This paper considers "frequency domain" methods for the derivation of Kalman-Bucy filters for a certain class of distributed systems. An integral representation for the optimal stationary filter gains is derived using Wiener-Hopf techniques, avoiding consideration of distributed Riccati equations.
{"title":"A distributed filter derivation without Riccati equations","authors":"Jon H. Davis","doi":"10.1137/0316039","DOIUrl":"https://doi.org/10.1137/0316039","url":null,"abstract":"This paper considers \"frequency domain\" methods for the derivation of Kalman-Bucy filters for a certain class of distributed systems. An integral representation for the optimal stationary filter gains is derived using Wiener-Hopf techniques, avoiding consideration of distributed Riccati equations.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121654802","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}
Weakening the constraints in a general non-linear optimal control problem we obtain a convex optimization program with the same value.
弱化一般非线性最优控制问题的约束条件，得到具有相同值的凸优化方案。
{"title":"Application of young's theory of flows to control","authors":"Richard Lewis","doi":"10.1109/CDC.1978.268061","DOIUrl":"https://doi.org/10.1109/CDC.1978.268061","url":null,"abstract":"Weakening the constraints in a general non-linear optimal control problem we obtain a convex optimization program with the same value.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"98 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":"117214850","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}
This paper is a condensed version of a recent two part report on applied analysis of linear multivariable systems [1], [2]. The basic thrust of the work is this: Singular value analysis, of proven power in applied analysis of systems of linear equations, can be applied in a very direct way to systems of linear differential equations as well. The essential fact revealed and exploited is that norm characteristics (l2 norm) of relevant maps are reflected, with no distortion, by norm characteristics of associated grammian matrices. The basic tools developed in the beginning of the paper are used to develop a framework where "near" uncontrollability/unobservability is well defined and is directly related to near redundancy of state variables. In this setting there is continuity between Kalman's minimal realization theory and model reduction based on elimination of nearly redundant state variables. One can view this process as the application of the mechanics of Kalman decomposition using working values of the relevant subspaces.
{"title":"Singular value analysis of linear systems","authors":"B. Moore","doi":"10.1109/CDC.1978.267894","DOIUrl":"https://doi.org/10.1109/CDC.1978.267894","url":null,"abstract":"This paper is a condensed version of a recent two part report on applied analysis of linear multivariable systems [1], [2]. The basic thrust of the work is this: Singular value analysis, of proven power in applied analysis of systems of linear equations, can be applied in a very direct way to systems of linear differential equations as well. The essential fact revealed and exploited is that norm characteristics (l2 norm) of relevant maps are reflected, with no distortion, by norm characteristics of associated grammian matrices. The basic tools developed in the beginning of the paper are used to develop a framework where \"near\" uncontrollability/unobservability is well defined and is directly related to near redundancy of state variables. In this setting there is continuity between Kalman's minimal realization theory and model reduction based on elimination of nearly redundant state variables. One can view this process as the application of the mechanics of Kalman decomposition using working values of the relevant subspaces.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"10 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120862753","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}
This paper is concerned with the time optimal control problem of a system whose state is evolving on the sphere S2. The system is described by a bilinear homogeneous set of ordinary differential equations. The controls act independently and are bounded in magnitude. A closed form solution has been obtained for optimal control law by exploiting the geometric structure of the state space. The solution is of bang-bang type with at most one switch required.
{"title":"Time optimal transfers on a sphere","authors":"Abraham Sharon, G. Blankenship","doi":"10.1109/CDC.1978.267989","DOIUrl":"https://doi.org/10.1109/CDC.1978.267989","url":null,"abstract":"This paper is concerned with the time optimal control problem of a system whose state is evolving on the sphere S2. The system is described by a bilinear homogeneous set of ordinary differential equations. The controls act independently and are bounded in magnitude. A closed form solution has been obtained for optimal control law by exploiting the geometric structure of the state space. The solution is of bang-bang type with at most one switch required.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"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":"127139068","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}
Generic examples from a class of nonlinear estimation problems involving parameterized Markov processes are formulated so that each is close to a linear, Kalman-Bucy filtering problem for a limited range of the parameter. Based on this approximation, an asymptotic analysis of each problem is outlined starting from the differential equation for the conditional density of the message given the observations.
{"title":"Asymptotic analysis of a class of nonlinear filtering problems-Part II: A general formulation","authors":"G. Blankenship","doi":"10.1109/CDC.1978.267904","DOIUrl":"https://doi.org/10.1109/CDC.1978.267904","url":null,"abstract":"Generic examples from a class of nonlinear estimation problems involving parameterized Markov processes are formulated so that each is close to a linear, Kalman-Bucy filtering problem for a limited range of the parameter. Based on this approximation, an asymptotic analysis of each problem is outlined starting from the differential equation for the conditional density of the message given the observations.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","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":"123242019","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}
This paper describes a collection of parallel initial costate search algorithms suitable for implementation on an advanced computer with the facility for large scale parallel processing. Specifically, a parallel nongradient algorithm and a parallel variable metric algorithm have been used to search for the initial costate vector that defines the solution to the optimal control problem. To avoid the computational problems sometimes associated with simultaneous forward integration of both the state and costate equations, a parallel shooting procedure based upon partitioning of the integration interval was considered. Application of this parallel procedure to a forced Van der Pol system indicates that convergence time is significantly less than that required by highly efficient serial procedures.
本文介绍了一组适合在具有大规模并行处理能力的先进计算机上实现的并行初始协同状态搜索算法。具体地说，使用并行非梯度算法和并行变度量算法来搜索定义最优控制问题解的初始协态向量。为避免状态方程和协态方程同时正积分的计算问题，提出了一种基于积分区间划分的并行射击方法。将该并行程序应用于强制Van der Pol系统表明，该程序的收敛时间明显小于高效串行程序所需的收敛时间。
{"title":"Parallel initial costate search algorithms for computing optimal controls","authors":"R. Travassos, H. Kaufman","doi":"10.1109/CDC.1978.267925","DOIUrl":"https://doi.org/10.1109/CDC.1978.267925","url":null,"abstract":"This paper describes a collection of parallel initial costate search algorithms suitable for implementation on an advanced computer with the facility for large scale parallel processing. Specifically, a parallel nongradient algorithm and a parallel variable metric algorithm have been used to search for the initial costate vector that defines the solution to the optimal control problem. To avoid the computational problems sometimes associated with simultaneous forward integration of both the state and costate equations, a parallel shooting procedure based upon partitioning of the integration interval was considered. Application of this parallel procedure to a forced Van der Pol system indicates that convergence time is significantly less than that required by highly efficient serial procedures.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","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":"125386915","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}
Recalling that the first order density function of a stationary diffusion process satifies a differential equation which can be derived from the forward equation of Kolmogorov and using nonparametric density estimation, an alternative approach to the estimation of the drift function is presented. Sufficient conditions on a measurable stationary process are given which ensure weak consistency estimation of the logarithmic derivative of its first order density function. Assumptions on a differential stochastic equation driven by Brownian motion are presented under which its stationary solution satisfies the above sufficient identifiability conditions.
{"title":"Nonparametric identification for difiusion processes","authors":"G. Banon","doi":"10.1109/CDC.1978.268069","DOIUrl":"https://doi.org/10.1109/CDC.1978.268069","url":null,"abstract":"Recalling that the first order density function of a stationary diffusion process satifies a differential equation which can be derived from the forward equation of Kolmogorov and using nonparametric density estimation, an alternative approach to the estimation of the drift function is presented. Sufficient conditions on a measurable stationary process are given which ensure weak consistency estimation of the logarithmic derivative of its first order density function. Assumptions on a differential stochastic equation driven by Brownian motion are presented under which its stationary solution satisfies the above sufficient identifiability conditions.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"27 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":"115577048","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}
Existing decision and control methodology does not appear to be adequate for complex, large-scale systems. One area of research that attempts to develop techniques for such systems is decentralized control theory, where "decentralized" applies not only to the control strategy, but also to the information structure. To explore the future directions of decentralized control, the panel members will address the following questions: 1) how has their training as students in decentralized control helped them in their current research, and 2) can the current state-of-the-art in centralized control theory be extended or is a whole new theory needed?
{"title":"A new look at large-scale systems and decentralized control: Recent graduates speak out","authors":"M. Kastner","doi":"10.1109/CDC.1978.267969","DOIUrl":"https://doi.org/10.1109/CDC.1978.267969","url":null,"abstract":"Existing decision and control methodology does not appear to be adequate for complex, large-scale systems. One area of research that attempts to develop techniques for such systems is decentralized control theory, where \"decentralized\" applies not only to the control strategy, but also to the information structure. To explore the future directions of decentralized control, the panel members will address the following questions: 1) how has their training as students in decentralized control helped them in their current research, and 2) can the current state-of-the-art in centralized control theory be extended or is a whole new theory needed?","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","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":"122707817","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 parameter estimation problem for class of linear hereditary systems is recast in a state space setting. A quasilinearization type algorithm is developed, based on the state space formulation. The resulting algorithm requires the solution of initial value problems for hereditary systems. A numerical example is given to illustrate the technique.
{"title":"An abstract quasilinearization algorithm for estimating parameters in hereditary systems","authors":"J. Burns, E. Cliff","doi":"10.1109/CDC.1978.267994","DOIUrl":"https://doi.org/10.1109/CDC.1978.267994","url":null,"abstract":"A parameter estimation problem for class of linear hereditary systems is recast in a state space setting. A quasilinearization type algorithm is developed, based on the state space formulation. The resulting algorithm requires the solution of initial value problems for hereditary systems. A numerical example is given to illustrate the technique.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"264 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":"128757367","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 designing an optimal regulator for a linear, discrete-time, state-space system with linear state equality constraints is discussed. The concepts of complete maintainability and uniform complete maintainability are introduced and investigated for these systems. When the system is uniformly completely maintainable, it is demonstrated that the optimal input policy is governed by a linear feedback control law for quadratic performance criteria.
{"title":"Optimal control of completely maintainable dynamic systems","authors":"D. Stengel","doi":"10.1109/CDC.1978.268046","DOIUrl":"https://doi.org/10.1109/CDC.1978.268046","url":null,"abstract":"The problem of designing an optimal regulator for a linear, discrete-time, state-space system with linear state equality constraints is discussed. The concepts of complete maintainability and uniform complete maintainability are introduced and investigated for these systems. When the system is uniformly completely maintainable, it is demonstrated that the optimal input policy is governed by a linear feedback control law for quadratic performance criteria.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"27 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":"129027692","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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