{"title":"A Doubly Singular Problem in Optimal Interplanetary Guidance","authors":"J. Breakwell","doi":"10.1137/0303007","DOIUrl":"https://doi.org/10.1137/0303007","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"36 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":"128513314","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}
{"title":"On Variational Theory and Optimal Control Theory","authors":"M. Hestenes","doi":"10.1137/0303003","DOIUrl":"https://doi.org/10.1137/0303003","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"4 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":"130794797","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}
{"title":"On stability in control systems.","authors":"E. Roxin","doi":"10.1137/0303024","DOIUrl":"https://doi.org/10.1137/0303024","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"171 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":"123267643","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}
{"title":"Stability and Control","authors":"J. P. Lasalle","doi":"10.1137/0301001","DOIUrl":"https://doi.org/10.1137/0301001","url":null,"abstract":"","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":"131151559","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}
{"title":"An Operator Theoretic Formulation of a Class of Control Problems and a Steepest Descent Method of Solution","authors":"A. Balakrishnant","doi":"10.1137/0301008","DOIUrl":"https://doi.org/10.1137/0301008","url":null,"abstract":"","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":"132566909","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}
{"title":"A Transformation Approach to Singular Subarcs in Optimal Trajectory and Control Problems","authors":"H. Kelley","doi":"10.1137/0302021","DOIUrl":"https://doi.org/10.1137/0302021","url":null,"abstract":"Mayer variational problems in which the control variable appears linearly are considered and a canonical form sought for the system equations which is somewhat analogous to that adopted by Wonham and Johnson for linear constant coefficient systems with cost functional quadratic in the state variables. A means of synthesizing a transformation to the canonical form in terms of the mutually independent solutions of a first order linear homogeneous partial differential equation is described. It is then shown how the Legendre-Clebsch necessary condition applied in the transformed system of variables may be employed to obtain information on the singular extremals of the problem and the possible appearance of singular subarcs in the solution.Two examples are employed for illustration, one a simple servomechanism problem and the other Goddard's problem of optimal thrust programming for a sounding rocket.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"25 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":"115199827","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}
{"title":"Penalty Functions and Bounded Phase Coordinate Control","authors":"D. Russell","doi":"10.1137/0302032","DOIUrl":"https://doi.org/10.1137/0302032","url":null,"abstract":"This paper studies the use of two different kinds of penalty functions to obtain approximate and, in the limit, exact solutions to a class of bounded phase coordinate optimal control problems. The first type of penalty function assumes small values within the phase constraint and large values outside, while the second type is defined only within the phase constraints, assuming small values away from the constraint boundary but increasing to infinity as that boundary is approached.","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":"125230294","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}
{"title":"Minimum Effort Control Of Several Terminal Components","authors":"J. V. Breakwellt, F. Tung","doi":"10.1137/0302025","DOIUrl":"https://doi.org/10.1137/0302025","url":null,"abstract":"The stochastic control problem of minimizing the total average velocity correction with several prescribed terminal variances in the presence of random injection and measurement errors is considered. It is shown that, for the case of linear feedback, this can be formulated as an optimization problem for an equivalent deterministic system whose states are the covariances of the predicted miss. However, the deterministic optimization problem is “degenerate” causing some difficulty in the computation of the feedback gain. It is shown that the optimum linear corrective strategy is, in general, discontinuous and consists of an initial period of no control, followed by a period of continuous control and finally a period of no control and possibly an impulse at the end. Equations are derived from which the variable feedback gain and the various time intervals can be computed. Two simple examples involving (1) the control of two terminal position components, and (2) the control of both the terminal position and t...","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"15 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":"125564158","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}
{"title":"Extraction and Detection Problems and Reproducing Kernel Hilbert Spaces","authors":"E. Parzen","doi":"10.1137/0301004","DOIUrl":"https://doi.org/10.1137/0301004","url":null,"abstract":"Problems involving the extraction, detection and prediction of signals in the presence of noise are among the central problems of statistical communication theory. Over the past few years I have sought to develop an approach to such problems which (i) would simultaneously apply to time series which are stationary or non-stationary, discrete parameter or continuous parameter, univariate or multivariate, and (ii) would distinguish between the statistical and analytical aspects of these problems, and in particular would clarify the role played by various widely employed analytical techniques (such as the Wiener-Hopf equation and eigenfunction expansions).In developing this approach, two basic concepts are used : the notion of the probability density functional of a time series and the notion of a reproducing kernel Hilbert space. The aim of this paper is to sketch some of the main results which may be obtained by means of this approach.In sections 1 and 2, it is shown how one may define and obtain a formula ...","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":"131287290","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}
{"title":"On Exponential Stability of Linear Differential Systems","authors":"N. Bhatia","doi":"10.1137/0302016","DOIUrl":"https://doi.org/10.1137/0302016","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"112 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":"131506963","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}