Multistage stochastic programming with recourse is formulated in terms of a recursive sequence of mathematical programming problems--P0,..., PK--with stochastic data. A polyhedral property of their feasible regions is used to derive a Lipschitz property of their objective functions. A slightly stronger property is used to conclude that any measurable decision rule satisfying the explicit and Implicit constraints of Pk(0 ¿ k ¿ K) almost surely can be redefined on a set of measure 0 so it satisfies the constraints for every possible realization of the random variables. Sufficient conditions for each of the two polyhedral convexity properties are given.
{"title":"Polyhedral convex feasible regions in stochastic programming with recourse","authors":"Paul Olsen","doi":"10.1109/CDC.1975.270573","DOIUrl":"https://doi.org/10.1109/CDC.1975.270573","url":null,"abstract":"Multistage stochastic programming with recourse is formulated in terms of a recursive sequence of mathematical programming problems--P0,..., PK--with stochastic data. A polyhedral property of their feasible regions is used to derive a Lipschitz property of their objective functions. A slightly stronger property is used to conclude that any measurable decision rule satisfying the explicit and Implicit constraints of Pk(0 ¿ k ¿ K) almost surely can be redefined on a set of measure 0 so it satisfies the constraints for every possible realization of the random variables. Sufficient conditions for each of the two polyhedral convexity properties are given.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130453004","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}
The problem of control of a linear stochastic system observed by both linear and hard limited measurements is considered. The control used is the LQG or deterministic linear feedback control where the state estimate is generated by a recursive nonlinear filter. It is shown that the feedback nature of the control induces a natural probing which activates the filter. The results of this feedback system with a nonlinear filter in the feedback loop is compated to a system with an extended Kalman filter in the feedback loop. The state estimation accuracy is also compared to the system without a control to demonstrate how the control activates the nonlinear filter.
{"title":"A certainty equivalence control with a nonlinear filter in the feedback loop","authors":"D. Alspach","doi":"10.1109/CDC.1975.270611","DOIUrl":"https://doi.org/10.1109/CDC.1975.270611","url":null,"abstract":"The problem of control of a linear stochastic system observed by both linear and hard limited measurements is considered. The control used is the LQG or deterministic linear feedback control where the state estimate is generated by a recursive nonlinear filter. It is shown that the feedback nature of the control induces a natural probing which activates the filter. The results of this feedback system with a nonlinear filter in the feedback loop is compated to a system with an extended Kalman filter in the feedback loop. The state estimation accuracy is also compared to the system without a control to demonstrate how the control activates the nonlinear filter.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127864763","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}
The pursuit-evasion problem of two aircraft in a horizontal plane is modelled as a zerosum differential game with capture time as payoff. The aircraft are modelled as point masses with thrust and bank angle controls. The games of kind and degree for this differential game are solved.
{"title":"The pursuit-evasion problem of two aircraft in a horizontal plane","authors":"N. Rajan, U. Prasad","doi":"10.1109/CDC.1975.270583","DOIUrl":"https://doi.org/10.1109/CDC.1975.270583","url":null,"abstract":"The pursuit-evasion problem of two aircraft in a horizontal plane is modelled as a zerosum differential game with capture time as payoff. The aircraft are modelled as point masses with thrust and bank angle controls. The games of kind and degree for this differential game are solved.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"18 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120903607","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}
A certain "star-product" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model, and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the discrete-time and continuous-time are noted.
{"title":"Scattering theory and linear least squares estimation: Part II: Discrete-time problems","authors":"B. Friedlander, T. Kailath, L. Ljung","doi":"10.1109/CDC.1975.270648","DOIUrl":"https://doi.org/10.1109/CDC.1975.270648","url":null,"abstract":"A certain \"star-product\" formalism in scattering theory as developed by Redheffer is shown to also be naturally applicable to discrete-time linear least-squares estimation problems. The formalism seems to provide a nice way of handling some of the well-known algebraic complications of the discrete-time case, e.g., the distinctions between time and measurement updates, predicted and filtered estimates, etc. Several other applications of the scattering framework are presented, including doubling formulas for the error covariance, a change of initial conditions formula, equations for a backwards Markov state model, and a new derivation of the Chandrasekhar-type equations for the constant parameter case. The differences between the discrete-time and continuous-time are noted.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116541377","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}
The purpose of this paper is to discuss, in an informal manner, some of the very interesting problems that arise when one examines decision strategies in dynamic communication networks. The study of such systems leads to natural decentralized control strategies associated with stochastic control problems with nonclassical information structure. Since this nonclassical information pattern is a consequence of the physical limitations on the speed of information transfer, we call this class of problems relativistic stochastic control problems.
{"title":"Relativistic control theory and the dynamic control of communication networks","authors":"N. Sandell, M. Athans","doi":"10.1109/CDC.1975.270733","DOIUrl":"https://doi.org/10.1109/CDC.1975.270733","url":null,"abstract":"The purpose of this paper is to discuss, in an informal manner, some of the very interesting problems that arise when one examines decision strategies in dynamic communication networks. The study of such systems leads to natural decentralized control strategies associated with stochastic control problems with nonclassical information structure. Since this nonclassical information pattern is a consequence of the physical limitations on the speed of information transfer, we call this class of problems relativistic stochastic control problems.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132781864","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}
The following definition of Economics is given by P. A. Samuelson: "Economics is the study of how men and society choose, with or without the use of money, to employ scarce productive resources, which could have alternative uses, to produce various commodities over time and distribute them for consumption, now and in the future, among various people and groups in society." Thus the study of economics is related to that of allocating scarce resources for alternative uses. This motivates the use of mathematical optimization techniques in economic problems such as consumer behavior, planning of production and inventory, economic growth, portfolio selections and many other things. The use of control theory seems to be a natural extension when one is interested in investigating the effect of certain changes on the whole motion or behavior over time of the economic system under investigation. When there are random variables or stochastic processes which may be involved in the economic system, the methods of stochastic control would seem to be appropriate. In the study of economics, one important class of problems is that of investigating the effects of a change (sometimes in an unknown way) in some internal parameter on the behavior of the system over time. For such a study, the concepts and methods of adaptive control are extremely valuable.
{"title":"Adaptive control in economics","authors":"E. Tse","doi":"10.1109/CDC.1975.270639","DOIUrl":"https://doi.org/10.1109/CDC.1975.270639","url":null,"abstract":"The following definition of Economics is given by P. A. Samuelson: \"Economics is the study of how men and society choose, with or without the use of money, to employ scarce productive resources, which could have alternative uses, to produce various commodities over time and distribute them for consumption, now and in the future, among various people and groups in society.\" Thus the study of economics is related to that of allocating scarce resources for alternative uses. This motivates the use of mathematical optimization techniques in economic problems such as consumer behavior, planning of production and inventory, economic growth, portfolio selections and many other things. The use of control theory seems to be a natural extension when one is interested in investigating the effect of certain changes on the whole motion or behavior over time of the economic system under investigation. When there are random variables or stochastic processes which may be involved in the economic system, the methods of stochastic control would seem to be appropriate. In the study of economics, one important class of problems is that of investigating the effects of a change (sometimes in an unknown way) in some internal parameter on the behavior of the system over time. For such a study, the concepts and methods of adaptive control are extremely valuable.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134128025","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}
Seismic exploration attempts to recover the acoustic structure of the earth from observations made at the accessible surface. Depositional history often makes a plane-layered model a reasonable first approximation to the structure. Field techniques do not correspond to the use of plane waves, but a method of extracting the equivalent of such observation from data will be discussed. Thus it is of interest to consider the inversion problem for this one-dimensional case. One method for performing such an inversion will be presented, and attendant problems will be discussed.
{"title":"One-dimensional inversion of seismograms","authors":"E. Eisner","doi":"10.1109/CDC.1975.270658","DOIUrl":"https://doi.org/10.1109/CDC.1975.270658","url":null,"abstract":"Seismic exploration attempts to recover the acoustic structure of the earth from observations made at the accessible surface. Depositional history often makes a plane-layered model a reasonable first approximation to the structure. Field techniques do not correspond to the use of plane waves, but a method of extracting the equivalent of such observation from data will be discussed. Thus it is of interest to consider the inversion problem for this one-dimensional case. One method for performing such an inversion will be presented, and attendant problems will be discussed.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130353486","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}
The use of digital computers for power system protection and control has been studied for the past decade. However, economic considerations, reliability problems, and system constraints have prohibited the actual use of computers in substation protection schemes. Recent advances in microcomputer technology have provided power system protection engineers with a new tool. A distributed microcomputer protection scheme is introduced and compared to present substation protection techniques. Speed, reliability, and operating advantages as well as the adaptive control possibilities of the proposed system are pursued.
{"title":"Application of microcomputers to the protection and control of power system substations","authors":"B. Russell","doi":"10.1109/CDC.1975.270571","DOIUrl":"https://doi.org/10.1109/CDC.1975.270571","url":null,"abstract":"The use of digital computers for power system protection and control has been studied for the past decade. However, economic considerations, reliability problems, and system constraints have prohibited the actual use of computers in substation protection schemes. Recent advances in microcomputer technology have provided power system protection engineers with a new tool. A distributed microcomputer protection scheme is introduced and compared to present substation protection techniques. Speed, reliability, and operating advantages as well as the adaptive control possibilities of the proposed system are pursued.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"326 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124605479","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}
The Riccati equation plays an equally important role in scattering theory as in linear least-squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. We show that this framework is very appropriate also for estimation problems, and that it enables us to give simple derivatitions of known results as well as to obtain several new results. Examples include the derivation of backwards equations to solve forwards Riccati equations; an analysis of the asymptotic behavior of the Riccati equation; the derivation of backwards Markovian representations of stochastic processes; and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.
{"title":"Scattering theory and linear least squares estimation: Part I: Continuous-time problems","authors":"L. Ljung, T. Kailath, B. Friedlander","doi":"10.1109/CDC.1975.270647","DOIUrl":"https://doi.org/10.1109/CDC.1975.270647","url":null,"abstract":"The Riccati equation plays an equally important role in scattering theory as in linear least-squares estimation theory. However, in the scattering literature, a somewhat different framework of treating the Riccati equation has been developed. We show that this framework is very appropriate also for estimation problems, and that it enables us to give simple derivatitions of known results as well as to obtain several new results. Examples include the derivation of backwards equations to solve forwards Riccati equations; an analysis of the asymptotic behavior of the Riccati equation; the derivation of backwards Markovian representations of stochastic processes; and new derivations and new insights into the Chandrasekhar and related Levinson and Cholesky equations.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121260646","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}
An algorithm for finding the set of all Pareto-optimal solutions of a linear multiple-objective optimization problem is presented in this paper. This algorithm is successful in detecting any Pareto-optimal solution and will systematically and efficiently determine the entire set of Pareto-optimal solutions. An example is given to illustrate the algorithm.
{"title":"A computational method for linear multiple-objective optimization problems","authors":"H. Shen, J. Lin","doi":"10.1109/CDC.1975.270578","DOIUrl":"https://doi.org/10.1109/CDC.1975.270578","url":null,"abstract":"An algorithm for finding the set of all Pareto-optimal solutions of a linear multiple-objective optimization problem is presented in this paper. This algorithm is successful in detecting any Pareto-optimal solution and will systematically and efficiently determine the entire set of Pareto-optimal solutions. An example is given to illustrate the algorithm.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115088168","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}
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