Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural ...Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix sp...The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.展开更多
An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some ...An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some suitable conditions, strong convergence results for the hierarchical circularly iterative sequence are proved in the setting of Hilbert spaces. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé.展开更多
Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iter...Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.展开更多
Background Co-salient object detection(Co-SOD)aims to identify and segment commonly salient objects in a set of related images.However,most current Co-SOD methods encounter issues with the inclusion of irrelevant info...Background Co-salient object detection(Co-SOD)aims to identify and segment commonly salient objects in a set of related images.However,most current Co-SOD methods encounter issues with the inclusion of irrelevant information in the co-representation.These issues hamper their ability to locate co-salient objects and significantly restrict the accuracy of detection.Methods To address this issue,this study introduces a novel Co-SOD method with iterative purification and predictive optimization(IPPO)comprising a common salient purification module(CSPM),predictive optimizing module(POM),and diminishing mixed enhancement block(DMEB).Results These components are designed to explore noise-free joint representations,assist the model in enhancing the quality of the final prediction results,and significantly improve the performance of the Co-SOD algorithm.Furthermore,through a comprehensive evaluation of IPPO and state-of-the-art algorithms focusing on the roles of CSPM,POM,and DMEB,our experiments confirmed that these components are pivotal in enhancing the performance of the model,substantiating the significant advancements of our method over existing benchmarks.Experiments on several challenging benchmark co-saliency datasets demonstrate that the proposed IPPO achieves state-of-the-art performance.展开更多
Norm optimal iterative learning control(NOILC) has recently been applied to iterative learning control(ILC) problems in which tracking is only required at a subset of isolated time points along the trial duration. Thi...Norm optimal iterative learning control(NOILC) has recently been applied to iterative learning control(ILC) problems in which tracking is only required at a subset of isolated time points along the trial duration. This problem addresses the practical needs of many applications, including industrial automation, crane control, satellite positioning and motion control within a medical stroke rehabilitation context. This paper provides a substantial generalization of this framework by providing a solution to the problem of convergence at intermediate points with simultaneous tracking of subsets of outputs to reference trajectories on subintervals. This formulation enables the NOILC paradigm to tackle tasks which mix "point to point" movements with linear tracking requirements and hence substantially broadens the application domain to include automation tasks which include welding or cutting movements, or human motion control where the movement is restricted by the task to straight line and/or planar segments. A solution to the problem is presented in the framework of NOILC and inherits NOILC s well-defined convergence properties. Design guidelines and supporting experimental results are included.展开更多
In this paper, a quasi-Newton-type optimized iterative learning control （ILC） algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learnin...In this paper, a quasi-Newton-type optimized iterative learning control （ILC） algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.展开更多
This paper analyses the concept of a Limit Set in Parameter Optimal Iterative Learning Control （ILC）. We investigate the existence of stable and unstable parts of Limit Set and demonstrates that they will often exis...This paper analyses the concept of a Limit Set in Parameter Optimal Iterative Learning Control （ILC）. We investigate the existence of stable and unstable parts of Limit Set and demonstrates that they will often exist in practice. This is illustrated via a 2-dimensional example where the convergence of the learning algorithm is analyzed from the error＇s dynamic behaviour. These ideas are extended to the N-dimensional cases by analogy and example.展开更多
Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial ...Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution.In the second type,the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively.The two methods are rederived by expanding the solution asymptotically upon a small Rossby number,and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution.For each rederived method,two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration.Upon testing with analytically formulated wavering jet flows on the synoptic,sub-synoptic and meso-αscales,the iterative procedure designed for the first method with the Poisson solver,named M1a,is found to be the most accurate and efficient.For the synoptic wavering jet flow in which the NBE is entirely elliptic,M1a is extremely accurate.For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic,M1a is sufficiently accurate.For the meso-αwavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed,M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow,but not for the anti-cyclonically curved part.展开更多
This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） metho...This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.展开更多
In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,wh...In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.展开更多
This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be dir...This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.展开更多
In the paper, an iterative method is presented to the optimal control of batch processes. Generally it is very difficult to acquire an accurate mechanistic model for a batch process. Because support vector machine is ...In the paper, an iterative method is presented to the optimal control of batch processes. Generally it is very difficult to acquire an accurate mechanistic model for a batch process. Because support vector machine is powerful for the problems characterized by small samples, nonlinearity, high dimension and local minima, support vector regression models are developed for the optimal control of batch processes where end-point properties are required. The model parameters are selected within the Bayesian evidence framework. Based on the model, an iterative method is used to exploit the repetitive nature of batch processes to determine the optimal operating policy. Numerical simulation shows that the iterative optimal control can improve the process performance through iterations.展开更多
This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization conc...This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter,the key idea of the algorithm is minimizing the approximation error by succes-sively modifying the design result through an iterative procedure under the condition of a fixed window length.In the iterative procedure,the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration.Because the approximation error can be specified variably,the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain.A design example is employed to illustrate the efficiency of the algorithm.展开更多
This paper addresses the shortcomings of the Sparrow and Eagle Optimization Algorithm (SBOA) in terms of convergence accuracy, convergence speed, and susceptibility to local optima. To this end, an improved Sparrow an...This paper addresses the shortcomings of the Sparrow and Eagle Optimization Algorithm (SBOA) in terms of convergence accuracy, convergence speed, and susceptibility to local optima. To this end, an improved Sparrow and Eagle Optimization Algorithm (HS-SBOA) is proposed. Initially, the algorithm employs Iterative Mapping to generate an initial sparrow and eagle population, enhancing the diversity of the population during the global search phase. Subsequently, an adaptive weighting strategy is introduced during the exploration phase of the algorithm to achieve a balance between exploration and exploitation. Finally, to avoid the algorithm falling into local optima, a Cauchy mutation operation is applied to the current best individual. To validate the performance of the HS-SBOA algorithm, it was applied to the CEC2021 benchmark function set and three practical engineering problems, and compared with other optimization algorithms such as the Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Whale Optimization Algorithm (WOA) to test the effectiveness of the improved algorithm. The simulation experimental results show that the HS-SBOA algorithm demonstrates significant advantages in terms of convergence speed and accuracy, thereby validating the effectiveness of its improved strategies.展开更多
A major bottleneck in large-scale eigenfrequency topology optimization is the repeated solution of the generalized eigenvalue problem.This work presents an efficient graphics processing unit(GPU)solver for threedimens...A major bottleneck in large-scale eigenfrequency topology optimization is the repeated solution of the generalized eigenvalue problem.This work presents an efficient graphics processing unit(GPU)solver for threedimensional(3D)topology optimization that maximizes the fundamental eigenfrequency.The Successive Iteration of Analysis and Design(SIAD)framework is employed to avoid solving a full eigenproblem at every iteration.The sequential approximation of the eigenpairs is solved by the GPU-accelerated multigrid-preconditioned conjugate gradient(MGPCG)method to efficiently improve the eigenvectors along with the topological evolution.The cluster-mean approach is adopted to address the non-differentiability issue caused by repeated eigenfrequencies.The corresponding sensitivity analysis method is provided.The parallelized gradient-based Zhang-Paulino-Ramos Jr.(ZPR)algorithm is employed to update the design variables.The effectiveness of the proposed solver is demonstrated through two large-scale numerical examples.The first example demonstrates the accuracy,efficiency,and scalability of the proposed solver by solving a 3D optimization problem of 50.33 million elements being solved in approximately 15.2 h over 300 iterations on a single NVIDIA Tesla V100 GPU.The second example validates the effectiveness of the proposed solver in the presence of repeated eigenfrequencies.Our findings also highlight that higher-resolution models produce distinct optimized structures with higher fundamental frequencies,underscoring the necessity of large-scale topology optimization.展开更多
In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense...In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.展开更多
Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal co...Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.展开更多
This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves t...This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.展开更多
基金supported by the National Key Research and Development Program of China(2023YFF0906502)the Postgraduate Research and Innovation Project of Hunan Province under Grant(CX20240473).
文摘Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金The National Natural Science Foundations of China (12202219)the Natural Science Foundations of Ningxia (2024AAC02009, 2023AAC05001)the Ningxia Youth Top Talents Training Project。
文摘The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.
文摘An hierarchical circularly iterative method is introduced for solving a system of variational circularly inequalities with set of fixed points of strongly quasi-nonexpansive mapping problems in this paper. Under some suitable conditions, strong convergence results for the hierarchical circularly iterative sequence are proved in the setting of Hilbert spaces. Our scheme can be regarded as a more general variant of the algorithm proposed by Maingé.
基金funded by the NSFC under Grant Nos.61803279,71471091,62003231 and 51874205in part by the Qing Lan Project of Jiangsu,in part by the China Postdoctoral Science Foundation under Grant Nos.2020M671596 and 2021M692369+2 种基金in part by the Suzhou Science and Technology Development Plan Project(Key Industry Technology Innovation)under Grant No.SYG202114in part by the Natural Science Foundation of Jiangsu Province under Grant No.BK20200989Postdoctoral Research Funding Program of Jiangsu Province.
文摘Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.
基金Supported by the National Natural Science Foundation of China under Grant(62301330,62101346)the Guangdong Basic and Applied Basic Research Foundation(2024A1515010496,2022A1515110101)+1 种基金the Stable Support Plan for Shenzhen Higher Education Institutions(20231121103807001)the Guangdong Provincial Key Laboratory under(2023B1212060076).
文摘Background Co-salient object detection(Co-SOD)aims to identify and segment commonly salient objects in a set of related images.However,most current Co-SOD methods encounter issues with the inclusion of irrelevant information in the co-representation.These issues hamper their ability to locate co-salient objects and significantly restrict the accuracy of detection.Methods To address this issue,this study introduces a novel Co-SOD method with iterative purification and predictive optimization(IPPO)comprising a common salient purification module(CSPM),predictive optimizing module(POM),and diminishing mixed enhancement block(DMEB).Results These components are designed to explore noise-free joint representations,assist the model in enhancing the quality of the final prediction results,and significantly improve the performance of the Co-SOD algorithm.Furthermore,through a comprehensive evaluation of IPPO and state-of-the-art algorithms focusing on the roles of CSPM,POM,and DMEB,our experiments confirmed that these components are pivotal in enhancing the performance of the model,substantiating the significant advancements of our method over existing benchmarks.Experiments on several challenging benchmark co-saliency datasets demonstrate that the proposed IPPO achieves state-of-the-art performance.
文摘Norm optimal iterative learning control(NOILC) has recently been applied to iterative learning control(ILC) problems in which tracking is only required at a subset of isolated time points along the trial duration. This problem addresses the practical needs of many applications, including industrial automation, crane control, satellite positioning and motion control within a medical stroke rehabilitation context. This paper provides a substantial generalization of this framework by providing a solution to the problem of convergence at intermediate points with simultaneous tracking of subsets of outputs to reference trajectories on subintervals. This formulation enables the NOILC paradigm to tackle tasks which mix "point to point" movements with linear tracking requirements and hence substantially broadens the application domain to include automation tasks which include welding or cutting movements, or human motion control where the movement is restricted by the task to straight line and/or planar segments. A solution to the problem is presented in the framework of NOILC and inherits NOILC s well-defined convergence properties. Design guidelines and supporting experimental results are included.
基金supported by the National Natural Science Foundation of China(Nos.F010114-60974140,61273135)
文摘In this paper, a quasi-Newton-type optimized iterative learning control （ILC） algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.
文摘This paper analyses the concept of a Limit Set in Parameter Optimal Iterative Learning Control （ILC）. We investigate the existence of stable and unstable parts of Limit Set and demonstrates that they will often exist in practice. This is illustrated via a 2-dimensional example where the convergence of the learning algorithm is analyzed from the error＇s dynamic behaviour. These ideas are extended to the N-dimensional cases by analogy and example.
基金the NSF of China Grants 91937301 and 41675060,the National Key Scientific and Technological Infrastructure Project"EarthLab",and the ONR Grants N000141712375 and N000142012449 to the University of Oklahoma(OU)The numerical experiments were performed at the OU supercomputer SchoonerCIMMS by NOAA/Office of Oceanic and Atmospheric Research under NOAA-OU Cooperative Agreement#NA110AR4320072,U.S.Department of Commerce.
文摘Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution.In the second type,the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively.The two methods are rederived by expanding the solution asymptotically upon a small Rossby number,and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution.For each rederived method,two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration.Upon testing with analytically formulated wavering jet flows on the synoptic,sub-synoptic and meso-αscales,the iterative procedure designed for the first method with the Poisson solver,named M1a,is found to be the most accurate and efficient.For the synoptic wavering jet flow in which the NBE is entirely elliptic,M1a is extremely accurate.For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic,M1a is sufficiently accurate.For the meso-αwavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed,M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow,but not for the anti-cyclonically curved part.
基金Project supported by the National Natural Science Foundation of China(No.11671106)the Fundamental Research Funds for the Central Universities(No.2016MS33)
文摘This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.
文摘In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.
基金Supported by the National Natural Science Foundation of China(U1162130)the National High Technology Research and Development Program of China(2006AA05Z226)Outstanding Youth Science Foundation of Zhejiang Province(R4100133)
文摘This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.
基金Project supported by the National Natural Science Foundation of China(Grant No.60504033)
文摘In the paper, an iterative method is presented to the optimal control of batch processes. Generally it is very difficult to acquire an accurate mechanistic model for a batch process. Because support vector machine is powerful for the problems characterized by small samples, nonlinearity, high dimension and local minima, support vector regression models are developed for the optimal control of batch processes where end-point properties are required. The model parameters are selected within the Bayesian evidence framework. Based on the model, an iterative method is used to exploit the repetitive nature of batch processes to determine the optimal operating policy. Numerical simulation shows that the iterative optimal control can improve the process performance through iterations.
基金the National Grand Fundamental Research 973 Program of China (No.2004CB318109)the National High-Technology Research and Development Plan of China (No.2006AA01Z452)
文摘This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter,the key idea of the algorithm is minimizing the approximation error by succes-sively modifying the design result through an iterative procedure under the condition of a fixed window length.In the iterative procedure,the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration.Because the approximation error can be specified variably,the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain.A design example is employed to illustrate the efficiency of the algorithm.
文摘This paper addresses the shortcomings of the Sparrow and Eagle Optimization Algorithm (SBOA) in terms of convergence accuracy, convergence speed, and susceptibility to local optima. To this end, an improved Sparrow and Eagle Optimization Algorithm (HS-SBOA) is proposed. Initially, the algorithm employs Iterative Mapping to generate an initial sparrow and eagle population, enhancing the diversity of the population during the global search phase. Subsequently, an adaptive weighting strategy is introduced during the exploration phase of the algorithm to achieve a balance between exploration and exploitation. Finally, to avoid the algorithm falling into local optima, a Cauchy mutation operation is applied to the current best individual. To validate the performance of the HS-SBOA algorithm, it was applied to the CEC2021 benchmark function set and three practical engineering problems, and compared with other optimization algorithms such as the Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and Whale Optimization Algorithm (WOA) to test the effectiveness of the improved algorithm. The simulation experimental results show that the HS-SBOA algorithm demonstrates significant advantages in terms of convergence speed and accuracy, thereby validating the effectiveness of its improved strategies.
基金support from the National Natural Science Foundation of China(Award No.52105240).
文摘A major bottleneck in large-scale eigenfrequency topology optimization is the repeated solution of the generalized eigenvalue problem.This work presents an efficient graphics processing unit(GPU)solver for threedimensional(3D)topology optimization that maximizes the fundamental eigenfrequency.The Successive Iteration of Analysis and Design(SIAD)framework is employed to avoid solving a full eigenproblem at every iteration.The sequential approximation of the eigenpairs is solved by the GPU-accelerated multigrid-preconditioned conjugate gradient(MGPCG)method to efficiently improve the eigenvectors along with the topological evolution.The cluster-mean approach is adopted to address the non-differentiability issue caused by repeated eigenfrequencies.The corresponding sensitivity analysis method is provided.The parallelized gradient-based Zhang-Paulino-Ramos Jr.(ZPR)algorithm is employed to update the design variables.The effectiveness of the proposed solver is demonstrated through two large-scale numerical examples.The first example demonstrates the accuracy,efficiency,and scalability of the proposed solver by solving a 3D optimization problem of 50.33 million elements being solved in approximately 15.2 h over 300 iterations on a single NVIDIA Tesla V100 GPU.The second example validates the effectiveness of the proposed solver in the presence of repeated eigenfrequencies.Our findings also highlight that higher-resolution models produce distinct optimized structures with higher fundamental frequencies,underscoring the necessity of large-scale topology optimization.
文摘In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.
文摘Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.
基金Supported by the National Natural Science Foundation of China (U1162130)the National High Technology Research and Development Program of China (2006AA05Z226)the Outstanding Youth Science Foundation,Zhejiang Province (R4100133)
文摘This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.
