Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In t...Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In this paper,we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the l_(1)-norm of coherence of the target quantum state,striving to make the prepared state and the target state as similar as possible.Here,we present the analytical solution for the optimal distance for any N given quantum states.We find that the optimal approximation problem for any N>4 quantum states can be transformed into an optimal approximation problem for no more than four quantum states,which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation.Ultimately,a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach.展开更多
We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of ...We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.展开更多
An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. Fr...An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. From the function approximation perspective, the OSA method shares the same separable approximation format to the one-way wave operator as other separable approximation methods but it is the only global function approximation among these methods. This leads to a difference in the phase error curve, impulse response, and migration result from other separable approximation methods. The difference is that the OSA method has higher accuracy, and the sensitivity to the velocity variation declines with increasing order.展开更多
In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, bas...In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.展开更多
Three heuristic algorithms for optimal polygonal approximation of digital planar curves is presented. With Genetic Algorithm (GA), improved Genetic Algorithm (IGA) based on Pareto optimal solution and Tabu Search (TS)...Three heuristic algorithms for optimal polygonal approximation of digital planar curves is presented. With Genetic Algorithm (GA), improved Genetic Algorithm (IGA) based on Pareto optimal solution and Tabu Search (TS), a near optimal polygonal approximation was obtained. Compared to the famous Teh chin algorithm, our algorithms have obtained the approximated polygons with less number of vertices and less approximation error. Compared to the dynamic programming algorithm, the processing time of our algorithms are much less expensive.展开更多
The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(M...The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.展开更多
In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal con...In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.展开更多
An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on t...An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.展开更多
The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward c...The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, whereas the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient since the seismic data are not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfied seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.展开更多
A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exist...A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.展开更多
There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to e...There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to ensure convergence for a set of irregular nodes. In this paper by means of an optimal binary interpolation formula given in a reproducing kernel space, a high precision overall two dimension numerical integral formula is established and its advantage is that it ensures the convergence for arbitrary irregular node set in the integral domain.展开更多
In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformat...In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.展开更多
In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the ta...In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .展开更多
Neighboring optimal guidance,a method to obtain a suboptimal guidance law by approximately solving the first-order necessary conditions based on a nominal trajectory,is widely used in the aerospace field due to its hi...Neighboring optimal guidance,a method to obtain a suboptimal guidance law by approximately solving the first-order necessary conditions based on a nominal trajectory,is widely used in the aerospace field due to its high computational efficiency and low resource usage.For more advanced scenarios,the existing methods still have a problem that the guidance accuracy and optimality will seriously degrade when the actual state largely deviates from the nominal trajectory.This is mainly caused by the approximate description of the first-order conditions in terms of total flight time and nonlinear constraints.To address this problem,a higher-order neighboring optimal guidance method is proposed.First,a novel total flight time updating strategy,together with a normalized time scale,is presented that transforms the optimal problem with free total flight time into a more tractable optimal problem with fixed total flight time.Then,using the vector partial derivative method,a higher-order approximation is adopted,instead of the first-order approximation,to accurately describe the nonlinear dynamical and terminal constraints,thus obtaining a polynomially constrained quadratic optimal problem.Finally,to numerically solve the polynomially constrained quadratic optimal problem,a Newton-type iterative algorithm based on the orthogonal decomposition is designed.Through the iterative solution within each guidance period,the corrections to control quantities and total flight time are generated.The proposed method is applied to a launch vehicle orbital injection problem,and simulation results show that it achieves high accuracy of orbital injection and optimality of performance index.展开更多
A real n×n symmetric matrix X=(x_(ij))_(n×n)is called a bisymmetric matrix if x_(ij)=x_(n+1-j,n+1-i).Based on the projection theorem,the canonical correlation de- composition and the generalized singular val...A real n×n symmetric matrix X=(x_(ij))_(n×n)is called a bisymmetric matrix if x_(ij)=x_(n+1-j,n+1-i).Based on the projection theorem,the canonical correlation de- composition and the generalized singular value decomposition,a method useful for finding the least-squares solutions of the matrix equation A^TXA=B over bisymmetric matrices is proposed.The expression of the least-squares solutions is given.Moreover, in the corresponding solution set,the optimal approximate solution to a given matrix is also derived.A numerical algorithm for finding the optimal approximate solution is also described.展开更多
On the basis of target transfer function with the early time and late time response together, a method for solving the feature coefficients of target is investigated by utilizing approximation theory and method. Then,...On the basis of target transfer function with the early time and late time response together, a method for solving the feature coefficients of target is investigated by utilizing approximation theory and method. Then, the feature coefficients are classified by the minimum distance criterion to identify targets automatically.展开更多
Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target function...Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target functions defined on some compact set of Rd, neural networks are at least as good as algebraic polynomials.展开更多
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients...For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.展开更多
The purpose of reoptimization using approximation methods—application of knowledge about the solution of the initial instance I, provided to achieve a better quality of approximation (approximation ratio) of an algor...The purpose of reoptimization using approximation methods—application of knowledge about the solution of the initial instance I, provided to achieve a better quality of approximation (approximation ratio) of an algorithm for determining optimal or close to it solutions of some “minor” changes of instance I. To solve the problem Ins-Max-EkCSP-P (reoptimization of Max-EkCSP-P with the addition of one constraint) with approximation resistant predicate P exists a polynomial threshold (optimal) -approximation algorithm, where the threshold “random” approximation ratio of P). When the unique games conjecture (UGC) is hold there exists a polynomial threshold (optimal) -approximation algorithm (where and the integrality gap of semidefinite relaxation of Max-EkCSP-P problem Z) to solve the problem Ins-Max-EkCSP-P.展开更多
In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the...In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.展开更多
基金supported by the Fundamental Research Projects of Shanxi Province(Grant No.202203021222225)the National Natural Science Foundation of China(Grant Nos.12175029,12011530014,and 11775040)the Key Research and Development Project of Liaoning Province(Grant No.2020JH2/10500003).
文摘Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory,offering critical guidance for experimental implementations.In this paper,we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the l_(1)-norm of coherence of the target quantum state,striving to make the prepared state and the target state as similar as possible.Here,we present the analytical solution for the optimal distance for any N given quantum states.We find that the optimal approximation problem for any N>4 quantum states can be transformed into an optimal approximation problem for no more than four quantum states,which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation.Ultimately,a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach.
基金supported by the National Natural Science Foundation of China(Grant Nos.12441502,12122506,12204230,and 12404554)the National Science and Technology Major Project of the Ministry of Science and Technology of China(2024ZD0300404)+6 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2021B1515020070)Shenzhen Science and Technology Program(Grant No.RCYX20200714114522109)China Postdoctoral Science Foundation(CPSF)(2024M762114)Postdoctoral Fellowship Program of CPSF(GZC20231727)supported by the National Natural Science Foundation of China(Grant Nos.92165206 and 11974330)Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301603)the Fundamental Research Funds for the Central Universities。
文摘We present a robust quantum optimal control framework for implementing fast entangling gates on ion-trap quantum processors.The framework leverages tailored laser pulses to drive the multiple vibrational sidebands of the ions to create phonon-mediated entangling gates and,unlike the state of the art,requires neither weakcoupling Lamb-Dicke approximation nor perturbation treatment.With the application of gradient-based optimal control,it enables finding amplitude-and phase-modulated laser control protocols that work without the Lamb-Dicke approximation,promising gate speeds on the order of microseconds comparable to the characteristic trap frequencies.Also,robustness requirements on the temperature of the ions and initial optical phase can be conveniently included to pursue high-quality fast gates against experimental imperfections.Our approach represents a step in speeding up quantum gates to achieve larger quantum circuits for quantum computation and simulation,and thus can find applications in near-future experiments.
基金sponsored by the National Natural Science Foundation of China (Nos. 40774069 and 40974074)the State Key Program of National Natural Science of China (No. 40830424)the National 973program (No. 007209603)
文摘An approximation for the one-way wave operator takes the form of separated space and wave-number variables and makes it possible to use the FFT, which results in a great improvement in the computational efficiency. From the function approximation perspective, the OSA method shares the same separable approximation format to the one-way wave operator as other separable approximation methods but it is the only global function approximation among these methods. This leads to a difference in the phase error curve, impulse response, and migration result from other separable approximation methods. The difference is that the OSA method has higher accuracy, and the sensitivity to the velocity variation declines with increasing order.
基金Supported by NSF of China(10531020)the Program of 985 Innovation Engieering on Information in Xiamen University(2004-2007).
文摘In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.
文摘Three heuristic algorithms for optimal polygonal approximation of digital planar curves is presented. With Genetic Algorithm (GA), improved Genetic Algorithm (IGA) based on Pareto optimal solution and Tabu Search (TS), a near optimal polygonal approximation was obtained. Compared to the famous Teh chin algorithm, our algorithms have obtained the approximated polygons with less number of vertices and less approximation error. Compared to the dynamic programming algorithm, the processing time of our algorithms are much less expensive.
基金supported by the Board of Research in Nuclear Sciences of the Department of Atomic Energy,India(2012/36/69-BRNS/2012)
文摘The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.
文摘In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.
基金This research is sponsored by China National Natural Science Foundation （N0. 40474047）.
文摘An accurate and wide-angle one-way propagator for wavefield extrapolation is an important topic for research on wave-equation prestack depth migration in the presence of large and rapid velocity variations. Based on the optimal separable approximation presented in this paper, the mixed domain algorithm with forward and inverse Fourier transforms is used to construct the 3D one-way wavefield extrapolation operator. This operator separates variables in the wavenumber and spatial domains. The phase shift operation is implemented in the wavenumber domain while the time delay for lateral velocity variation is corrected in the spatial domain. The impulse responses of the one-way wave operator show that the numeric computation is consistent with the theoretical value for each velocity, revealing that the operator constructed with the optimal separable approximation can be applied to lateral velocity variations for the case of small steps. Imaging results of the SEG/EAGE model and field data indicate that the new method can be used to image complex structure.
基金This paper is supported by the National Natural Science Foundation of China (No. 40474047)State Key Laboratory of Geological Processes and Mineral Resources (No. GPMR200654)the Focused Subject Program of Beijing (No. XK104910598).
文摘The offset-domain prestack depth migration with optimal separable approximation, based on the double square root equation, is used to image complex media with large and rapid velocity variations. The method downward continues the source and the receiver wavefields simultaneously. The mixed domain algorithm with forward Fourier and inverse Fourier transform is used to construct the double square root equation wavefield extrapolation operator. This operator separates variables in the wave number domain and variables in the space domain. The phase operation is implemented in the wave number domain, whereas the time delay for lateral velocity variation is corrected in the space domain. The migration algorithm is efficient since the seismic data are not computed shot by shot. The data set test of the Marmousi model indicates that the offset-domain migration provides a satisfied seismic migration section on which complex geologic structures are imaged in media with large and rapid lateral velocity variations.
文摘A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.
文摘There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to ensure convergence for a set of irregular nodes. In this paper by means of an optimal binary interpolation formula given in a reproducing kernel space, a high precision overall two dimension numerical integral formula is established and its advantage is that it ensures the convergence for arbitrary irregular node set in the integral domain.
基金supported by the Open Research Project from SKLMCCS (Grant No. 20120106)the Fundamental Research Funds for the Central Universities of China (Grant No. FRF-TP-13-018A)+1 种基金the Postdoctoral Science Foundation of China (Grant No. 2013M530527)the National Natural Science Foundation of China (Grant Nos. 61304079, 61125306, and 61034002)
文摘In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.
文摘In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .
基金This study was co-supported by the National Natural Science Foundation of China(No.62103014).
文摘Neighboring optimal guidance,a method to obtain a suboptimal guidance law by approximately solving the first-order necessary conditions based on a nominal trajectory,is widely used in the aerospace field due to its high computational efficiency and low resource usage.For more advanced scenarios,the existing methods still have a problem that the guidance accuracy and optimality will seriously degrade when the actual state largely deviates from the nominal trajectory.This is mainly caused by the approximate description of the first-order conditions in terms of total flight time and nonlinear constraints.To address this problem,a higher-order neighboring optimal guidance method is proposed.First,a novel total flight time updating strategy,together with a normalized time scale,is presented that transforms the optimal problem with free total flight time into a more tractable optimal problem with fixed total flight time.Then,using the vector partial derivative method,a higher-order approximation is adopted,instead of the first-order approximation,to accurately describe the nonlinear dynamical and terminal constraints,thus obtaining a polynomially constrained quadratic optimal problem.Finally,to numerically solve the polynomially constrained quadratic optimal problem,a Newton-type iterative algorithm based on the orthogonal decomposition is designed.Through the iterative solution within each guidance period,the corrections to control quantities and total flight time are generated.The proposed method is applied to a launch vehicle orbital injection problem,and simulation results show that it achieves high accuracy of orbital injection and optimality of performance index.
文摘A real n×n symmetric matrix X=(x_(ij))_(n×n)is called a bisymmetric matrix if x_(ij)=x_(n+1-j,n+1-i).Based on the projection theorem,the canonical correlation de- composition and the generalized singular value decomposition,a method useful for finding the least-squares solutions of the matrix equation A^TXA=B over bisymmetric matrices is proposed.The expression of the least-squares solutions is given.Moreover, in the corresponding solution set,the optimal approximate solution to a given matrix is also derived.A numerical algorithm for finding the optimal approximate solution is also described.
文摘On the basis of target transfer function with the early time and late time response together, a method for solving the feature coefficients of target is investigated by utilizing approximation theory and method. Then, the feature coefficients are classified by the minimum distance criterion to identify targets automatically.
文摘Using some regular matrices we present a method to express any multivariate algebraic polynomial of total order n in a normal form. Consequently, we prove constructively that, to approximate continuous target functions defined on some compact set of Rd, neural networks are at least as good as algebraic polynomials.
文摘For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.
文摘The purpose of reoptimization using approximation methods—application of knowledge about the solution of the initial instance I, provided to achieve a better quality of approximation (approximation ratio) of an algorithm for determining optimal or close to it solutions of some “minor” changes of instance I. To solve the problem Ins-Max-EkCSP-P (reoptimization of Max-EkCSP-P with the addition of one constraint) with approximation resistant predicate P exists a polynomial threshold (optimal) -approximation algorithm, where the threshold “random” approximation ratio of P). When the unique games conjecture (UGC) is hold there exists a polynomial threshold (optimal) -approximation algorithm (where and the integrality gap of semidefinite relaxation of Max-EkCSP-P problem Z) to solve the problem Ins-Max-EkCSP-P.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374096 and 61104048)the Natural Science Foundation of Zhejiang Province of China(Grant No.Y6110751)
文摘In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.
