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Stability Criteria for Nonlinear Ordinary Differential Equations 非线性常微分方程的稳定性判据
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0301018
O. Mangasarian
{"title":"Stability Criteria for Nonlinear Ordinary Differential Equations","authors":"O. Mangasarian","doi":"10.1137/0301018","DOIUrl":"https://doi.org/10.1137/0301018","url":null,"abstract":"The main results of this work are three sufficient conditions for the (1) stability, (2) uniform asymptotic stability in the large and (3) instability, of the equilibrium point $x = 0$ of the system of differential equations: $dot x = f(t,x)$, $f(t,0) = 0$. Stated roughly these conditions are: The point $x = 0$ is (1) stable if $x'f(t,x)$ is a concave function of x, (2) uniformly asymptotically stable in the large if $x'f(t,x)$ is a concave function of x is a strictly concave function of x, and (3) unstable if $x'f(t,x)$ is a strictly convex function of x. These results are obtained by using the stability and instability criteria of Liapunov and properties of concave and convex functions.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"38 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":"123765387","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: 14
Asymptotic Control Theory 渐近控制理论
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302002
R. Bellman, R. Bucy
{"title":"Asymptotic Control Theory","authors":"R. Bellman, R. Bucy","doi":"10.1137/0302002","DOIUrl":"https://doi.org/10.1137/0302002","url":null,"abstract":"Abstract : Some general problems are described concerning the asymptotic behavior of control processes as the time-interval becomes infinite. Some partial results in the general case, and a detailed analysis of a one- dimensional control process are presented.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"31 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":"122599465","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: 17
Analysis of Linear Systems by Means of Laguerre Functions 用拉盖尔函数分析线性系统
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302031
J. C. I. Dooge
{"title":"Analysis of Linear Systems by Means of Laguerre Functions","authors":"J. C. I. Dooge","doi":"10.1137/0302031","DOIUrl":"https://doi.org/10.1137/0302031","url":null,"abstract":"The use of Laguerre functions is proposed for the analysis of heavily damped linear systems where the input is not subject to experimental control. An equation is derived which links the corresponding coefficients in the Laguerre function expansions of the input, the impulse response and the output of a linear system. This equation enables the third set of Laguerre coefficients to be calculated when the other two sets of coefficients are known. The connection between the Laguerre function expansion and the representation of the system response by a series of gamma distributions is noted and the latter series identified as defining an analog system composed entirely of branches of linear storage elements.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"45 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":"121868672","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: 30
Time-Optimal Control of Solutions of Operational Differenital Equations 微分方程解的时间最优控制
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302005
H. Fattorini
{"title":"Time-Optimal Control of Solutions of Operational Differenital Equations","authors":"H. Fattorini","doi":"10.1137/0302005","DOIUrl":"https://doi.org/10.1137/0302005","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"21 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":"128371303","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
PSEUDO-CONVEX FUNCTIONS PSEUDO-CONVEX功能
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303020
O. Mangasarian
{"title":"PSEUDO-CONVEX FUNCTIONS","authors":"O. Mangasarian","doi":"10.1137/0303020","DOIUrl":"https://doi.org/10.1137/0303020","url":null,"abstract":"The purpose of this work is to, introduce pseudo-convex functions and to describe some of their properties and applications. The class of all pseudo-convex functions over a convex set C includes the class of all differentiable convex functions on C and is included in the class of all differentiable quasi-convex functions on C. An interesting property of pseudo-convex functions is that a local condition, such as the vanishing of the gradient, is a global optimality condition. One of the main results of this work consists of showing that the Kuhn-Tucker differential conditions are sufficient for optimality when the objective function is pseudo-convex and the constraints are quasi-convex. Other results of this work are a strict converse duality theorem for mathematical programming and a stability criterion for ordinary differential equations.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"7 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":"114878641","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: 265
Existence Theorems for Optimal Solutions in Pontryagin and Lagrange Problems 庞特里亚金和拉格朗日问题最优解的存在性定理
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303032
L. Cesari
{"title":"Existence Theorems for Optimal Solutions in Pontryagin and Lagrange Problems","authors":"L. Cesari","doi":"10.1137/0303032","DOIUrl":"https://doi.org/10.1137/0303032","url":null,"abstract":"","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"88 14 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":"126311879","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: 49
On the Existence of Lyapunov Function for the Problem of Lur’e 关于Lur 'e问题Lyapunov函数的存在性
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303025
K. Meyer
{"title":"On the Existence of Lyapunov Function for the Problem of Lur’e","authors":"K. Meyer","doi":"10.1137/0303025","DOIUrl":"https://doi.org/10.1137/0303025","url":null,"abstract":"Existence of Liapunov functions for problem of Lure with removal of complete controllability and observability","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"89 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":"132411066","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: 64
A Time Optimal Control Problem for Systems Described by Differential Difference Equations 用微分差分方程描述系统的时间最优控制问题
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0301017
M. N. Ogˇuztöreli
{"title":"A Time Optimal Control Problem for Systems Described by Differential Difference Equations","authors":"M. N. Ogˇuztöreli","doi":"10.1137/0301017","DOIUrl":"https://doi.org/10.1137/0301017","url":null,"abstract":"The aim of this paper is to establish the solution of an optimal time control problem for a physical system whose state is described by a linear differential-difference equation with retarded argument. We have obtained here a generalisation of the results of Bellman and his collaborators Glicksberg, Gross and Kalaba, and of LaSalie and Neustadt by using a technique due to LaSalle, with the help of the kernel matrix representation of Bellman and Cooke and also a new integral representation for the solutions of linear differential-difference equations.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"21 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":"130080361","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: 21
The Application of Lyapunov’s Second Method to Interconnected Systems 李亚普诺夫第二方法在互联系统中的应用
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0303030
F. Bailey
{"title":"The Application of Lyapunov’s Second Method to Interconnected Systems","authors":"F. Bailey","doi":"10.1137/0303030","DOIUrl":"https://doi.org/10.1137/0303030","url":null,"abstract":"As many engineering systems are made up of an interconnection of simple subsystems, it is natural to attempt to utilize this interconnection structure in developing system analysis techniques. In this paper interconnection information is used in conjunction with properties of the individual subsystems to obtain sufficient conditions for asymptotic stability-in-the-large. This method may be applied to a broad class of linear, nonlinear and time-varying interconnected systems as indicated in the following three steps.First, the Lyapun-ov functions and comparison equations are found for the individual subsystems. Second, the comparison equations are interconnected, following the interconnections in the original system, into a system of comparison equations. This system is linear, with constant coefficients and of order equal to the number of subsystems in the original interconnected system. Finally, the stability of the null solution of this auxiliary system is examined. If it is asymptotically stable, then ...","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":"128855505","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: 155
Some Types of Optimal Control of Stochastic Systems 几种类型的随机系统最优控制
Journal of The Society for Industrial and Applied Mathematics, Series A: Control Pub Date : 1900-01-01 DOI: 10.1137/0302010
S. Dreyfus
{"title":"Some Types of Optimal Control of Stochastic Systems","authors":"S. Dreyfus","doi":"10.1137/0302010","DOIUrl":"https://doi.org/10.1137/0302010","url":null,"abstract":"Abstract : The optimal control of stochastic systems is considered. Under various assumptions concerning the information available to the controller, different optimal control rules result. For certain specific problems, the different control schemes are analyzed and compared, and the vast superiority of feedback over open-loop control is demonstrated.","PeriodicalId":215491,"journal":{"name":"Journal of The Society for Industrial and Applied Mathematics, Series A: Control","volume":"39 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":"122044186","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: 108
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