In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained f...In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.展开更多
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for...An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.展开更多
In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared wi...In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.展开更多
It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used suc...It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations.展开更多
This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introdu...This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter.The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations.The convergence rate of the algorithm is dependent on the adjustable parameter.Furthermore,a numerical example is provided to show the effectiveness of the presented algorithms.展开更多
In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the origin...In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the original equation and the adjoint equation iteratively. We present numerical examples and show the well performance of these variational iterative algorithms.展开更多
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with...Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.展开更多
Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and ...Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and subsolution of CP to QCP; Equation of Schwarz algorithm.展开更多
To investigate the effect of rail pad viscoelasticity on vehicle-track-bridge coupled vibration,the fractional Voigt and Maxwell model in parallel(FVMP)was used to characterize the viscoelastic properties of the rail ...To investigate the effect of rail pad viscoelasticity on vehicle-track-bridge coupled vibration,the fractional Voigt and Maxwell model in parallel(FVMP)was used to characterize the viscoelastic properties of the rail pad based on dynamic performance test results.The FVMP model was then incorporated into the vehicle-track-bridge nonlinear coupled model,and its dynamic response was solved using a cross-iteration algorithm with a relaxation factor.Results indicate that the nonlinear coupled model achieves good convergence when the time step is less than 0.001 s,with the cross-iteration algorithm adjusting the wheel-rail force.In particular,the best convergence is achieved when the relaxation factor is within the range of 0.3-0.5.The FVMP model effectively characterizes the viscoelasticity of rail pads across a temperature range of±20℃and a frequency range of 1-1000 Hz.The viscoelasticity of rail pads significantly affects high-frequency vibrations in the coupled system,particularly around 50 Hz,corresponding to the wheel-rail coupled resonance range.Considering rail pad viscoelasticity is essential for accurately predicting track structure vibrations.展开更多
Satellite Internet(SI)provides broadband access as a critical information infrastructure in 6G.However,with the integration of the terrestrial Internet,the influx of massive terrestrial traffic will bring significant ...Satellite Internet(SI)provides broadband access as a critical information infrastructure in 6G.However,with the integration of the terrestrial Internet,the influx of massive terrestrial traffic will bring significant threats to SI,among which DDoS attack will intensify the erosion of limited bandwidth resources.Therefore,this paper proposes a DDoS attack tracking scheme using a multi-round iterative Viterbi algorithm to achieve high-accuracy attack path reconstruction and fast internal source locking,protecting SI from the source.Firstly,to reduce communication overhead,the logarithmic representation of the traffic volume is added to the digests after modeling SI,generating the lightweight deviation degree to construct the observation probability matrix for the Viterbi algorithm.Secondly,the path node matrix is expanded to multi-index matrices in the Viterbi algorithm to store index information for all probability values,deriving the path with non-repeatability and maximum probability.Finally,multiple rounds of iterative Viterbi tracking are performed locally to track DDoS attack based on trimming tracking results.Simulation and experimental results show that the scheme can achieve 96.8%tracking accuracy of external and internal DDoS attack at 2.5 seconds,with the communication overhead at 268KB/s,effectively protecting the limited bandwidth resources of SI.展开更多
To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achiev...To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achieves high-quality AFM imaging via line-by-line corrections for each distorted profile along the fast axis.The key to this line-by-line correction is to accurately simulate the profile distortion of each scanning row.Therefore,a data preprocessing approach is first developed to roughly filter out most of the height data that impairs the accuracy of distortion modeling.This process is implemented through an internal double-screening mechanism.A line-fitting method is adopted to preliminarily screen out the obvious specimens.Lifting wavelet analysis is then carried out to identify the base parts that are mistakenly filtered out as specimens so as to preserve most of the base profiles and provide a good basis for further distortion modeling.Next,an iterative thresholding algorithm is developed to precisely simulate the profile distortion.By utilizing the roughly screened base profile,the optimal threshold,which is used to screen out the pure bases suitable for distortion modeling,is determined through iteration with a specified error rule.On this basis,the profile distortion is accurately modeled through line fitting on the finely screened base data,and the correction is implemented by subtracting the modeling result from the distorted profile.Finally,the effectiveness of the proposed method is verified through experiments and applications.展开更多
This paper studies thee convergence properties of multiplicative iterative algorithms with inexact line search. We prove that the convergence can be guaranteed for a general form of line search rille, under the assu...This paper studies thee convergence properties of multiplicative iterative algorithms with inexact line search. We prove that the convergence can be guaranteed for a general form of line search rille, under the assumption of convexity of objective function or the assumption of convergence of the sequence generated by the algorithm. This answers an open problem put forward by lusem.展开更多
An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programmin...An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.展开更多
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems...A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings展开更多
A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is ...A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.展开更多
In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,wh...In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.展开更多
For a class of non-uniform output sampling hybrid system with actuator faults and bounded disturbances,an iterative learning fault diagnosis algorithm is proposed.Firstly,in order to measure the impact of fault on sys...For a class of non-uniform output sampling hybrid system with actuator faults and bounded disturbances,an iterative learning fault diagnosis algorithm is proposed.Firstly,in order to measure the impact of fault on system between every consecutive output sampling instants,the actual fault function is transformed to obtain an equivalent fault model by using the integral mean value theorem,then the non-uniform sampling hybrid system is converted to continuous systems with timevarying delay based on the output delay method.Afterwards,an observer-based fault diagnosis filter with virtual fault is designed to estimate the equivalent fault,and the iterative learning regulation algorithm is chosen to update the virtual fault repeatedly to make it approximate the actual equivalent fault after some iterative learning trials,so the algorithm can detect and estimate the system faults adaptively.Simulation results of an electro-mechanical control system model with different types of faults illustrate the feasibility and effectiveness of this algorithm.展开更多
Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design...Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.展开更多
Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the...Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the rotor vibration in AMBs is to adopt a notch filter or adaptive filter in the AMB controller. However, these methods cannot obtain the precise amplitude and phase of the compensation current. Thus, they are not so effective in terms of suppressing the vibrations of the fundamental and other harmonic orders over the whole speed range. To improve the vibration suppression performance of AMBs,an adaptive filter based on Least Mean Square(LMS) is applied to extract the vibration signals from the rotor displacement signal. An Iterative Search Algorithm(ISA) is proposed in this paper to obtain the corresponding relationship between the compensation current and vibration signals. The ISA is responsible for searching the compensating amplitude and shifting phase online for the LMS filter, enabling the AMB controller to generate the corresponding compensation force for vibration suppression. The results of ISA are recorded to suppress vibration using the Look-Up Table(LUT) in variable speed range. Comprehensive simulations and experimental validations are carried out in fixed and variable speed range, and the results demonstrate that by employing the ISA, vibrations of the fundamental and other harmonic orders are suppressed effectively.展开更多
文摘In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.
基金Project supported by the National Natural Science Foundation of China (No.10472061)
文摘An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.
基金Project supported by the National Natural Science Foundation of China （Grant No.10271074）, and the Special Funds for Major Specialities of Shanghai Education Commission （Grant No.J50101）
文摘In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples.
文摘It has long been realized that the problem of radar imaging is a special case of image reconstruction in which the data are incomplete and noisy. In other fields, iterative reconstruction algorithms have been used successfully to improve the image quality. This paper studies the application of iterative algorithms in radar imaging. A discrete model is first derived, and the iterative algorithms are then adapted to radar imaging. Although such algorithms are usually time consuming, this paper shows that, if the algorithms are appropriately simplified, it is possible to realize them even in real time. The efficiency of iterative algorithms is shown through computer simulations.
基金supported by the Shenzhen Municipal Basic Research Project for Discipline Layout(Grant No.JCYJ20170811160715620)the National Natural Science Foundation of China for Excellent Young Scholars(Grant No.61822305)+1 种基金the Shenzhen Municipal Project for International Cooperation(Grant No.GJHZ20180420180849805)the Guangdong Natural Science Foundation(Grant No.2017A030313340)。
文摘This study is concerned with the problem to solve the continuous coupled Riccati matrix equations in It?Markov jump systems.A new iterative algorithm is developed by using the latest estimation information and introducing a tuning parameter.The iterative solution obtained by the proposed algorithm with zero initial conditions converges to the unique positive definite solution of the considered equations.The convergence rate of the algorithm is dependent on the adjustable parameter.Furthermore,a numerical example is provided to show the effectiveness of the presented algorithms.
文摘In this paper, we investigate the adjoint equation in photoacoustic tomography with variable sound speed, and propose three variational iterative algorithms. The basic idea of these algorithms is to compute the original equation and the adjoint equation iteratively. We present numerical examples and show the well performance of these variational iterative algorithms.
基金the National Natural Science Foundation of China(No.10671060)the Doctoral Fund of Ministry of Education of China granted[2003]0532006
文摘Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
文摘Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and subsolution of CP to QCP; Equation of Schwarz algorithm.
基金Project(2023ZDZX0008)supported by the Sichuan Major Science and Technology Project,ChinaProject(52308468)supported by the National Natural Science Foundation of ChinaProject(2022JBQY009)supported by the Fundamental Research Funds for the Central Universities(Science and Technology Leading Talent Team Project),China。
文摘To investigate the effect of rail pad viscoelasticity on vehicle-track-bridge coupled vibration,the fractional Voigt and Maxwell model in parallel(FVMP)was used to characterize the viscoelastic properties of the rail pad based on dynamic performance test results.The FVMP model was then incorporated into the vehicle-track-bridge nonlinear coupled model,and its dynamic response was solved using a cross-iteration algorithm with a relaxation factor.Results indicate that the nonlinear coupled model achieves good convergence when the time step is less than 0.001 s,with the cross-iteration algorithm adjusting the wheel-rail force.In particular,the best convergence is achieved when the relaxation factor is within the range of 0.3-0.5.The FVMP model effectively characterizes the viscoelasticity of rail pads across a temperature range of±20℃and a frequency range of 1-1000 Hz.The viscoelasticity of rail pads significantly affects high-frequency vibrations in the coupled system,particularly around 50 Hz,corresponding to the wheel-rail coupled resonance range.Considering rail pad viscoelasticity is essential for accurately predicting track structure vibrations.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1005000)the National Natural Science Foundation of China(Grant No.62025110 and 62101308).
文摘Satellite Internet(SI)provides broadband access as a critical information infrastructure in 6G.However,with the integration of the terrestrial Internet,the influx of massive terrestrial traffic will bring significant threats to SI,among which DDoS attack will intensify the erosion of limited bandwidth resources.Therefore,this paper proposes a DDoS attack tracking scheme using a multi-round iterative Viterbi algorithm to achieve high-accuracy attack path reconstruction and fast internal source locking,protecting SI from the source.Firstly,to reduce communication overhead,the logarithmic representation of the traffic volume is added to the digests after modeling SI,generating the lightweight deviation degree to construct the observation probability matrix for the Viterbi algorithm.Secondly,the path node matrix is expanded to multi-index matrices in the Viterbi algorithm to store index information for all probability values,deriving the path with non-repeatability and maximum probability.Finally,multiple rounds of iterative Viterbi tracking are performed locally to track DDoS attack based on trimming tracking results.Simulation and experimental results show that the scheme can achieve 96.8%tracking accuracy of external and internal DDoS attack at 2.5 seconds,with the communication overhead at 268KB/s,effectively protecting the limited bandwidth resources of SI.
基金supported by the National Natural Science Foundation of China under Grant No.21933006.
文摘To eliminate distortion caused by vertical drift and illusory slopes in atomic force microscopy(AFM)imaging,a lifting-wavelet-based iterative thresholding correction method is proposed in this paper.This method achieves high-quality AFM imaging via line-by-line corrections for each distorted profile along the fast axis.The key to this line-by-line correction is to accurately simulate the profile distortion of each scanning row.Therefore,a data preprocessing approach is first developed to roughly filter out most of the height data that impairs the accuracy of distortion modeling.This process is implemented through an internal double-screening mechanism.A line-fitting method is adopted to preliminarily screen out the obvious specimens.Lifting wavelet analysis is then carried out to identify the base parts that are mistakenly filtered out as specimens so as to preserve most of the base profiles and provide a good basis for further distortion modeling.Next,an iterative thresholding algorithm is developed to precisely simulate the profile distortion.By utilizing the roughly screened base profile,the optimal threshold,which is used to screen out the pure bases suitable for distortion modeling,is determined through iteration with a specified error rule.On this basis,the profile distortion is accurately modeled through line fitting on the finely screened base data,and the correction is implemented by subtracting the modeling result from the distorted profile.Finally,the effectiveness of the proposed method is verified through experiments and applications.
文摘This paper studies thee convergence properties of multiplicative iterative algorithms with inexact line search. We prove that the convergence can be guaranteed for a general form of line search rille, under the assumption of convexity of objective function or the assumption of convergence of the sequence generated by the algorithm. This answers an open problem put forward by lusem.
基金The National Natural Science Foundation of China(No. 50908235 )China Postdoctoral Science Foundation (No.201003520)
文摘An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.
基金Project supported by the Natural Science Foundation of Sichuan Educational Commission (No.2003A081)
文摘A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings
基金supported by the National Outstanding Young Scientists Fund of China (No. 10725209)the National ScienceFoundation of China (No. 10672092)+1 种基金Shanghai Municipal Education Commission Scientific Research Project (No. 07ZZ07)Shanghai Leading Academic Discipline Project (No. Y0103).
文摘A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.
文摘In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.
基金supported by the National Natural Science Foundation of China(61273070,61203092)the Enterprise-college-institute Cooperative Project of Jiangsu Province(BY2015019-21)+1 种基金111 Project(B12018)the Fun-damental Research Funds for the Central Universities(JUSRP51733B)
文摘For a class of non-uniform output sampling hybrid system with actuator faults and bounded disturbances,an iterative learning fault diagnosis algorithm is proposed.Firstly,in order to measure the impact of fault on system between every consecutive output sampling instants,the actual fault function is transformed to obtain an equivalent fault model by using the integral mean value theorem,then the non-uniform sampling hybrid system is converted to continuous systems with timevarying delay based on the output delay method.Afterwards,an observer-based fault diagnosis filter with virtual fault is designed to estimate the equivalent fault,and the iterative learning regulation algorithm is chosen to update the virtual fault repeatedly to make it approximate the actual equivalent fault after some iterative learning trials,so the algorithm can detect and estimate the system faults adaptively.Simulation results of an electro-mechanical control system model with different types of faults illustrate the feasibility and effectiveness of this algorithm.
基金Project supported by the National Natural Science Foundation of China(No.61603322)the Research Foundation of Education Bureau of Hunan Province of China(No.16C1542)
文摘Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.
基金supported by the Natural Science Foundation of China (U22A20214)。
文摘Active Magnetic Bearing(AMB) is a kind of electromagnetic support that makes the rotor movement frictionless and can suppress rotor vibration by controlling the magnetic force. The most common approach to restrain the rotor vibration in AMBs is to adopt a notch filter or adaptive filter in the AMB controller. However, these methods cannot obtain the precise amplitude and phase of the compensation current. Thus, they are not so effective in terms of suppressing the vibrations of the fundamental and other harmonic orders over the whole speed range. To improve the vibration suppression performance of AMBs,an adaptive filter based on Least Mean Square(LMS) is applied to extract the vibration signals from the rotor displacement signal. An Iterative Search Algorithm(ISA) is proposed in this paper to obtain the corresponding relationship between the compensation current and vibration signals. The ISA is responsible for searching the compensating amplitude and shifting phase online for the LMS filter, enabling the AMB controller to generate the corresponding compensation force for vibration suppression. The results of ISA are recorded to suppress vibration using the Look-Up Table(LUT) in variable speed range. Comprehensive simulations and experimental validations are carried out in fixed and variable speed range, and the results demonstrate that by employing the ISA, vibrations of the fundamental and other harmonic orders are suppressed effectively.
