A design procedure for minimal-order observers for linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state are given.
{"title":"A frequency domain approach to minimal-order observer design for several linear functions of the state","authors":"D. Russell, T. Bullock","doi":"10.1109/CDC.1975.270618","DOIUrl":"https://doi.org/10.1109/CDC.1975.270618","url":null,"abstract":"A design procedure for minimal-order observers for linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state 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":"129987203","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 autopilot design discussed here is based on the algebraic inversion of the system equations A natural manifold for this procedure is proposed and discussed.
本文讨论的自动驾驶仪设计是基于系统方程的代数反演，提出并讨论了该过程的自然流形。
{"title":"An application of differential geometry to the analysis of a nonlinear autopilot design","authors":"C. Martin, G. Meyer","doi":"10.1109/CDC.1975.270729","DOIUrl":"https://doi.org/10.1109/CDC.1975.270729","url":null,"abstract":"The autopilot design discussed here is based on the algebraic inversion of the system equations A natural manifold for this procedure is proposed and discussed.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"16 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":"116220801","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 the comparison of two adaptive methods based upon sensitivity equations for use in the surveillance and diagnosis of an experimental nuclear reactor. The surveillance and diagnosis are obtained by a real-time comparison of reference parameters and the actual parameters given by the adaptive algorithm. The first algorithm uses an on-line, steepest descent method. Results obtained with this algorithm using experimental data from a reactor are given using two different criteria. The second algorithm uses both sensitivity equations and a recursive least squares method. An example is given using the experimental model of the same reactor. Both algorithms described in this paper are easily implementable on a mini computer and are not sensitive to a priori knowledge of the statistical properties of the noise. These algorithms are also suitable for the surveillance of nonlinear processes.
{"title":"Comparison of two adaptive identification methods for monitoring and diagnosis of an experimental nuclear reactor","authors":"G. Zwingelstein, P. Blanc","doi":"10.1109/CDC.1975.270727","DOIUrl":"https://doi.org/10.1109/CDC.1975.270727","url":null,"abstract":"This paper deals with the comparison of two adaptive methods based upon sensitivity equations for use in the surveillance and diagnosis of an experimental nuclear reactor. The surveillance and diagnosis are obtained by a real-time comparison of reference parameters and the actual parameters given by the adaptive algorithm. The first algorithm uses an on-line, steepest descent method. Results obtained with this algorithm using experimental data from a reactor are given using two different criteria. The second algorithm uses both sensitivity equations and a recursive least squares method. An example is given using the experimental model of the same reactor. Both algorithms described in this paper are easily implementable on a mini computer and are not sensitive to a priori knowledge of the statistical properties of the noise. These algorithms are also suitable for the surveillance of nonlinear processes.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"14 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":"116223597","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 two dimensional discrete stochastic model for representing images is developed. This representation leads to a "hybrid" algorithm for spatial filtering of images. A "hybrid" algorithm is one where the filter equations are solved in a transform domain in one direction and in spatial domain in the other. Application of the model to linear filtering of images leads to scalar recursive filtering equations requiring only O(N2log2N) computations for N×N images. Examples on a 255 × 255 image are given.
{"title":"Semicausal recursive filtering of images","authors":"Anilk . Jain","doi":"10.1109/CDC.1975.270651","DOIUrl":"https://doi.org/10.1109/CDC.1975.270651","url":null,"abstract":"A two dimensional discrete stochastic model for representing images is developed. This representation leads to a \"hybrid\" algorithm for spatial filtering of images. A \"hybrid\" algorithm is one where the filter equations are solved in a transform domain in one direction and in spatial domain in the other. Application of the model to linear filtering of images leads to scalar recursive filtering equations requiring only O(N2log2N) computations for N×N images. Examples on a 255 × 255 image are given.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"25 3 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":"116819642","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}
Motivated by the complexity and the large quantity of on-line operations required for nonlinear filtering problems, observers for nonlinear stochastic systems are constructed based on a Liapunov-like method. Sufficient conditions on the structure of a nonlinear stochastic system for the existence of an exponentially bounded observer are given. These conditions can be applied off-line. The stabilization of unstable nonlinear stochastic systems using observer feedback are investigated. Sufficient conditions to stabilize cascaded control and observer in a feedback arrangement are given.
{"title":"Observers for nonlinear stochastic systems","authors":"T. Tarn, Y. Rasis","doi":"10.1109/CDC.1975.270610","DOIUrl":"https://doi.org/10.1109/CDC.1975.270610","url":null,"abstract":"Motivated by the complexity and the large quantity of on-line operations required for nonlinear filtering problems, observers for nonlinear stochastic systems are constructed based on a Liapunov-like method. Sufficient conditions on the structure of a nonlinear stochastic system for the existence of an exponentially bounded observer are given. These conditions can be applied off-line. The stabilization of unstable nonlinear stochastic systems using observer feedback are investigated. Sufficient conditions to stabilize cascaded control and observer in a feedback arrangement are given.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"35 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":"134223934","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 augmented error signal concept, recently introduced, can be useful in designing model reference adaptive systems for plants with inputs which are subject to hard saturation. Liapunov's Direct Method is used as the basis for these designs. Figure 1 shows the configuration for the types of systems considered. The adaptive control acts to null the augmented error, and, in the process, also assures that the true error between plant and model approaches zero.
{"title":"Adaptive control for systems with hard saturation","authors":"R. Monopoli","doi":"10.1109/CDC.1975.270621","DOIUrl":"https://doi.org/10.1109/CDC.1975.270621","url":null,"abstract":"The augmented error signal concept, recently introduced, can be useful in designing model reference adaptive systems for plants with inputs which are subject to hard saturation. Liapunov's Direct Method is used as the basis for these designs. Figure 1 shows the configuration for the types of systems considered. The adaptive control acts to null the augmented error, and, in the process, also assures that the true error between plant and model approaches zero.","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":"132940321","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}
In this paper, the problem of obtaining a pair of relatively prime polynomial matrices from two given polynomial matrices is considered. A method to check relative primeness, in the form of a rank condition on a constant matrix, as well as an algorithm to obtain relatively polynomial matrices is developed.
{"title":"Relatively prime polynomial matrices: Algorithms","authors":"E. Emre, L. Silverman","doi":"10.1109/CDC.1975.270676","DOIUrl":"https://doi.org/10.1109/CDC.1975.270676","url":null,"abstract":"In this paper, the problem of obtaining a pair of relatively prime polynomial matrices from two given polynomial matrices is considered. A method to check relative primeness, in the form of a rank condition on a constant matrix, as well as an algorithm to obtain relatively polynomial matrices is developed.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"121 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":"134162802","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 consider stochastic optimal control problems of Mayer type with dynamics in the form of a system of ordinary differential equations perturbed by a countable state Markov process, and we prove the existence of an optimal control in the class of non-anticipative functions. The proof takes the same approach as the "direct" method of the calculus of variations, used extensively in deterministic problems, but substitutes probabilistic concepts where necessary.
{"title":"Existence of an optimal control for systems with jump Markov disturbances","authors":"Robert M. Goor","doi":"10.1137/0314057","DOIUrl":"https://doi.org/10.1137/0314057","url":null,"abstract":"We consider stochastic optimal control problems of Mayer type with dynamics in the form of a system of ordinary differential equations perturbed by a countable state Markov process, and we prove the existence of an optimal control in the class of non-anticipative functions. The proof takes the same approach as the \"direct\" method of the calculus of variations, used extensively in deterministic problems, but substitutes probabilistic concepts where necessary.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"40 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":"132394649","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}
In a radically new approach to linear estimation, Lainiotis [9-11] obtained fundamentally new discrete filtering and smoothing algorithms in a "partitioned" or decomposed form. The partitioned algorithms were shown to have several theoretically interesting and computationally attractive properties. In this paper, a companion to part I on continuous models [13], the fundamental nature of the partitioned algorithms is demonstrated by showing that the discrete partitioned algorithms serve as the basis of a unifying approach to discrete linear filtering and smoothing. Specifically, generalized discrete partitioned algorithms are presented that are theoretically interesting, computationally attractive, and all encompassing. The all encompassing nature of the generalized partitioned algorithms is demonstrated by showing that they contain as special cases all previous major filtering and smoothing algorithms. More importantly, they yield important generalizations, of past well-known algorithms, as well as whole families of such algorithms.
{"title":"A unifying approach to linear estimation via the partitioned algorithms, II: Discrete models","authors":"D. Lainiotis, K. Govindaraj","doi":"10.1109/CDC.1975.270587","DOIUrl":"https://doi.org/10.1109/CDC.1975.270587","url":null,"abstract":"In a radically new approach to linear estimation, Lainiotis [9-11] obtained fundamentally new discrete filtering and smoothing algorithms in a \"partitioned\" or decomposed form. The partitioned algorithms were shown to have several theoretically interesting and computationally attractive properties. In this paper, a companion to part I on continuous models [13], the fundamental nature of the partitioned algorithms is demonstrated by showing that the discrete partitioned algorithms serve as the basis of a unifying approach to discrete linear filtering and smoothing. Specifically, generalized discrete partitioned algorithms are presented that are theoretically interesting, computationally attractive, and all encompassing. The all encompassing nature of the generalized partitioned algorithms is demonstrated by showing that they contain as special cases all previous major filtering and smoothing algorithms. More importantly, they yield important generalizations, of past well-known algorithms, as well as whole families of such algorithms.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"41 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":"116605426","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 formulate an Optimal control problem which is useful for computing management schemes for ecological systems. Three basic constraints on the problem are considered. The optimal control should maximize a performance measure which reflects a maximization of a selected sum of time-weighted averages of state variables with a sufficient penalty on control. The control should be a positive time function corresponding to an input of material to the system. Finally, the control should be T-periodic in order to be compatible with the cyclic behavior of the ecosystem. Conditions are derived which provide for the existence of controls applicable to ecological problems.
{"title":"Periodic optimal control of ecological systems","authors":"R. Mulholland, W. Emanuel","doi":"10.1109/CDC.1975.270666","DOIUrl":"https://doi.org/10.1109/CDC.1975.270666","url":null,"abstract":"The purpose of this paper is to formulate an Optimal control problem which is useful for computing management schemes for ecological systems. Three basic constraints on the problem are considered. The optimal control should maximize a performance measure which reflects a maximization of a selected sum of time-weighted averages of state variables with a sufficient penalty on control. The control should be a positive time function corresponding to an input of material to the system. Finally, the control should be T-periodic in order to be compatible with the cyclic behavior of the ecosystem. Conditions are derived which provide for the existence of controls applicable to ecological problems.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"51 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":"122038469","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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