This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulat...This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.展开更多
It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H...It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H∞norm and control parameters.An optimal-Lyapunov-function-based controller design concept is proposed,and a minimum amplitude control scheme is presented under amplitude-bounded disturbances.Firstly,the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞norm,and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given.Secondly,the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation,and the accurate quantitative relationship between the system H∞norm and control parameters is given.Finally,the control parameter optimization method is proposed according to the quantitative relationship between the system H∞norm and control parameters.Unlike robust optimization control methods,the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design,and provides a novel way to design the minimum amplitude control under the given control accuracy.A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
The rapid evolution of unmanned aerial vehicle(UAV)technology and autonomous capabilities has positioned UAV as promising last-mile delivery means.Vehicle and onboard UAV collaborative delivery is introduced as a nove...The rapid evolution of unmanned aerial vehicle(UAV)technology and autonomous capabilities has positioned UAV as promising last-mile delivery means.Vehicle and onboard UAV collaborative delivery is introduced as a novel delivery mode.Spatiotemporal collaboration,along with energy consumption with payload and wind conditions play important roles in delivery route planning.This paper introduces the traveling salesman problem with time window and onboard UAV(TSPTWOUAV)and emphasizes the consideration of real-world scenarios,focusing on time collaboration and energy consumption with wind and payload.To address this,a mixed integer linear programming(MILP)model is formulated to minimize the energy consumption costs of vehicle and UAV.Furthermore,an adaptive large neighborhood search(ALNS)algorithm is applied to identify high-quality solutions efficiently.The effectiveness of the proposed model and algorithm is validated through numerical tests on real geographic instances and sensitivity analysis of key parameters is conducted.展开更多
To guarantee the safety of the high speed maglev train system, a novel model based on the winding function theory is proposed for the long-stator linear synchronous motor（LSM）, which is suitable for the real-time ca...To guarantee the safety of the high speed maglev train system, a novel model based on the winding function theory is proposed for the long-stator linear synchronous motor（LSM）, which is suitable for the real-time calculation of the running state. The accurate coupled mathematical models under different internal fault conditions of the LSM are derived based on the normal model. Then the fault currents and electromagnetic forces are simulated and calculated for the major potential internal faults of the LSM, such as the single-phase short circuit, the phase-phase short circuit and the single-phase open circuit. The characteristic curve between the electromagnetic force and the armature current of the LSM, which is compared with the results from the finite element method, proves the validation of the proposed method. The fault rule is determined and the proposed analytical model also shows its feasibility in the fast fault diagnosis through the comparison of the simulation results of currents and electromagnetic forces under different internal fault types and short circuit ratios.展开更多
In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic℘-function for the(n+1)-dimensional generalized Kadomtsev–Petviashvili equation by Darbou...In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic℘-function for the(n+1)-dimensional generalized Kadomtsev–Petviashvili equation by Darboux transformation,the associated linear spectral problem with the Weierstrass function as the external potential is studied by utilizing the Laméfunction.The degenerate solutions of the nonlinear waves have also been obtained by approaching the limits of the half-periodsω_(1) andω_(2) of℘(x).At the same time,the evolution and nonlinear dynamics of various nonlinear waves under different parameter regimes are systematically discussed.The findings may open avenues for related experimental investigations and potential applications in various nonlinear science domains,such as nonlinear optics and oceanography.展开更多
In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous aut...In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function,and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas.Currently,the BDF is only defined for continuous signals.However,for both simulation and experimental purposes,the signals must be discrete.This necessitates the development of a BDF analysis workflow for discrete signals.In this work,we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts.Our results permit more accurate simulations using BDFs,which will be useful in applying them to problems such as partial coherence.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr...In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.展开更多
Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=...Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=L(t,x,)+(t ,x,) also possesses similar exponential estimate. For α=0, a similar result is given.展开更多
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro...In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.展开更多
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize...In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.展开更多
In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ...In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.展开更多
This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this w...This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean-square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.展开更多
This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectru...This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.展开更多
In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard n...In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.展开更多
A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure ass...A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.展开更多
Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasi...Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.展开更多
基金supported in part by the National Natural Science Foundation of China(62473221)the Natural Science Foundation of Shandong Province,China(ZR2024MF006)Qingdao Natural Science Foundation(24-4-4-zrjj-165-jch)。
文摘This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.
基金supported in part by the National Natural Science Foundation of China(62373089).
文摘It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H∞norm and control parameters.An optimal-Lyapunov-function-based controller design concept is proposed,and a minimum amplitude control scheme is presented under amplitude-bounded disturbances.Firstly,the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞norm,and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given.Secondly,the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation,and the accurate quantitative relationship between the system H∞norm and control parameters is given.Finally,the control parameter optimization method is proposed according to the quantitative relationship between the system H∞norm and control parameters.Unlike robust optimization control methods,the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design,and provides a novel way to design the minimum amplitude control under the given control accuracy.A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
基金Fundamental Research Funds for the Central Universities(2024JBZX038)National Natural Science F oundation of China(62076023)。
文摘The rapid evolution of unmanned aerial vehicle(UAV)technology and autonomous capabilities has positioned UAV as promising last-mile delivery means.Vehicle and onboard UAV collaborative delivery is introduced as a novel delivery mode.Spatiotemporal collaboration,along with energy consumption with payload and wind conditions play important roles in delivery route planning.This paper introduces the traveling salesman problem with time window and onboard UAV(TSPTWOUAV)and emphasizes the consideration of real-world scenarios,focusing on time collaboration and energy consumption with wind and payload.To address this,a mixed integer linear programming(MILP)model is formulated to minimize the energy consumption costs of vehicle and UAV.Furthermore,an adaptive large neighborhood search(ALNS)algorithm is applied to identify high-quality solutions efficiently.The effectiveness of the proposed model and algorithm is validated through numerical tests on real geographic instances and sensitivity analysis of key parameters is conducted.
文摘To guarantee the safety of the high speed maglev train system, a novel model based on the winding function theory is proposed for the long-stator linear synchronous motor（LSM）, which is suitable for the real-time calculation of the running state. The accurate coupled mathematical models under different internal fault conditions of the LSM are derived based on the normal model. Then the fault currents and electromagnetic forces are simulated and calculated for the major potential internal faults of the LSM, such as the single-phase short circuit, the phase-phase short circuit and the single-phase open circuit. The characteristic curve between the electromagnetic force and the armature current of the LSM, which is compared with the results from the finite element method, proves the validation of the proposed method. The fault rule is determined and the proposed analytical model also shows its feasibility in the fast fault diagnosis through the comparison of the simulation results of currents and electromagnetic forces under different internal fault types and short circuit ratios.
基金supported by the National Natural Science Foundation of China (Grant Nos. 12475007 and 12171433)。
文摘In order to investigate physically meaning localized nonlinear waves on the periodic background defined by Weierstrass elliptic℘-function for the(n+1)-dimensional generalized Kadomtsev–Petviashvili equation by Darboux transformation,the associated linear spectral problem with the Weierstrass function as the external potential is studied by utilizing the Laméfunction.The degenerate solutions of the nonlinear waves have also been obtained by approaching the limits of the half-periodsω_(1) andω_(2) of℘(x).At the same time,the evolution and nonlinear dynamics of various nonlinear waves under different parameter regimes are systematically discussed.The findings may open avenues for related experimental investigations and potential applications in various nonlinear science domains,such as nonlinear optics and oceanography.
基金the support of the University College Dublin through a John Sheridan Scholarship.Min Wan thanks 4TU.RECENTRE program(Award No.OA102070)the National Growth Fund programme PhotonDelta in The Netherlands.
文摘In recent years,many phase space distributions have been proposed,and one of the more independently interesting is the Bai distribution function(BDF).The BDF has been shown to interpolate between the instantaneous auto-correlation function and the Wigner distribution function,and be applied in linear frequency modulated signal parameter estimation and optical partial coherence areas.Currently,the BDF is only defined for continuous signals.However,for both simulation and experimental purposes,the signals must be discrete.This necessitates the development of a BDF analysis workflow for discrete signals.In this work,we analyze the sampling requirements imposed by the BDF and demonstrate their correctness by comparing the continuous BDFs of continuous test signals with their numerically approximated counterparts.Our results permit more accurate simulations using BDFs,which will be useful in applying them to problems such as partial coherence.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
基金Supported by the Natural Science Foundation of Hubei Province (2008CDZD47)
文摘In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.
基金Research supported by China National Science Foundation
文摘Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=L(t,x,)+(t ,x,) also possesses similar exponential estimate. For α=0, a similar result is given.
文摘In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.
基金This work was supported by National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT).
文摘In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.
基金Supported by the National Natural Science Foundation of China(11071069, 11171307)the Natural Science Foundation of Hunan Province(09JJ6003)
文摘In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.
基金Supported by University Science Research Project of Anhui Province(2023AH052921)Outstanding Youth Talent Project of Anhui Province(gxyq2021254)。
文摘In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.
文摘This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse （BP） function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean-square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.
基金Project partially supported by the China Postdoctoral Science Foundation (Grant No. 20060400705)Tianjin University Research Foundation (Grant No. TJU-YFF-08B06)
文摘This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.
文摘In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.
文摘A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.
文摘Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.
