Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind oftonstrained one in intrinsic quality because its amplitude is always non-negative Classification of the bifurcations with the...Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind oftonstrained one in intrinsic quality because its amplitude is always non-negative Classification of the bifurcations with the type of constraint was discussed. All its six types of transition sets are derived, in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.展开更多
To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are show...To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.展开更多
An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model stru...An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra...By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.展开更多
In this paper,we present an optimal neuro-control scheme for continuous-time(CT)nonlinear systems with asymmetric input constraints.Initially,we introduce a discounted cost function for the CT nonlinear systems in ord...In this paper,we present an optimal neuro-control scheme for continuous-time(CT)nonlinear systems with asymmetric input constraints.Initially,we introduce a discounted cost function for the CT nonlinear systems in order to handle the asymmetric input constraints.Then,we develop a Hamilton-Jacobi-Bellman equation(HJBE),which arises in the discounted cost optimal control problem.To obtain the optimal neurocontroller,we utilize a critic neural network(CNN)to solve the HJBE under the framework of reinforcement learning.The CNN's weight vector is tuned via the gradient descent approach.Based on the Lyapunov method,we prove that uniform ultimate boundedness of the CNN's weight vector and the closed-loop system is guaranteed.Finally,we verify the effectiveness of the present optimal neuro-control strategy through performing simulations of two examples.展开更多
An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace def...An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.展开更多
This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transf...This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.展开更多
Exact estimation of space object attitude parameters is a great challenge.The effectiveness of conventional attitude estimation approaches based on target sizes suffers a significant reduction when occlusion exists.Th...Exact estimation of space object attitude parameters is a great challenge.The effectiveness of conventional attitude estimation approaches based on target sizes suffers a significant reduction when occlusion exists.This paper proposes an innovative approach to estimate the attitude parameters for space objects based on inverse synthetic aperture radar(ISAR)image sequences.The formulation for nonlinear size constraints(NSC)is developed by accounting for the characteristics of object size variation in ISAR image sequences.The multi-start framework for global optimization and the Broyden-Fletcher-Goldfarb-Shanno(BFGS)based quasi-Newton iterative method are combined with and used for more accurate estimation of space object’s attitude parameters.Furthermore,the Cramer-Rao lower bound(CRLB)of attitude parameter estimates is derived.Comparative experiments demonstrate the effectiveness and robustness of the proposed method.展开更多
This paper focuses on the study for the stability of stochastic nonlinear programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the fe...This paper focuses on the study for the stability of stochastic nonlinear programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are guaranteed. Importantly,it is proved that, if the linear independence constraint qualification and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush-Kuhn-Tucker conditions.展开更多
This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures.The geometrical nonlinearity is firstly included to re...This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures.The geometrical nonlinearity is firstly included to reflect the structural response and the joint load distribution under large deformation.To avoid a failure of fastener joints,topology optimization is then carried out to minimize the structural end compliance in the equilibrium state while controlling joint loads intensities over fasteners.During nonlinear analysis and optimization,a novel implementation of adjoint vector sensitivity analysis along with super element condensation is introduced to address numerical instability issues.The degrees of freedom of weak regions are condensed so that their influences are excluded from the iterative Newton-Raphson(NR)solution.Numerical examples are presented to validate the efficiency and robustness of the proposed method.The effects of joint load constraints and geometrical nonlinearity are highlighted by comparing numerical optimization results.展开更多
An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w...An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed....A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.展开更多
In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. F...In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively. With the restriction of nonholonomic constraints to the initial conditions being considered, the solutions of the dynamics equations of variable mass nonlinear nonholonomic system in noninertial reference frame are obtained.展开更多
One of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems is the EM algorithm.However,when the parameters satisfy a set of nonlinear restrictions,It is difficult ...One of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems is the EM algorithm.However,when the parameters satisfy a set of nonlinear restrictions,It is difficult to apply the EM algorithm directly.In this paper,we propose an asymptotic maximum likelihood estimation procedure under a set of nonlinear inequalities restrictions on the parameters,in which the EM algorithm can be used.Essentially this kind of estimation problem is a stochastic optimization problem in the M-step.We make use of methods in stochastic optimization to overcome the difficulty caused by nonlinearity in the given constraints.展开更多
文摘Bifurcation of periodic solutions widely existed in nonlinear dynamical systems is a kind oftonstrained one in intrinsic quality because its amplitude is always non-negative Classification of the bifurcations with the type of constraint was discussed. All its six types of transition sets are derived, in which three types are newly found and a method is proposed for analyzing the constrained bifurcation.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11572025,11202013 and 51420105008
文摘To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.
文摘An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously.
基金supported by the National Natural Science Foundation of China(61973228,61973330)
文摘In this paper,we present an optimal neuro-control scheme for continuous-time(CT)nonlinear systems with asymmetric input constraints.Initially,we introduce a discounted cost function for the CT nonlinear systems in order to handle the asymmetric input constraints.Then,we develop a Hamilton-Jacobi-Bellman equation(HJBE),which arises in the discounted cost optimal control problem.To obtain the optimal neurocontroller,we utilize a critic neural network(CNN)to solve the HJBE under the framework of reinforcement learning.The CNN's weight vector is tuned via the gradient descent approach.Based on the Lyapunov method,we prove that uniform ultimate boundedness of the CNN's weight vector and the closed-loop system is guaranteed.Finally,we verify the effectiveness of the present optimal neuro-control strategy through performing simulations of two examples.
基金Supported by The Natural Science Fundations of China and Jiangsu
文摘An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm.
基金supported by National Natural Science Foundation of China (No. 60574014, No. 60425310)Doctor Subject Foundation of China (No. 200805330004)+2 种基金Program for New Century Excellent Talents in University (No. NCET-06-0679)Natural Science Foundation of Hunan Province of China (No. 08JJ1010)Science Foundation of Education Department of Hunan Province (No. 08C106)
文摘This paper investigates the robust tracking control problcm for a class of nonlinear networked control systems （NCSs） using the Takagi-Sugeno （T-S） fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints （IQCs） are satisfied while both time-varying network- induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities （LMIs） and parallel distributed compensation （PDC）. Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.
文摘Exact estimation of space object attitude parameters is a great challenge.The effectiveness of conventional attitude estimation approaches based on target sizes suffers a significant reduction when occlusion exists.This paper proposes an innovative approach to estimate the attitude parameters for space objects based on inverse synthetic aperture radar(ISAR)image sequences.The formulation for nonlinear size constraints(NSC)is developed by accounting for the characteristics of object size variation in ISAR image sequences.The multi-start framework for global optimization and the Broyden-Fletcher-Goldfarb-Shanno(BFGS)based quasi-Newton iterative method are combined with and used for more accurate estimation of space object’s attitude parameters.Furthermore,the Cramer-Rao lower bound(CRLB)of attitude parameter estimates is derived.Comparative experiments demonstrate the effectiveness and robustness of the proposed method.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571059 11731013)
文摘This paper focuses on the study for the stability of stochastic nonlinear programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are guaranteed. Importantly,it is proved that, if the linear independence constraint qualification and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush-Kuhn-Tucker conditions.
基金co-supported by National Key Research and Development Program(No.2017YFB1102800)NSFC for Excellent Young Scholars(No.11722219)Key Project of NSFC(Nos.51790171,5171101743,51735005,11620101002,and 11432011).
文摘This paper presents an extended topology optimization approach considering joint load constraints with geo-metrical nonlinearity in design of assembled structures.The geometrical nonlinearity is firstly included to reflect the structural response and the joint load distribution under large deformation.To avoid a failure of fastener joints,topology optimization is then carried out to minimize the structural end compliance in the equilibrium state while controlling joint loads intensities over fasteners.During nonlinear analysis and optimization,a novel implementation of adjoint vector sensitivity analysis along with super element condensation is introduced to address numerical instability issues.The degrees of freedom of weak regions are condensed so that their influences are excluded from the iterative Newton-Raphson(NR)solution.Numerical examples are presented to validate the efficiency and robustness of the proposed method.The effects of joint load constraints and geometrical nonlinearity are highlighted by comparing numerical optimization results.
基金supported by the National Natural Science Foundation of China (60632050)National Basic Research Program of Jiangsu Province University (08KJB520003)
文摘An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金project supported by the National Natural Science Foundation of China(Nos.10501009 and 60471039)the Natural Science Foundation of Guangxi Province(No.0728206)
文摘A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.
文摘In this paper, the integration methods of dynamics equations of relative motion of variable mass nonlinear nonholonomic system are given such as the gradient method, the single-component method and the field method. Firstly, the dynamics equations are written in the canonical form and the field form. Secondly, the gradient method, the single-component method and the field method are used to integrate the dynamics equations of the corresponding constant mass holonomic system in inertial reference frame respectively. With the restriction of nonholonomic constraints to the initial conditions being considered, the solutions of the dynamics equations of variable mass nonlinear nonholonomic system in noninertial reference frame are obtained.
基金Supported by Teaching reform project of Zhengzhou University of Science and Technology(KFCZ201909)National Foundation for Cultivating Scientific Research Projects of Zhengzhou Institute of Technology(GJJKTPY2018K4)+1 种基金Henan Big Data Double Base of Zhengzhou Institute of Technology(20174101546503022265)the Key Scientific Research Foundation of Education Bureau of Henan Province(20B110020)
文摘One of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems is the EM algorithm.However,when the parameters satisfy a set of nonlinear restrictions,It is difficult to apply the EM algorithm directly.In this paper,we propose an asymptotic maximum likelihood estimation procedure under a set of nonlinear inequalities restrictions on the parameters,in which the EM algorithm can be used.Essentially this kind of estimation problem is a stochastic optimization problem in the M-step.We make use of methods in stochastic optimization to overcome the difficulty caused by nonlinearity in the given constraints.
