Pub Date : 1900-01-01DOI: 10.1080/17442507908833135
L. Ljung, P. Caines
A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and that stationarity is not required.
{"title":"Asymptotic normality of prediction error estimators for approximate system models","authors":"L. Ljung, P. Caines","doi":"10.1080/17442507908833135","DOIUrl":"https://doi.org/10.1080/17442507908833135","url":null,"abstract":"A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and that stationarity is not required.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"58 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":"128524776","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 performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a designer can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices are available.
{"title":"Bounds on estimation errors of discrete-time filters under modeling uncertainty","authors":"R. Patel, M. Toda","doi":"10.1109/CDC.1978.268002","DOIUrl":"https://doi.org/10.1109/CDC.1978.268002","url":null,"abstract":"The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a designer can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices are available.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"17 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":"127416632","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 present here a summary of the results of [1]. Related work appears in [15], [16]. We consider the time-invariant system of r first-order coupled linear differential equations E x(t) = A x(t) + B u(t) (1a) y(t) = C x(t) (1b) where x is an r-vector of internal variables, u is an m-vector of control inputs or forcing functions, and y is a p-vector of outputs.
我们在这里总结了[1]的结果。相关工作见于[15]、[16]。我们考虑r个一阶耦合线性微分方程E x(t) = A x(t) + B u(t) (1a) y(t) = C x(t) (1b)的定常系统，其中x是内部变量的r向量，u是控制输入或强制函数的m向量，y是输出的p向量。
{"title":"Generalized state-space systems","authors":"G. Verghese, B. Levy, T. Kailath","doi":"10.1109/CDC.1978.267983","DOIUrl":"https://doi.org/10.1109/CDC.1978.267983","url":null,"abstract":"We present here a summary of the results of [1]. Related work appears in [15], [16]. We consider the time-invariant system of r first-order coupled linear differential equations E x(t) = A x(t) + B u(t) (1a) y(t) = C x(t) (1b) where x is an r-vector of internal variables, u is an m-vector of control inputs or forcing functions, and y is a p-vector of outputs.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"3 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":"129025904","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 new algorithm for the GCD extraction of a set of polynomial matrices is given. The approach is based on system theoretic notions of feedback.
给出了一种新的多项式矩阵集的GCD提取算法。该方法基于反馈的系统理论概念。
{"title":"A system theoretic approach for GCD extraction","authors":"L. Silverman, P. Dooren","doi":"10.1109/CDC.1978.267985","DOIUrl":"https://doi.org/10.1109/CDC.1978.267985","url":null,"abstract":"A new algorithm for the GCD extraction of a set of polynomial matrices is given. The approach is based on system theoretic notions of feedback.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","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":"128831294","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 estimation algorithm for nonlinear transient operation of multivariable gas turbine engines was developed and evaluated. Kalman methodology and model-mismatch compensation procedures were employed in defining the filtering logic. The estimation algorithm was evaluated by application to noise-corrupted measurement data generated by a nonlinear digital dynamic F100/F401 engine simulation. Estimation of unmeasurable as well as measurable key engine variables from (1) nominalengine data, (2) degraded-engine data, and (3) engine data with off-nominal noise statistics was evaluated. Results obtained indicate that the nonlinear estimation algorithm provides a viable approach to estimating key engine variables under realistic operating conditions.
{"title":"Estimation for advanced technology engines","authors":"F. Farrar, G. Michael","doi":"10.1109/CDC.1978.267948","DOIUrl":"https://doi.org/10.1109/CDC.1978.267948","url":null,"abstract":"An estimation algorithm for nonlinear transient operation of multivariable gas turbine engines was developed and evaluated. Kalman methodology and model-mismatch compensation procedures were employed in defining the filtering logic. The estimation algorithm was evaluated by application to noise-corrupted measurement data generated by a nonlinear digital dynamic F100/F401 engine simulation. Estimation of unmeasurable as well as measurable key engine variables from (1) nominalengine data, (2) degraded-engine data, and (3) engine data with off-nominal noise statistics was evaluated. Results obtained indicate that the nonlinear estimation algorithm provides a viable approach to estimating key engine variables under realistic operating conditions.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"77 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":"126253594","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 study the sinusoidally forced vibrations of a buckled beam. Experimental work indicates that the beam's response is 'chaotic', being a nonperiodic motion which contains appreciable energy at all frequencies. The governing nonlinear partial differential equation is shown to generate a dynamical system on a suitable function space and, since the excitation is periodic, a global Poincaré map, P¿, can be defined and the problem recast as one involving bifurcations of this map. We study the behavior as physical parameters such as force amplitude, ¿, are varied. We argue that much of the behavior can be captured by a single degree of freedom nonlinear oscillator, the Poincaré map of which is a diffeomorphism of the plane, and we indicate the importance of homoclinic orbits arising in global bifurcations of this map.
{"title":"Global bifurcations and chaos in the forced oscillations of buckled structures","authors":"P. Holmes","doi":"10.1109/CDC.1978.267916","DOIUrl":"https://doi.org/10.1109/CDC.1978.267916","url":null,"abstract":"We study the sinusoidally forced vibrations of a buckled beam. Experimental work indicates that the beam's response is 'chaotic', being a nonperiodic motion which contains appreciable energy at all frequencies. The governing nonlinear partial differential equation is shown to generate a dynamical system on a suitable function space and, since the excitation is periodic, a global Poincaré map, P¿, can be defined and the problem recast as one involving bifurcations of this map. We study the behavior as physical parameters such as force amplitude, ¿, are varied. We argue that much of the behavior can be captured by a single degree of freedom nonlinear oscillator, the Poincaré map of which is a diffeomorphism of the plane, and we indicate the importance of homoclinic orbits arising in global bifurcations of this map.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"190 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":"126388513","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 present research has sought to expand our understanding of human information processing and control behavior in target tracking tasks. Specifically, it has focused on the problem of quantifying the human's "internal" model that characterizes his perception of short-term target motion, and on the development of con-commitant adaptive schemes for generating estimates of target velocity and acceleration using these models. A combined experimental and analytic program has studied simulated target tracking performance as modified by short periods (~ 1 sec) of target blanking. The blankings occur at pseudo-random times during a flyby. During the blanking period, human operator performance is governed almost entirely by his internal model representation of the target's motion. Ensemble data from blanking experiments has been used to suitably refine the Optimal Control manual tracking model, including the target submodel.
{"title":"Adaptive estimation schemes for minimizing uncertainty in manual control tasks","authors":"P. Rao, D. Kleinman, A. Ephrath","doi":"10.1109/CDC.1978.268134","DOIUrl":"https://doi.org/10.1109/CDC.1978.268134","url":null,"abstract":"The present research has sought to expand our understanding of human information processing and control behavior in target tracking tasks. Specifically, it has focused on the problem of quantifying the human's \"internal\" model that characterizes his perception of short-term target motion, and on the development of con-commitant adaptive schemes for generating estimates of target velocity and acceleration using these models. A combined experimental and analytic program has studied simulated target tracking performance as modified by short periods (~ 1 sec) of target blanking. The blankings occur at pseudo-random times during a flyby. During the blanking period, human operator performance is governed almost entirely by his internal model representation of the target's motion. Ensemble data from blanking experiments has been used to suitably refine the Optimal Control manual tracking model, including the target submodel.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"51 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":"121603292","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}
Computer realizations for the optimal nonlinear phase estimator are discussed, with emphasis on parallel computer architectures. Implementation of the nonlinear filter on various computer architectures, including the CDC6600/ 7600, CDC STAR-100, Illiac IV, the CRAY-1, and the Floating Point Systems AP120B is reviewed. Implications concerning the ideal computer architecture for nonlinear filter realization are discussed.
{"title":"Computing frontiers in nonlinear filtering","authors":"R. Bucy, K. Senne","doi":"10.1109/CDC.1978.267930","DOIUrl":"https://doi.org/10.1109/CDC.1978.267930","url":null,"abstract":"Computer realizations for the optimal nonlinear phase estimator are discussed, with emphasis on parallel computer architectures. Implementation of the nonlinear filter on various computer architectures, including the CDC6600/ 7600, CDC STAR-100, Illiac IV, the CRAY-1, and the Floating Point Systems AP120B is reviewed. Implications concerning the ideal computer architecture for nonlinear filter realization are discussed.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"125 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":"123058092","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 specific objective of this paper is to develop direct digital control strategies for an ammonia reactor using quadratic regulator theory and compare the performance of the resultant control system with that under conventional PID regulators. The controller design studies are based on a ninth order state-space model obtained from the exact nonlinear distributed model using linearization and lumping approximations. The evaluation of these controllers with reference to their disturbance rejection capabilities and transient response characteristics, is carried out using hybrid computer simulation.
{"title":"Discrete control algorithms for a tubular ammonia reactor","authors":"L. Patnaik, N. Viswanadham, I. Sarma","doi":"10.1109/CDC.1978.268050","DOIUrl":"https://doi.org/10.1109/CDC.1978.268050","url":null,"abstract":"The specific objective of this paper is to develop direct digital control strategies for an ammonia reactor using quadratic regulator theory and compare the performance of the resultant control system with that under conventional PID regulators. The controller design studies are based on a ninth order state-space model obtained from the exact nonlinear distributed model using linearization and lumping approximations. The evaluation of these controllers with reference to their disturbance rejection capabilities and transient response characteristics, is carried out using hybrid computer simulation.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"2 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":"114238917","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 are often faced With the problem of estimating the number of parameters, as well as their values, for a model that will fit a given set of observations. When a family of models includes (or is assumed to include) the true system, the consistency of the estimated model has, for example, been studied recently by using the maximum entropy criterion as a measure of fit. However, to establish this test, stationarity and the knowledge of the p. d. f. for the observed data are required. In this paper we define a criterion of measure of fit which enables us to treat the non-stationary case without knowledge of the p.d.f. of the data or without specifying the p. d. f. of model outputs. Based on this criterion, we study the order determination problem for the linear time-varying AR models.
{"title":"The order determination for linear time-varying AR models","authors":"F. Nakajima, F. Kozin","doi":"10.1109/CDC.1978.268072","DOIUrl":"https://doi.org/10.1109/CDC.1978.268072","url":null,"abstract":"We are often faced With the problem of estimating the number of parameters, as well as their values, for a model that will fit a given set of observations. When a family of models includes (or is assumed to include) the true system, the consistency of the estimated model has, for example, been studied recently by using the maximum entropy criterion as a measure of fit. However, to establish this test, stationarity and the knowledge of the p. d. f. for the observed data are required. In this paper we define a criterion of measure of fit which enables us to treat the non-stationary case without knowledge of the p.d.f. of the data or without specifying the p. d. f. of model outputs. Based on this criterion, we study the order determination problem for the linear time-varying AR models.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"30 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":"116084287","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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