We discuss the nature of the equivalence of (1) the nonsingularity of the asymptotic information matrix of a given process, i.e. the limit of the Hessian matrix (with respect to the parameter ¿) of the log likelihood function and (2) local identifiability of the parameter ¿. Second order local identifiability is given a structural definition related to those of [3], [5], [6]. The proof of the main equivalence theorem differs from that of Rothenberg [6] in that it does not involve differential equations.
{"title":"Necessary and sufficient conditions for local second order identifiability","authors":"R. Goodrich, Peter E. Caines","doi":"10.1109/CDC.1978.267931","DOIUrl":"https://doi.org/10.1109/CDC.1978.267931","url":null,"abstract":"We discuss the nature of the equivalence of (1) the nonsingularity of the asymptotic information matrix of a given process, i.e. the limit of the Hessian matrix (with respect to the parameter ¿) of the log likelihood function and (2) local identifiability of the parameter ¿. Second order local identifiability is given a structural definition related to those of [3], [5], [6]. The proof of the main equivalence theorem differs from that of Rothenberg [6] in that it does not involve differential equations.","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":"128489557","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 investigate the controllability problem and the observability problem for a distributed parameter system of parabolic type. For a distributed parameter system of parabolic type, both problems are not well-posed in general. A well-posed approximation method which regularizes the problems is presented. The method is analyzed under the assumption that the system is controllable at time T and observable at time T.
{"title":"Regularization of controllability problems and observability problems for distributed parameter systems of parabolic type","authors":"T. Kobayashi","doi":"10.1109/CDC.1978.267940","DOIUrl":"https://doi.org/10.1109/CDC.1978.267940","url":null,"abstract":"The purpose of this paper is to investigate the controllability problem and the observability problem for a distributed parameter system of parabolic type. For a distributed parameter system of parabolic type, both problems are not well-posed in general. A well-posed approximation method which regularizes the problems is presented. The method is analyzed under the assumption that the system is controllable at time T and observable at time T.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"5 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":"114236624","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}
Discrete-time dynamical systems defined on input, state, and output sets which do not admit binary operations have recently been studied with regard to the regulator problem of feedback control theory. If it is assumed that the regulation condition places no constraint on control states, that the exosystem can be observed from the controller, that all exosystem states are effective in generating output requests, and that feedback is inoperative when the regulation condition is satisfied, then it is known that the controller contains an algebraic model of the exosystem, provided that a suitable exosubset of regulator states exists to represent the action of the exosystem within the context of the overall regulator. This paper examines the possibility of directly constructing the exosubset from elementary dynamical descriptions of plant, exosystem, and controller, with the aid of quotient set representation of exosystem states. The construction indicates that exosubset existence is a non-trivial question, and brings out the importance of product versus coproduct state descriptions for the regulator.
{"title":"On exosubsets and internal models","authors":"M. Sain","doi":"10.1109/CDC.1978.268095","DOIUrl":"https://doi.org/10.1109/CDC.1978.268095","url":null,"abstract":"Discrete-time dynamical systems defined on input, state, and output sets which do not admit binary operations have recently been studied with regard to the regulator problem of feedback control theory. If it is assumed that the regulation condition places no constraint on control states, that the exosystem can be observed from the controller, that all exosystem states are effective in generating output requests, and that feedback is inoperative when the regulation condition is satisfied, then it is known that the controller contains an algebraic model of the exosystem, provided that a suitable exosubset of regulator states exists to represent the action of the exosystem within the context of the overall regulator. This paper examines the possibility of directly constructing the exosubset from elementary dynamical descriptions of plant, exosystem, and controller, with the aid of quotient set representation of exosystem states. The construction indicates that exosubset existence is a non-trivial question, and brings out the importance of product versus coproduct state descriptions for the regulator.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"87 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":"127411447","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 nonlinear optimal control law is derived for a ramjet powered missile using singular perturbation theory. The singular perturbation analysis, together with multiple time scaling converts the solution of the two point boundary value problem into the extremization of nonlinear algebraic equations. The derivation of the control law takes into account the various operational constraints and an algorithm is outlined describing the various steps in the computation of the control law. The control law has a feed-back form and is a good candidate for real-time implementation.
{"title":"Trajectory optimization of a Ramjet-powered missile using singular perturbation methods","authors":"B. Sridhar","doi":"10.1109/CDC.1978.267954","DOIUrl":"https://doi.org/10.1109/CDC.1978.267954","url":null,"abstract":"A nonlinear optimal control law is derived for a ramjet powered missile using singular perturbation theory. The singular perturbation analysis, together with multiple time scaling converts the solution of the two point boundary value problem into the extremization of nonlinear algebraic equations. The derivation of the control law takes into account the various operational constraints and an algorithm is outlined describing the various steps in the computation of the control law. The control law has a feed-back form and is a good candidate for real-time implementation.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"9 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":"125600793","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 control technology for interior building environments has evolved through heuristic techniques. Only in the past 15 years has modeling and mathematical analysis been applied successfully in the design of controllers. Coincident with the analytical tool development was the development of modern control theory (adaptive and optimal control theory) and the emergence of inexpensive but powerful microcomputers. The combination of these ingredients will reset in better controllers and control systems, but this will not occur until several hurdles are overcome. This paper outlines these issues and suggests areas for future work.
{"title":"Design considerations for adaptive control of buildings","authors":"J. Tobias","doi":"10.1109/CDC.1978.267922","DOIUrl":"https://doi.org/10.1109/CDC.1978.267922","url":null,"abstract":"The control technology for interior building environments has evolved through heuristic techniques. Only in the past 15 years has modeling and mathematical analysis been applied successfully in the design of controllers. Coincident with the analytical tool development was the development of modern control theory (adaptive and optimal control theory) and the emergence of inexpensive but powerful microcomputers. The combination of these ingredients will reset in better controllers and control systems, but this will not occur until several hurdles are overcome. This paper outlines these issues and suggests areas for future work.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"72 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":"127133772","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}
Robust methods provide a fresh approach to the problem of treatment of wild observations in filtering and smoothing problems. The robust M-estimates of regression are extended to filtering and fixed lag smoothing employing a pseudodensity of the observations in a maximum likelihood derivation of the filter and fixed lag smoother. These robust methods have been applied to simulated and real tracking data to obtain improved estimstion performance in the presence of wild observations.
{"title":"Application of robust filtering and smoothing to tracking data","authors":"W. Agee, Robert Turner","doi":"10.1109/CDC.1978.267899","DOIUrl":"https://doi.org/10.1109/CDC.1978.267899","url":null,"abstract":"Robust methods provide a fresh approach to the problem of treatment of wild observations in filtering and smoothing problems. The robust M-estimates of regression are extended to filtering and fixed lag smoothing employing a pseudodensity of the observations in a maximum likelihood derivation of the filter and fixed lag smoother. These robust methods have been applied to simulated and real tracking data to obtain improved estimstion performance in the presence of wild observations.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"44 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":"124411748","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 type filter, called a Decision Tree Filter, is developed that promises substantial performance benefits in a wide variety of applications. For gun fire control against a spectrum of maneuvering and non-maneuvering targets, a relatively simple Decision Tree Filter showed a performance improvement of 2 to 1 in hit probability and a 4 to 1 reduction in computation when compared to a Kalman filter.
{"title":"Decision tree filters - a nonlinear approach to filtering for fire control applications","authors":"F. Nesline, P. Zarchan","doi":"10.1109/CDC.1978.267902","DOIUrl":"https://doi.org/10.1109/CDC.1978.267902","url":null,"abstract":"A new type filter, called a Decision Tree Filter, is developed that promises substantial performance benefits in a wide variety of applications. For gun fire control against a spectrum of maneuvering and non-maneuvering targets, a relatively simple Decision Tree Filter showed a performance improvement of 2 to 1 in hit probability and a 4 to 1 reduction in computation when compared to a Kalman filter.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"25 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":"121593841","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 method for studying the chemical control of breathing in man is described which uses a Pseudo Random Binary Sequence (PRBS) inhalation of CO2. Impulse responses of endtidal CO2, minute ventilation, tidal volume, inspiratory and expiratory durations were estimated by cross-correlating outputs with the PRBS input. Data collected in seven normal men suggest that impulse responses may be useful in isolating the contribution of peripheral chemoreceptors. Estimates of peripheral sensitivity to CO2 based on PRBS show significantly smaller intrasubject variability than those based on sinusoidal test inputs. Application of a Nelder-Mead parameter estimation procedure demonstrated that a third order model is sufficient to explain impulse response dynamics.
{"title":"Application of pseudo random binary sequence input to identification of respiratory control dynamics","authors":"S. Sohrab, P. Reischl, F. Grodins, S. Yamashiro","doi":"10.1109/CDC.1978.268130","DOIUrl":"https://doi.org/10.1109/CDC.1978.268130","url":null,"abstract":"A new method for studying the chemical control of breathing in man is described which uses a Pseudo Random Binary Sequence (PRBS) inhalation of CO2. Impulse responses of endtidal CO2, minute ventilation, tidal volume, inspiratory and expiratory durations were estimated by cross-correlating outputs with the PRBS input. Data collected in seven normal men suggest that impulse responses may be useful in isolating the contribution of peripheral chemoreceptors. Estimates of peripheral sensitivity to CO2 based on PRBS show significantly smaller intrasubject variability than those based on sinusoidal test inputs. Application of a Nelder-Mead parameter estimation procedure demonstrated that a third order model is sufficient to explain impulse response dynamics.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"102 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":"121736197","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}
Linear closed-loop Stackelberg strategies for systems with slow and fast modes are considered. The asymptotic behavior of the solution is studied and used to derive near optimal strategies which does not require the knowledge of the small singular perturbation parameter.
{"title":"Closed-loop stackelberg strategies for singularly perturbed linear quadratic problems","authors":"H. Khalil, J. Medanic","doi":"10.1109/CDC.1978.268105","DOIUrl":"https://doi.org/10.1109/CDC.1978.268105","url":null,"abstract":"Linear closed-loop Stackelberg strategies for systems with slow and fast modes are considered. The asymptotic behavior of the solution is studied and used to derive near optimal strategies which does not require the knowledge of the small singular perturbation parameter.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"70 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":"125612873","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}
Linear q-dimensional (q-D) systems and externally-bilinear q-D systems are investigated. Externally-bilinear q-D systems arise in the study of multidimensional signal processors containing signal multipliers. For example, it is shown that the cross-correlation between two locally-stationary 2-D signals can be computed using an externally-bilinear 2-D system. A class Lq of linear q-D systems and a class Bq of externally-bilinear q-D systems are defined and then a 1-1 and onto correspondence is constructed between Bq and L2q for each fixed positive integer q. Via this correspondence, it is shown that results on stability and recursive realizations of a linear 2q-D system can be carried over to the corresponding externally-bilinear q-D system.
{"title":"Linear and externally-bilinear multidimensional systems","authors":"E. Kamen, F. Lewis","doi":"10.1109/CDC.1978.268009","DOIUrl":"https://doi.org/10.1109/CDC.1978.268009","url":null,"abstract":"Linear q-dimensional (q-D) systems and externally-bilinear q-D systems are investigated. Externally-bilinear q-D systems arise in the study of multidimensional signal processors containing signal multipliers. For example, it is shown that the cross-correlation between two locally-stationary 2-D signals can be computed using an externally-bilinear 2-D system. A class Lq of linear q-D systems and a class Bq of externally-bilinear q-D systems are defined and then a 1-1 and onto correspondence is constructed between Bq and L2q for each fixed positive integer q. Via this correspondence, it is shown that results on stability and recursive realizations of a linear 2q-D system can be carried over to the corresponding externally-bilinear q-D system.","PeriodicalId":375119,"journal":{"name":"1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes","volume":"26 4 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":"116520177","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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