to relations and theorems presented in this paper, it is possible to formally express logical controllers specifications, to automatically detect inconsistencies in specifications, and to obtain automatically the set of solutions or to choose an optimal solution according to given optimization criteria. The application of this synthesis method to an example allows illustrating its main advantages.

In this paper, we propose a robust tactile sensing image recognition scheme for automatic robotic assembly. First, an image reprocessing procedure is designed to enhance the contrast of the tactile image. In the second layer, geometric features and Fourier descriptors are extracted from the image. Then, kernel principal component analysis (kernel PCA) is applied to transform the features into ones with better discriminating ability, which is the kernel PCA-based feature fusion. The transformed features are fed into the third layer for classification. In this paper, we design a classifier by combining the multiple kernel learning (MKL) algorithm and support vector machine (SVM). We also design and implement a tactile sensing array consisting of 10-by-10 sensing elements. Experimental results, carried out on real tactile images acquired by the designed tactile sensing array, show that the kernel PCA-based feature fusion can significantly improve the discriminating performance of the geometric features and Fourier descriptors. Also, the designed MKL-SVM outperforms the regular SVM in terms of recognition accuracy. The proposed recognition scheme is able to achieve a high recognition rate of over 85% for the classification of 12 commonly used metal parts in industrial applications.

In recent years, there has been a renewed interest in finding methods to construct orthogonal transforms. This interest is driven by the large number of applications of the orthogonal transforms in image analysis and compression, especially for colour images. Inspired by this motivation, this paper first introduces a new orthogonal transform known as a discrete fractional COSHAD (FrCOSHAD) using the Kronecker product of eigenvectors and the eigenvalues of the COSHAD kernel functions. Next, this study discusses the properties of the FrCOSHAD kernel function, such as angle additivity. Using the algebra of quaternions, the study presents quaternion COSHAD/FrCOSHAD transforms to represent colour images in a holistic manner. This paper also develops an inverse polynomial reconstruction method (IPRM) in the discrete COSHAD/FrCOSHAD domains. This method can effectively recover a piecewise smooth signal from the finite set of its COSHAD/FrCOSHAD coefficients, with high accuracy. The convergence theorem has proved that the partial sum of COSHAD provides a spectrally accurate approximation to the underlying piecewise smooth signal. The experimental results verify the numerical stability and accuracy of the proposed methods.

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.

Many applications based on Internet of Things (IoT) technology have recently founded in industry monitoring area. Thousands of sensors with different types work together in an industry monitoring system. Sensors at different locations can generate streaming data, which can be analyzed in the data center. In this paper, we propose a framework for online sensor fault detection. We motivate our technique in the context of the problem of the data value fault detection and event detection. We use the Statistics Sliding Windows (SSW) to contain the recent sensor data and regress each window by Gaussian distribution. The regression result can be used to detect the data value fault. Devices on a production line may work in different workloads and the associate sensors will have different status. We divide the sensors into several status groups according to different part of production flow chat. In this way, the status of a sensor is associated with others in the same group. We fit the values in the Status Transform Window (STW) to get the slope and generate a group trend vector. By comparing the current trend vector with history ones, we can detect a rational or irrational event. In order to determine parameters for each status group we build a self-learning worker thread in our framework which can edit the corresponding parameter according to the user feedback. Group-based fault detection (GbFD) algorithm is proposed in this paper. We test the framework with a simulation dataset extracted from real data of an oil field. Test result shows that GbFD detects 95% sensor fault successfully.

Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT) in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.

Letx(t)be a locally self-similar Gaussian random function. Denote byrxx(τ)the autocorrelation function (ACF) ofx(t). Forx(t)that is sufficiently smooth on(0,∞), there is an asymptotic expression given byrxx(0)-rxx(τ)~c|τ|αfor|τ|→0, wherecis a constant andαis the fractal index ofx(t). If the above is true, the fractal dimension ofx(t), denoted byD, is given byD=D(α)=2−α/2. Conventionally,αis strictly restricted to0<α≤2so as to make sure thatD∈[1,2). The generalized Cauchy (GC) process is an instance of this type of random functions. Another instance is fractional Brownian motion (fBm) and its increment process, that is, fractional Gaussian noise (fGn), which strictly follow the case ofD∈[1,2)or0<α≤2. In this paper, I claim that the fractal indexαofx(t)may be relaxed to the rangeα>0as long as its ACF keeps valid forα>0. With this claim, I extend the GC process to allowα>0and call this extension, for simplicity, the extended GC (EGC for short) process. I will address that there are dimensions0≤D(α)<1for2<α≤4and furtherD(α)<0for4<αfor the EGC processes. I will explain thatx(t)with1≤D<2is locally rougher than that with0≤D<1. Moreover,x(t)withD<0is locally smoother than that with0≤D<1. The local smoothestx(t)occurs in the limitD→−∞. The focus of this paper is on the fractal dimensions of random functions. The EGC processes presented in this paper can be either long-range dependent (LRD) or short-range dependent (SRD). Though applications of such class of random functions forD<1remain unknown, I will demonstrate the realizations of the EGC processes forD<1. The above result regarding negatively fractal dimension on random functions can be further extended to describe a class of random fields with negative dimensions, which are also briefed in this paper.

The traveling wave equation is an essential tool in the study of vibrations and oscillating systems. This paper introduces an important extension to the Fourier/Laplace transform that is needed for the analysis of signals that are represented by traveling wave equations. Another objective of the paper is to present a mathematical technique for the simulation of the behavior of large systems of optical oscillators.

The periodic nonuniform sampling plays an important role in digital signal processing and other engineering fields. In this paper, we introduce the Gaussian regularization method to accelerate the convergence rate of periodic nonuniform sampling series. We prove that the truncation error of the Gaussian regularized periodic nonuniform sampling series decays exponentially. Numerical experiments are presented to demonstrate our result.

The design of adaptive chattering-free sliding mode controller (SMC) for chaotic systems with unknown input nonlinearities is studied in this paper. A smooth hyperbolic tangent function is utilized to replace the discontinuous sign function; therefore, the proposed adaptive SMC ensures that not only the chaos phenomenon can be suppressed effectively but also the chattering often appearing in the traditional discontinuous SMC with sign function is eliminated, even when the unknown input nonlinearity is present. A sufficient condition for stability of closed-loop system is acquired by Lyapunov theory. The numerical simulation results are illustrated to verify the proposed adaptive sliding mode control method.

In this paper, we introduce an iterative method for approximating a common solution of monotone inclusion problem and fixed point of Bregman nonspreading mappings in a reflexive Banach space. Using the Bregman distance function, we study the composition of the resolvent of a maximal monotone operator and the antiresolvent of a Bregman inverse strongly monotone operator and introduce a Halpern-type iteration for approximating a common zero of a maximal monotone operator and a Bregman inverse strongly monotone operator which is also a fixed point of a Bregman nonspreading mapping. We further state and prove a strong convergence result using the iterative algorithm introduced. This result extends many works on finding a common solution of the monotone inclusion problem and fixed-point problem for nonlinear mappings in a real Hilbert space to a reflexive Banach space.