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Journal of The Society for Industrial and Applied Mathematics, Series A: Control最新文献

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Optimal Programs for an Ascending Missile 升天导弹的最优方案
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302007
G. Ewing, W. Haseltine
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引用次数: 5
Some Mathematical Theory of the Penalty Method for Solving Optimum Control Problems 求解最优控制问题惩罚法的一些数学理论
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302026
K. Okamura
{"title":"Some Mathematical Theory of the Penalty Method for Solving Optimum Control Problems","authors":"K. Okamura","doi":"10.1137/0302026","DOIUrl":"https://doi.org/10.1137/0302026","url":null,"abstract":"The penalty method is a powerful technique for solving the optimum control problems involving systems subject to holonomic side constraints. In the usual calculus of variations, the above problems are formulated in consideration of the Weierstrass-Erdmann corner conditions which add considerable complexity in practice. In the penalty method, however, the side constraints are eliminated by introducing a sequence of approximate formulations. Thus the Weierstrass-Erdmann corner conditions need not be checked.When the penalty method is applied in the ordinary calculus the sequence of approximate formulations is proved to be equivalent to the original formulation in the limiting case. However, no mathematical rigor has been claimed when the penalty method is applied to the variational problems.The author establishes, in this paper, some mathematical basis for the penalty method applied in the calculus of variations, particularly optimum control problems.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133980748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 26
On the Existence of Optimal Stochastic Controls 关于最优随机控制的存在性
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303031
H. Kushner
{"title":"On the Existence of Optimal Stochastic Controls","authors":"H. Kushner","doi":"10.1137/0303031","DOIUrl":"https://doi.org/10.1137/0303031","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133698158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 73
Modes of finite response time control. 有限响应时间控制模式。
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302006
C. Harvey
{"title":"Modes of finite response time control.","authors":"C. Harvey","doi":"10.1137/0302006","DOIUrl":"https://doi.org/10.1137/0302006","url":null,"abstract":"A linear autonomous system with a single control variable is considered. There are, in general, several modes of finite response time control for such a system. The concepts of single component regulation and multiple component regulation are defined. It is then shown that a multiple component regulation problem can be transformed into a single component regulation problem. Thus it is possible to express any of the modes of control considered as control of a single input, single output system.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"309 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115831286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Remark on Complete Controllability 关于完全可控性的注解
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303029
H. Chu
{"title":"A Remark on Complete Controllability","authors":"H. Chu","doi":"10.1137/0303029","DOIUrl":"https://doi.org/10.1137/0303029","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"329 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122835682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Optimal-Thrust Trajectories in an Arbitrary Gravitational Field 任意引力场中的最佳推力轨迹
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302033
J. G. Gurley
{"title":"Optimal-Thrust Trajectories in an Arbitrary Gravitational Field","authors":"J. G. Gurley","doi":"10.1137/0302033","DOIUrl":"https://doi.org/10.1137/0302033","url":null,"abstract":"The problem of optimal-thrust trajectories is studied using a slight variation of the usual calculus of variations technique. The results include the usual first-order criteria for optimality, which are that the direction of thrust must be everywhere parallel to a solution $psi $ of the adjoint differential equation, and that the magnitude of the thrust must be zero in regions where the magnitude of $psi $ is less than a critical value, and equal to the maximum permissible value in regions where the magnitude of $psi $ is greater than the critical value. Singular arcs, on which the magnitude of $psi $ is continuously equal to the critical value, are shown to exist in the case of all except the simplest gravitational fields, and in some cases may form part of an optimal trajectory. A means of calculating the unique value of thrust required to sustain a singular arc is described, and a test for the optimality of such arcs is given. The test shows that a family of singular arcs discovered by D. F. Lawden...","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128969577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Convex Programming and Optimal Control 凸规划与最优控制
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303012
A. Goldstein
{"title":"Convex Programming and Optimal Control","authors":"A. Goldstein","doi":"10.1137/0303012","DOIUrl":"https://doi.org/10.1137/0303012","url":null,"abstract":"The use of convex programming to attack problems of optimal control is not new, but it is becoming of increasing interest. Techniques of steepest descent and gradient projection have been used by Balakrishnan [1], Goldstein [2], [3], Neustadt [4], and Neustadt and Paiewonsky [5]. For the case of unbounded fuel-optimal linear controls Neustadt [4] has shown that the problem may be cast into the form of an infinite linear program. More recently Dantzig [7] and Van Slyke [8] have obtained results in this direction for bounded linear controls. This paper will be concerned with the case of fuel-optimal linear controls. This problem will be reduced to the case of minimizing a convex function on $E_n $, and techniques of infinite convex programming will be applied. In the important case when the thrust magnitude is constrained, the convex function is continuously differentiable, and techniques of steepest descent may be applied. This approach has already been suggested by Neustadt and Paiewonsky [5].","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121232032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On Steepest Descent 最陡降落
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303013
A. Goldstein
{"title":"On Steepest Descent","authors":"A. Goldstein","doi":"10.1137/0303013","DOIUrl":"https://doi.org/10.1137/0303013","url":null,"abstract":"Abstract : This paper continues studies concerning iterative methods of driving the gradient to zero (A. A. Goldstein. Minimizing functionals on Hilbert space. Computer methods in optimization problems. New York, Academic Press, 1964, p. 159-165). Those studies were concerned with functions which were twice differentiable; in this paper only first derivatives will be assumed. Other results included are a fixed point theorem for 'gradient' operators and a simple proof of the classical method of steepest descent.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123688134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 159
On a Certain Problem for Parabolic Differential Equations Connected with Optimal Pursuit 一类带最优追求的抛物型微分方程问题
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303006
E. Mishchenko
{"title":"On a Certain Problem for Parabolic Differential Equations Connected with Optimal Pursuit","authors":"E. Mishchenko","doi":"10.1137/0303006","DOIUrl":"https://doi.org/10.1137/0303006","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"30 12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126169016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Controllability and Observability in Multivariable Control Systems 多变量控制系统的可控性与可观测性
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0301009
E. Gilbert
{"title":"Controllability and Observability in Multivariable Control Systems","authors":"E. Gilbert","doi":"10.1137/0301009","DOIUrl":"https://doi.org/10.1137/0301009","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116977623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 275
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