A simple matrix method is described for solving the equation ax + by = d, where a and b are given, and x, y and the greatest common divisor (g.c.d.) d are to be determined. All the polynomials are expressed relative to an arbitrary given basis of orthogonal polynomials, and there are no conversions to power form. The procedure utilizes the comrade matrix, a generalization of the companion matrix, and involves elementary row operations performed on easily constructed matrices.
本文描述了求解方程ax + by = d的一种简单矩阵法，其中已知A和b，并求出x、y和最大公约数d。所有的多项式都是相对于正交多项式的任意给定基来表示的，并且没有幂形式的转换。该程序利用同伴矩阵，一种同伴矩阵的推广，并涉及在容易构造的矩阵上执行的初等行运算。
{"title":"Solution of ax + by = d for generalized polynomials","authors":"S. Barnett","doi":"10.1109/CDC.1984.272439","DOIUrl":"https://doi.org/10.1109/CDC.1984.272439","url":null,"abstract":"A simple matrix method is described for solving the equation ax + by = d, where a and b are given, and x, y and the greatest common divisor (g.c.d.) d are to be determined. All the polynomials are expressed relative to an arbitrary given basis of orthogonal polynomials, and there are no conversions to power form. The procedure utilizes the comrade matrix, a generalization of the companion matrix, and involves elementary row operations performed on easily constructed matrices.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122991025","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}
We solve a Bellman equation in Hilbert spaces and give an application to an optimal control problem.
我们解了Hilbert空间中的Bellman方程，并给出了最优控制问题的一个应用。
{"title":"Dynamic programming and Bellman equation in Hilbert space","authors":"G. Prato","doi":"10.1109/CDC.1984.272199","DOIUrl":"https://doi.org/10.1109/CDC.1984.272199","url":null,"abstract":"We solve a Bellman equation in Hilbert spaces and give an application to an optimal control problem.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121809568","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 special quadratic programming problem in complex variables is investigated for a closed form solution. Two different approaches are used. The first is a direct approach that leads to a family of solutions because of a singular matrix encountered in the solution process. The second is an indirect approach based on parametrizing the objective function. It leads to a solution which is a member in the above family and which is shown to be bounded.
{"title":"A closed form solution to a quadratic programming problem in complex variables","authors":"M. Hanna, M. Simaan","doi":"10.1109/CDC.1984.272180","DOIUrl":"https://doi.org/10.1109/CDC.1984.272180","url":null,"abstract":"A special quadratic programming problem in complex variables is investigated for a closed form solution. Two different approaches are used. The first is a direct approach that leads to a family of solutions because of a singular matrix encountered in the solution process. The second is an indirect approach based on parametrizing the objective function. It leads to a solution which is a member in the above family and which is shown to be bounded.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121906471","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 paper deals with the development of a simple method for the redesign of a recent hybrid adaptive control scheme by using adaptive sampling. The main objective of the proposed technique is to improve the adaptation transients by taking advantage of the knowledge about it goodness in classical (i.e., those nonneeding parameter adaptation) problems concerned with the transient behaviours in terms of acceptable tracking error deviations.
{"title":"Improving the adaptation transients in hybrid adaptive control","authors":"M. L. la Sen, M. Paz","doi":"10.1109/CDC.1984.272099","DOIUrl":"https://doi.org/10.1109/CDC.1984.272099","url":null,"abstract":"The paper deals with the development of a simple method for the redesign of a recent hybrid adaptive control scheme by using adaptive sampling. The main objective of the proposed technique is to improve the adaptation transients by taking advantage of the knowledge about it goodness in classical (i.e., those nonneeding parameter adaptation) problems concerned with the transient behaviours in terms of acceptable tracking error deviations.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122772180","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 deals with problems related to the stabilizability of linear time-varying systems. One of the central results of the paper is that if a system can be stabilized by dynamic state feedback, it can also be stabilized by memoryless (static) state feed-back. A stable-proper factorization theory for linear time-varying systems is also introduced.
{"title":"On the stabilizability of linear time-varying systems","authors":"P. Khargonekar, K. Poolla","doi":"10.1109/CDC.1984.272308","DOIUrl":"https://doi.org/10.1109/CDC.1984.272308","url":null,"abstract":"This paper deals with problems related to the stabilizability of linear time-varying systems. One of the central results of the paper is that if a system can be stabilized by dynamic state feedback, it can also be stabilized by memoryless (static) state feed-back. A stable-proper factorization theory for linear time-varying systems is also introduced.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125690742","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 Galerkin method is presented as a way to develop finite-dimensional controllers for linear distributed parameter systems (DPS). The direct approach approximates the open-loop DPS and then generates the controller from this approximation; the indirect approach approximates the infinite-dimensional stabilizing controller. The indirect approach is shown to converge to the stable closed-loop system consisting of DPS and infinite-dimensional controller; conditions are presented on the behavior of the Galerkin method for the open loop DPS which guarantee closed-loop stability for large enough finite-dimensional approximations.
{"title":"Exponentially stabilizing finite-dimensional controllers for linear distributed parameter systems","authors":"M. Balas","doi":"10.1109/CDC.1984.272298","DOIUrl":"https://doi.org/10.1109/CDC.1984.272298","url":null,"abstract":"The Galerkin method is presented as a way to develop finite-dimensional controllers for linear distributed parameter systems (DPS). The direct approach approximates the open-loop DPS and then generates the controller from this approximation; the indirect approach approximates the infinite-dimensional stabilizing controller. The indirect approach is shown to converge to the stable closed-loop system consisting of DPS and infinite-dimensional controller; conditions are presented on the behavior of the Galerkin method for the open loop DPS which guarantee closed-loop stability for large enough finite-dimensional approximations.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129791289","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}
Pub Date : 1984-12-01DOI: 10.1109/TAC.1985.1104093
L. Ljung
Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.
{"title":"Asymptotic variance expressions for identified black-box transfer function models","authors":"L. Ljung","doi":"10.1109/TAC.1985.1104093","DOIUrl":"https://doi.org/10.1109/TAC.1985.1104093","url":null,"abstract":"Identification of black-box transfer function models is considered. It is assumed that the transfer function models possess a certain shift-property, which is satisfied for example by all polynomial-type models. Expressions for the variances of the transfer function estimates are derived, that are asymptotic both in the number of observed data and in the model orders. The result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance, respectively, is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise. The factor of proportionality is the ratio of model order to number of data. This result is independent of the particular model structure used. The result is applied to evaluate the performance degradation due to variance for a number of typical model uses. Some consequences for input design are also drawn.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129445997","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 optimal design of a Kalman filter is considered in respect of its finite wordlength (FWL) characteristics taking into account the round-off noise due to state quantization. The issues are particularly relevant in the design of FWL Kalman filters for continuous-time systems operating under a fast sampling rate. The optimum filter structure includes state residue feedback compensation which can result in the saving of many bits of additional state wordlength.
{"title":"Finite state wordlength compensation in digital Kalman filters","authors":"D. Williamson","doi":"10.1109/CDC.1984.272222","DOIUrl":"https://doi.org/10.1109/CDC.1984.272222","url":null,"abstract":"The optimal design of a Kalman filter is considered in respect of its finite wordlength (FWL) characteristics taking into account the round-off noise due to state quantization. The issues are particularly relevant in the design of FWL Kalman filters for continuous-time systems operating under a fast sampling rate. The optimum filter structure includes state residue feedback compensation which can result in the saving of many bits of additional state wordlength.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124589835","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 'filtered' martingale problem is defined for the problem of estimating a process X from observations of Y, where (X,Y) is Markov. We give conditions on the generator of (X,Y) that imply that the conditional distribution is the unique solution to this filtered martingale problem. We apply this result to prove uniqueness of solutions of the Kushner-Stratonovich and Zakai equations of non-linear filtering.
{"title":"Unique characterization of conditional distributions in nonlinear filtering","authors":"Thomas G. Kurtz, D. Ocone","doi":"10.1109/CDC.1984.272100","DOIUrl":"https://doi.org/10.1109/CDC.1984.272100","url":null,"abstract":"A 'filtered' martingale problem is defined for the problem of estimating a process X from observations of Y, where (X,Y) is Markov. We give conditions on the generator of (X,Y) that imply that the conditional distribution is the unique solution to this filtered martingale problem. We apply this result to prove uniqueness of solutions of the Kushner-Stratonovich and Zakai equations of non-linear filtering.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131303837","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}
Much research has been generated concerning the problem of finding necessary and sufficient conditions that a nonlinear system be equivalent to a linear system. In this paper we take a nonlinear control system with output and examine certain Lie derivatives. Necessary and sufficient conditions (which can be tested in a finite number of steps) that we actually have a linear system with linear output are determined.
{"title":"Recognizing linear systems","authors":"L. Hunt, M. Luksic, R. Su","doi":"10.1109/CDC.1984.272406","DOIUrl":"https://doi.org/10.1109/CDC.1984.272406","url":null,"abstract":"Much research has been generated concerning the problem of finding necessary and sufficient conditions that a nonlinear system be equivalent to a linear system. In this paper we take a nonlinear control system with output and examine certain Lie derivatives. Necessary and sufficient conditions (which can be tested in a finite number of steps) that we actually have a linear system with linear output are determined.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126969733","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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