The realization theory of stationary linear analytic systems is investigated by means of a class of invariants known as the exceptional points. Concepts like Carleman linearization, multivariable Laplace transform, and semi-lattice are discussed to prepare for the main theorem which characterizes the degree of minimal realization in terms of the minimal generators of the exceptional points. The results here lay the foundation for further work in the realization problem of stationary linear analytic systems. These ideas also have potential application to nonlinear identification and parameter estimation problems.
{"title":"Nonlinear system invariants with applications to identification","authors":"W. Wong","doi":"10.1109/CDC.1980.271879","DOIUrl":"https://doi.org/10.1109/CDC.1980.271879","url":null,"abstract":"The realization theory of stationary linear analytic systems is investigated by means of a class of invariants known as the exceptional points. Concepts like Carleman linearization, multivariable Laplace transform, and semi-lattice are discussed to prepare for the main theorem which characterizes the degree of minimal realization in terms of the minimal generators of the exceptional points. The results here lay the foundation for further work in the realization problem of stationary linear analytic systems. These ideas also have potential application to nonlinear identification and parameter estimation problems.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126120427","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}
It is perhaps possible to distinguish between two main approaches to problem of model reduction [1]. The first uses open-loop criteria (not necessarily optimal) for producing low-order models [2,3], while in the second, criteria which are optimal in some sense are employed. The latter approach can too be divided into two subgroups. In the first, error criteria are used to optimally approximate the open-loop behaviour of the original system [4,5]. In the second, either a given low-order model is optimally controlled and the resultant controller is used to (sub-optimally) control the original system [6]; or, a low-order model, whose dimension equals the number of outputs of the original system, is designed such that the error between the optimally controlled model and original system is minimized [7]. A completely different approach is considered in this paper. For a desired model order, the model is designed such that, controlling it by a constant state-variable feedback and using the resulting input to control the original system, the performance index of the original system, is minimized. Therefore, we are not contrained a priori by the model order (as in [7] for example, where a single-output original system necessarily results in a first order model). Furthermore, the performance index of the original system itself is being minimized under the constraint of the desired order model. Notice, however, that the proposed solution could not be considered open-loop in some sense and thus, could not be used for designing low-order models for unstable systems.
{"title":"Design of reduced-order linear quadratic optimal regulators","authors":"G. Langholz, U. Shaked","doi":"10.1109/CDC.1980.271806","DOIUrl":"https://doi.org/10.1109/CDC.1980.271806","url":null,"abstract":"It is perhaps possible to distinguish between two main approaches to problem of model reduction [1]. The first uses open-loop criteria (not necessarily optimal) for producing low-order models [2,3], while in the second, criteria which are optimal in some sense are employed. The latter approach can too be divided into two subgroups. In the first, error criteria are used to optimally approximate the open-loop behaviour of the original system [4,5]. In the second, either a given low-order model is optimally controlled and the resultant controller is used to (sub-optimally) control the original system [6]; or, a low-order model, whose dimension equals the number of outputs of the original system, is designed such that the error between the optimally controlled model and original system is minimized [7]. A completely different approach is considered in this paper. For a desired model order, the model is designed such that, controlling it by a constant state-variable feedback and using the resulting input to control the original system, the performance index of the original system, is minimized. Therefore, we are not contrained a priori by the model order (as in [7] for example, where a single-output original system necessarily results in a first order model). Furthermore, the performance index of the original system itself is being minimized under the constraint of the desired order model. Notice, however, that the proposed solution could not be considered open-loop in some sense and thus, could not be used for designing low-order models for unstable systems.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124744314","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}
Previously suggested model reference adaptive schemes are analyzed with respect to convergence in a stochastic environment. The role of different filtering polynomials is clarified and it is pointed out which algorithms seem favorable from the convergence point of view.
{"title":"Stochastic convergence analysis of model reference adaptive controllers","authors":"B. Egardt","doi":"10.1109/CDC.1980.271979","DOIUrl":"https://doi.org/10.1109/CDC.1980.271979","url":null,"abstract":"Previously suggested model reference adaptive schemes are analyzed with respect to convergence in a stochastic environment. The role of different filtering polynomials is clarified and it is pointed out which algorithms seem favorable from the convergence point of view.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125022996","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}
Frequency domain methods are used to develop necessary and sufficient conditions for the existence of an internal model precompensator that provides internal stability and output regulation when specified structural perturbations occur in plant parameters. It is shown that if the exogenous signal modes are invariant under parameter perturbations and if nominal plant transmission zeros do not coincide with these modes, then a suitable precompensator exists.
{"title":"On internal models for specified plant parameter variations","authors":"R. Cavin, J. McGrath","doi":"10.1109/CDC.1980.271930","DOIUrl":"https://doi.org/10.1109/CDC.1980.271930","url":null,"abstract":"Frequency domain methods are used to develop necessary and sufficient conditions for the existence of an internal model precompensator that provides internal stability and output regulation when specified structural perturbations occur in plant parameters. It is shown that if the exogenous signal modes are invariant under parameter perturbations and if nominal plant transmission zeros do not coincide with these modes, then a suitable precompensator exists.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"247 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128588595","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, it is shown that there exists a linear interconnected system whose optimal control for a quadratic performance index can be actualized by means of decentralized control.
本文证明了存在一个线性互联系统，其对二次型性能指标的最优控制可以通过分散控制来实现。
{"title":"On decentrally optimizable interconnected systems","authors":"K. Yasuda, T. Hikata, K. Hirai","doi":"10.1109/CDC.1980.271854","DOIUrl":"https://doi.org/10.1109/CDC.1980.271854","url":null,"abstract":"In this paper, it is shown that there exists a linear interconnected system whose optimal control for a quadratic performance index can be actualized by means of decentralized control.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127215677","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}
By way of the solution to a long standing problem in production lines, we illustrate how to apply a well known control theoretic technique to discrete event dynamical systems.
{"title":"Computing co-state variables for discrete event systems","authors":"Y. Ho, C. Cassandras","doi":"10.1109/CDC.1980.271891","DOIUrl":"https://doi.org/10.1109/CDC.1980.271891","url":null,"abstract":"By way of the solution to a long standing problem in production lines, we illustrate how to apply a well known control theoretic technique to discrete event dynamical systems.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129060022","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 algorithm is presented for optimal resource allocation in large-scale systems. The approach is based on a two-step non-iterative decomposition technique: subsystem optimization is performed locally and the results are combined to provide a global optimum. The unique feature of the approach is that it performs the optimization in a completely decentralized manner, without a central coordinator.
{"title":"A decentralized strategy for resource allocation","authors":"B. Friedlander","doi":"10.1109/CDC.1980.271850","DOIUrl":"https://doi.org/10.1109/CDC.1980.271850","url":null,"abstract":"An algorithm is presented for optimal resource allocation in large-scale systems. The approach is based on a two-step non-iterative decomposition technique: subsystem optimization is performed locally and the results are combined to provide a global optimum. The unique feature of the approach is that it performs the optimization in a completely decentralized manner, without a central coordinator.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"48 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132772599","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}
After a short description of a Disturbance Analysis System for nuclear plant based on real time dynamic modelling and simulation, a scheme for generating aggregated reduced models of high order systems is presented. This method allows the choice of dominant dynamic modes and its efficiency is illustrated for the case of a 29th order nuclear plant model.
{"title":"Application of aggregation techniques for model order reduction of nuclear plants for operator guidance systems","authors":"G. Zwingelstein","doi":"10.1109/CDC.1980.272032","DOIUrl":"https://doi.org/10.1109/CDC.1980.272032","url":null,"abstract":"After a short description of a Disturbance Analysis System for nuclear plant based on real time dynamic modelling and simulation, a scheme for generating aggregated reduced models of high order systems is presented. This method allows the choice of dominant dynamic modes and its efficiency is illustrated for the case of a 29th order nuclear plant model.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130957833","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}
Identification and control when plant output is corrupted with disturbance and when plant parameters vary with time are considered. It is shown how the error model can be described by a non-homogeneous differential equation. Subject to bounded disturbance and parameter variation and sufficiently rich input the parameter error vector remains bounded and explicit bounds are derived. For inputs that are not sufficiently rich some sufficient conditions for stability and some examples of instability are given. Finally, a non-linear adaptation algorithm is presented for the control problem that insures the boundedness of the parameter error vector and all signals in the system.
{"title":"Bounded error adaptive control","authors":"K. Narendra, B. Peterson","doi":"10.1109/CDC.1980.271867","DOIUrl":"https://doi.org/10.1109/CDC.1980.271867","url":null,"abstract":"Identification and control when plant output is corrupted with disturbance and when plant parameters vary with time are considered. It is shown how the error model can be described by a non-homogeneous differential equation. Subject to bounded disturbance and parameter variation and sufficiently rich input the parameter error vector remains bounded and explicit bounds are derived. For inputs that are not sufficiently rich some sufficient conditions for stability and some examples of instability are given. Finally, a non-linear adaptation algorithm is presented for the control problem that insures the boundedness of the parameter error vector and all signals in the system.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129237712","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 decentralized controller for a mechanical analog of human biceps/triceps control of forearm movement has been designed and tested. The analysis, design, and implementation of this system should be of interest not only as a control application, but also because it brings out some important features which are generic to the positioning of tendon arms of all types. Most particularly, a crude but effective form of load compensation is shown to be possible without (the equivalent of) proprioceptive feedback; this supports recent physiological findings which suggest that large arm movements in primates may be predominantly open-loop processes of final position control.
{"title":"Final-position of a single degree-of-freedom tendon arm","authors":"P. H. Riemenschneider, T. Johnson, K. Chen","doi":"10.1109/CDC.1980.271966","DOIUrl":"https://doi.org/10.1109/CDC.1980.271966","url":null,"abstract":"A decentralized controller for a mechanical analog of human biceps/triceps control of forearm movement has been designed and tested. The analysis, design, and implementation of this system should be of interest not only as a control application, but also because it brings out some important features which are generic to the positioning of tendon arms of all types. Most particularly, a crude but effective form of load compensation is shown to be possible without (the equivalent of) proprioceptive feedback; this supports recent physiological findings which suggest that large arm movements in primates may be predominantly open-loop processes of final position control.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121058817","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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