Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+...Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.展开更多
Nereididae is a prolific annelid family widely distributed in the world oceans,especially in the Indo-Pacific Convergence Zone(IPCZ).However,its biogeographic pattern remains unexplored in IPCZ.To contribute to the un...Nereididae is a prolific annelid family widely distributed in the world oceans,especially in the Indo-Pacific Convergence Zone(IPCZ).However,its biogeographic pattern remains unexplored in IPCZ.To contribute to the understanding of biodiversity and biogeography of Nereididae in the IPCZ,we integrated historical data of species distributions with those of model-predicted ones to determine the biogeographic patterns of nereid species,from which we projected to its future distribution patterns for 2090-2100 under different climate scenarios(SSP1-1.9 and SSP5-8.5).Functional diversity within IPCZ was assessed using functional richness,functional evenness,and functional disparity.Divergence times within Nereididae were estimated using three DNA marker genes(COI,16S,and 18S rRNA),and a time tree was constructed based on a strict molecular clock model.The IPCZ was established as a key Nereididae biodiversity hotspot through distribution modelling of 256 species(44 genera),and temperature emerging as the predominant climatic driver of species distribution patterns.The distribution of species and functional diversity is notable for its non-centralized pattern.We projected that by the end of the century,areas of medium-to-high species richness will expand significantly under the low-emission SSP1-1.9 climate scenario.However,under the high-emission SSP5-8.5 scenario,the suitability of these regions significantly declines,posing an increasingly severe threat to biodiversity.In addition,by molecular clock analysis,we revealed that the evolutionary divergence of extant nereidid species occurred mainly in the Cretaceous and Jurassic,suggesting that paleogeographical and environmental events,such as oceanic anoxic events,might have played a pivotal role in shaping the evolutionary trajectory and ecological adaptations of marine annelids.These findings highlight the importance of considering both current biodiversity patterns and historical contexts in conservation planning,and provided insights into the potential factors on the biogeographic distribution and evolutionary processes of Nereididae.展开更多
In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which ...In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.展开更多
Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite ele...Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = （λn）. Because this sequences are just the sequences x = （xk） = （k） and x = （xk） = （1） respectively and any term of thes...The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = （λn）. Because this sequences are just the sequences x = （xk） = （k） and x = （xk） = （1） respectively and any term of these sequences can not be 0. In this short not we give Example 3＊ and Example 4＊ to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some λ = （λn） , α and β such that 0 α β ≤ 1.展开更多
Target tracking control for wheeled mobile robot(WMR)need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system...Target tracking control for wheeled mobile robot(WMR)need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.展开更多
In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of ...In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.展开更多
The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. T...The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.展开更多
This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and so...This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and some other known methods.展开更多
In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the per...In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.展开更多
In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α an...In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α and strong Nα （p）-summability. Furthermore, some relations between the spaces Nθα （p） and Sθα are examined.展开更多
In this paper,we introduce the concept of λ-statistical convergence of order α.Also some relations between the λ-statistical convergence of order α and strong（V,λ）-summability of order α are given.
Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by ...Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton＇s iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.展开更多
In this paper, a discrete-frequency technique is developed for analyzing sufficiency and necessity of monotone convergence of a proportional higher-order-derivative iterative learning control scheme for a class of lin...In this paper, a discrete-frequency technique is developed for analyzing sufficiency and necessity of monotone convergence of a proportional higher-order-derivative iterative learning control scheme for a class of linear time-invariant systems with higher-order relative degree. The technique composes of two steps. The first step is to expand the iterative control signals, its driven outputs and the relevant signals as complex-form Fourier series and then to deduce the properties of the Fourier coefficients. The second step is to analyze the sufficiency and necessity of monotone convergence of the proposed proportional higher-order-derivative iterative learning control scheme by assessing the tracking errors in the forms of Paserval s energy modes. Numerical simulations are illustrated to exhibit the validity and the effectiveness.展开更多
The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ana...The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.展开更多
In this paper, a one-step Steffensen-type method with super-cubic convergence for solving nonlinear equations is suggested. The convergence order 3.383 is proved theoretically and demonstrated numerically. This super-...In this paper, a one-step Steffensen-type method with super-cubic convergence for solving nonlinear equations is suggested. The convergence order 3.383 is proved theoretically and demonstrated numerically. This super-cubic convergence is obtained by self-accelerating second-order Steffensen’s method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Its theoretical results and high computational efficiency is confirmed by Numerical examples.展开更多
In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity o...In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.展开更多
Stochastic two-stage linear optimization is an important and widely used optimization model. Efficiency of numerical integration of the second stage value function is critical. However, the second stage value function...Stochastic two-stage linear optimization is an important and widely used optimization model. Efficiency of numerical integration of the second stage value function is critical. However, the second stage value function is piecewise linear convex, which imposes challenges for applying the modern efficient spare grid method. In this paper, we prove the first order convergence rate of the sparse grid method for this important stochastic optimization model, utilizing convexity analysis and measure theory. The result is two-folded: it establishes a theoretical foundation for applying the sparse grid method in stochastic programming, and extends the convergence theory of sparse grid integration method to piecewise linear and convex functions.展开更多
Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such conve...Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such convergence for all continuous functions are given.展开更多
In this paper,an improved high-order model-free adaptive iterative control(IHOMFAILC)method for a class of nonlinear discrete-time systems is proposed based on the compact format dynamic linearization method.This meth...In this paper,an improved high-order model-free adaptive iterative control(IHOMFAILC)method for a class of nonlinear discrete-time systems is proposed based on the compact format dynamic linearization method.This method adds the differential of tracking error in the criteria function to compensate for the effect of the random disturbance.Meanwhile,a high-order estimation algorithmis used to estimate the value of pseudo partial derivative(PPD),that is,the current value of PPD is updated by that of previous iterations.Thus the rapid convergence of the maximumtracking error is not limited by the initial value of PPD.The convergence of the maximumtracking error is deduced in detail.This method can track the desired output with enhanced convergence and improved tracking performance.Two examples are used to verify the convergence and effectiveness of the proposed method.展开更多
基金Supported by the Academic Achievement Re-cultivation Projects of Jingdezhen Ceramic University(Grant Nos.215/20506341215/20506277)the Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)。
文摘Assume that{a_(i),−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{X_(n)=Σ_(i=−∞)^(∞)a_(i)Y_(i+n),n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space.
基金Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB42000000)the National Natural Science Foundation of China(No.42376092)the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(No.2022QNLM030004)。
文摘Nereididae is a prolific annelid family widely distributed in the world oceans,especially in the Indo-Pacific Convergence Zone(IPCZ).However,its biogeographic pattern remains unexplored in IPCZ.To contribute to the understanding of biodiversity and biogeography of Nereididae in the IPCZ,we integrated historical data of species distributions with those of model-predicted ones to determine the biogeographic patterns of nereid species,from which we projected to its future distribution patterns for 2090-2100 under different climate scenarios(SSP1-1.9 and SSP5-8.5).Functional diversity within IPCZ was assessed using functional richness,functional evenness,and functional disparity.Divergence times within Nereididae were estimated using three DNA marker genes(COI,16S,and 18S rRNA),and a time tree was constructed based on a strict molecular clock model.The IPCZ was established as a key Nereididae biodiversity hotspot through distribution modelling of 256 species(44 genera),and temperature emerging as the predominant climatic driver of species distribution patterns.The distribution of species and functional diversity is notable for its non-centralized pattern.We projected that by the end of the century,areas of medium-to-high species richness will expand significantly under the low-emission SSP1-1.9 climate scenario.However,under the high-emission SSP5-8.5 scenario,the suitability of these regions significantly declines,posing an increasingly severe threat to biodiversity.In addition,by molecular clock analysis,we revealed that the evolutionary divergence of extant nereidid species occurred mainly in the Cretaceous and Jurassic,suggesting that paleogeographical and environmental events,such as oceanic anoxic events,might have played a pivotal role in shaping the evolutionary trajectory and ecological adaptations of marine annelids.These findings highlight the importance of considering both current biodiversity patterns and historical contexts in conservation planning,and provided insights into the potential factors on the biogeographic distribution and evolutionary processes of Nereididae.
基金supported by the Project for Outstanding Young Talents in Bagui of Guangxi,the Natural Science Foundation of Guangxi(2021GXNSFFA196004,2024GXNSFBA010337)the NSFC(12371312)+2 种基金the Natural Science Foundation of Chongqing(CSTB2024NSCQ-JQX0033)supported by the Postdoctoral Fellowship Program of CPSF(GZC20241534)the Startup Project of Postdoctoral Scientific Research of Zhejiang Normal University(ZC304023924).
文摘In this paper,we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect,in which the contact conditions are described by a Signorini’s condition and Coulomb’s friction law.We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities.Then,we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem.Moreover,we demonstrate the convergence of a penalty method for this contact problem under consideration.Finally,finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.
基金the National Natural Science Foundation of China(No.50678093)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT00736)
文摘Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
文摘The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = （λn）. Because this sequences are just the sequences x = （xk） = （k） and x = （xk） = （1） respectively and any term of these sequences can not be 0. In this short not we give Example 3＊ and Example 4＊ to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some λ = （λn） , α and β such that 0 α β ≤ 1.
基金supported by National Natural Science Foundation of China(Grant No.61075081)State Key Laboratory of Robotics Technique and System Foundation,Harbin Institute of Technology,China(Grant No.SKIRS200802A02)
文摘Target tracking control for wheeled mobile robot(WMR)need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.
文摘In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.
文摘The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.
文摘This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and some other known methods.
文摘In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.
文摘In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α and strong Nα （p）-summability. Furthermore, some relations between the spaces Nθα （p） and Sθα are examined.
文摘In this paper,we introduce the concept of λ-statistical convergence of order α.Also some relations between the λ-statistical convergence of order α and strong（V,λ）-summability of order α are given.
文摘Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton＇s iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.
基金supported by National Natural Science Foundation of China(Nos.F010114-60974140 and 61273135)
文摘In this paper, a discrete-frequency technique is developed for analyzing sufficiency and necessity of monotone convergence of a proportional higher-order-derivative iterative learning control scheme for a class of linear time-invariant systems with higher-order relative degree. The technique composes of two steps. The first step is to expand the iterative control signals, its driven outputs and the relevant signals as complex-form Fourier series and then to deduce the properties of the Fourier coefficients. The second step is to analyze the sufficiency and necessity of monotone convergence of the proposed proportional higher-order-derivative iterative learning control scheme by assessing the tracking errors in the forms of Paserval s energy modes. Numerical simulations are illustrated to exhibit the validity and the effectiveness.
文摘The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
文摘In this paper, a one-step Steffensen-type method with super-cubic convergence for solving nonlinear equations is suggested. The convergence order 3.383 is proved theoretically and demonstrated numerically. This super-cubic convergence is obtained by self-accelerating second-order Steffensen’s method twice with memory, but without any new function evaluations. The proposed method is very efficient and convenient, since it is still a derivative-free two-point method. Its theoretical results and high computational efficiency is confirmed by Numerical examples.
基金supported by the National Natural Science Foundation of China (No.12271518)the Key Program of the National Natural Science Foundation of China (No.62333016)。
文摘In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.
文摘Stochastic two-stage linear optimization is an important and widely used optimization model. Efficiency of numerical integration of the second stage value function is critical. However, the second stage value function is piecewise linear convex, which imposes challenges for applying the modern efficient spare grid method. In this paper, we prove the first order convergence rate of the sparse grid method for this important stochastic optimization model, utilizing convexity analysis and measure theory. The result is two-folded: it establishes a theoretical foundation for applying the sparse grid method in stochastic programming, and extends the convergence theory of sparse grid integration method to piecewise linear and convex functions.
文摘Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such convergence for all continuous functions are given.
文摘In this paper,an improved high-order model-free adaptive iterative control(IHOMFAILC)method for a class of nonlinear discrete-time systems is proposed based on the compact format dynamic linearization method.This method adds the differential of tracking error in the criteria function to compensate for the effect of the random disturbance.Meanwhile,a high-order estimation algorithmis used to estimate the value of pseudo partial derivative(PPD),that is,the current value of PPD is updated by that of previous iterations.Thus the rapid convergence of the maximumtracking error is not limited by the initial value of PPD.The convergence of the maximumtracking error is deduced in detail.This method can track the desired output with enhanced convergence and improved tracking performance.Two examples are used to verify the convergence and effectiveness of the proposed method.
