This paper presents some explicit results on solution, stability, and transformation of a fairly broad class of linear time-varying systems. It is shown that for this special class of linear time-varying systems, the solution can be represented as a product of two matrix exponential functions and the system stability can be determined directly from eigenvalues of two constant matrices. Furthermore the system can be reduced to a linear time-invariant system by successive applications of an algebraic transformation and a t¿¿ transformation. The generalized results given here contain several previously reported results as special Cases.
{"title":"On solution, stability, and transformation of linear time-varying systems","authors":"Min-yen Wu, Isaac Horowitz, J. Dennison","doi":"10.1109/CDC.1975.270710","DOIUrl":"https://doi.org/10.1109/CDC.1975.270710","url":null,"abstract":"This paper presents some explicit results on solution, stability, and transformation of a fairly broad class of linear time-varying systems. It is shown that for this special class of linear time-varying systems, the solution can be represented as a product of two matrix exponential functions and the system stability can be determined directly from eigenvalues of two constant matrices. Furthermore the system can be reduced to a linear time-invariant system by successive applications of an algebraic transformation and a t¿¿ transformation. The generalized results given here contain several previously reported results as special Cases.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"55 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":"114304503","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 geometric relationship between the optimal solutions to the sampled-data and continuous linear quadratic regulator problems is investigated in a Hilbert space framework. It is shown that the optimal sampled-data solution, excluding the response due to the initial condition, is the projection of the optimal continuous solution onto the set of all solutions that satisfy the sampled-data constraint. That is, the optimal sampled-data solution is an optimal approximation to the continuous solution. In fact, it is shown that the sampled-data solution can be obtained by solving a sampled-data tracking problem with the continuous solution as the desired trajectory.
{"title":"On the relation between the sampled-data and the continuous optimal linear regulator problems","authors":"A. Caglayan, N. Halyo","doi":"10.1109/CDC.1975.270603","DOIUrl":"https://doi.org/10.1109/CDC.1975.270603","url":null,"abstract":"In this paper, the geometric relationship between the optimal solutions to the sampled-data and continuous linear quadratic regulator problems is investigated in a Hilbert space framework. It is shown that the optimal sampled-data solution, excluding the response due to the initial condition, is the projection of the optimal continuous solution onto the set of all solutions that satisfy the sampled-data constraint. That is, the optimal sampled-data solution is an optimal approximation to the continuous solution. In fact, it is shown that the sampled-data solution can be obtained by solving a sampled-data tracking problem with the continuous solution as the desired trajectory.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"5 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":"114500437","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 relation of eigenvalue location properties of weakly coupled systems and systems with slow and fast modes in singular perturbation analysis is considered. A "weak interconnection" condition that does not require a set of eigenvalues to be smaller in modulus than another set is introduced. Stability, controllability, sensitivity and optimality are discussed.
{"title":"On the weak interconnection of composite dynamic systems","authors":"U. Ozguner","doi":"10.1109/CDC.1975.270616","DOIUrl":"https://doi.org/10.1109/CDC.1975.270616","url":null,"abstract":"The relation of eigenvalue location properties of weakly coupled systems and systems with slow and fast modes in singular perturbation analysis is considered. A \"weak interconnection\" condition that does not require a set of eigenvalues to be smaller in modulus than another set is introduced. Stability, controllability, sensitivity and optimality are discussed.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"9 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":"122056216","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 treats one aspect of the identification of state-derivative-coupled systems, such as Mx(t) = Ax(t) + Bu(t)+ w(t) where M ¿ I and M is invertible. This equation can also be written as x(t) = F1x(t) + F2u(t) + w(t). We assume that reduced form parameters (F1,F2) are identifiable and develop a sequence of tests for establishing the identifiability of structural parameters (M, A, B) from (F1,F2). The tests are constructive, in that they can not only be used to ascertain the identifiability of (M, A, B); but, if (M, A, B) are not identifiable, can also indicate corrective actions to be taken so that (M, A, B) are identifiable.
本文研究了状态导数耦合系统辨识的一个方面，如Mx(t) = Ax(t) + Bu(t)+ w(t)，其中M和M是可逆的。这个方程也可以写成x(t) = F1x(t) + F2u(t) + w(t)。我们假设简化形式参数(F1,F2)是可识别的，并开发了一系列测试，以从(F1,F2)建立结构参数(M, a, B)的可识别性。这些测试是建设性的，因为它们不仅可以用来确定(M、A、B)的可识别性;但是，如果(M, A, B)不可识别，也可以指出要采取的纠正措施，使(M, A, B)可识别。
{"title":"On the identification of state-derivative-coupled systems","authors":"J. Mendel","doi":"10.1109/CDC.1975.270749","DOIUrl":"https://doi.org/10.1109/CDC.1975.270749","url":null,"abstract":"This paper treats one aspect of the identification of state-derivative-coupled systems, such as Mx(t) = Ax(t) + Bu(t)+ w(t) where M ¿ I and M is invertible. This equation can also be written as x(t) = F1x(t) + F2u(t) + w(t). We assume that reduced form parameters (F1,F2) are identifiable and develop a sequence of tests for establishing the identifiability of structural parameters (M, A, B) from (F1,F2). The tests are constructive, in that they can not only be used to ascertain the identifiability of (M, A, B); but, if (M, A, B) are not identifiable, can also indicate corrective actions to be taken so that (M, A, B) are identifiable.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"55 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":"127040378","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}
There has been a very rapid increase in the size of power systems, and it is still growing. This growth has made the present day systems very big and complex. The complexity is arising especially due to many Interconnections, different types of loads and larger generating units. Also there is uncertainty in load forecasting. With EHV interconnections the disturbances are felt even in geographically distant parts of the system, increasing the severity of the disturbances. These factors make the satisfactory operating of the system a more difficult task. Added to this, Society is becoming more dependent on electric power; and it is essential to make the power available to customers without any interruption and within certain limits of voltage and frequency variations. This means that there is a great need to ensure that a system is as economical, reliable and secure as possible [1]. High reliability of the system is usually obtained by following the principles of bulk power supply planning. However, due to delay in commissioning of new plants and equipment, equipment outages, unexpected load demands and disturbances, the system may be forced to operate in or close to critical and emergency conditions. Hence, in addition to sophisticated planning and designing of the system, an effective operation and control of power systems is essential. The maintenance of a system in a reliable and secure mode is becoming an Important part of the Job of the operators. In the past, more emphasis was given to economic operation; but in view of the consequences of power failures, reliable and secure operation of the system is being given more importance. Security assessment deals with the tracking of the system and deciding whether the present state is secure or not. If the system's state is found to be insecure, it forewarns the operator to take possible remedial action or to be ready for the disturbance if it takes place. This is done before any disturbance (which may lead to failure or deterioration in the quality of supply) occurS. Thus security evaluation is essentially an on-line procedure. The paper will discuss the different operating states of a power system, system security and different approaches for transient security assessment. Recent research results applying the pattern recognition approach will be summarized and presented.
{"title":"Application of pattern recognition to security assessment and enhancement in power systems","authors":"A. El-Abiad","doi":"10.1109/CDC.1975.270572","DOIUrl":"https://doi.org/10.1109/CDC.1975.270572","url":null,"abstract":"There has been a very rapid increase in the size of power systems, and it is still growing. This growth has made the present day systems very big and complex. The complexity is arising especially due to many Interconnections, different types of loads and larger generating units. Also there is uncertainty in load forecasting. With EHV interconnections the disturbances are felt even in geographically distant parts of the system, increasing the severity of the disturbances. These factors make the satisfactory operating of the system a more difficult task. Added to this, Society is becoming more dependent on electric power; and it is essential to make the power available to customers without any interruption and within certain limits of voltage and frequency variations. This means that there is a great need to ensure that a system is as economical, reliable and secure as possible [1]. High reliability of the system is usually obtained by following the principles of bulk power supply planning. However, due to delay in commissioning of new plants and equipment, equipment outages, unexpected load demands and disturbances, the system may be forced to operate in or close to critical and emergency conditions. Hence, in addition to sophisticated planning and designing of the system, an effective operation and control of power systems is essential. The maintenance of a system in a reliable and secure mode is becoming an Important part of the Job of the operators. In the past, more emphasis was given to economic operation; but in view of the consequences of power failures, reliable and secure operation of the system is being given more importance. Security assessment deals with the tracking of the system and deciding whether the present state is secure or not. If the system's state is found to be insecure, it forewarns the operator to take possible remedial action or to be ready for the disturbance if it takes place. This is done before any disturbance (which may lead to failure or deterioration in the quality of supply) occurS. Thus security evaluation is essentially an on-line procedure. The paper will discuss the different operating states of a power system, system security and different approaches for transient security assessment. Recent research results applying the pattern recognition approach will be summarized and presented.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"29 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":"130146675","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 earlier work [7, 8] on the joint adaptive plant and measurement control problem has been restricted to stochastic systems with time-invariant (constant) unknown parameters. This paper extends the results to stochastic systems with time-varying unknown parameters. It is shown that the plant and measurement control calculations can be separated which simplifies the implementation of the scheme.
{"title":"On the simultaneous choice of plant and measurement control for linear stochastic systems with unknown time-varying parameters","authors":"T. Upadhyay","doi":"10.1109/CDC.1975.270629","DOIUrl":"https://doi.org/10.1109/CDC.1975.270629","url":null,"abstract":"The earlier work [7, 8] on the joint adaptive plant and measurement control problem has been restricted to stochastic systems with time-invariant (constant) unknown parameters. This paper extends the results to stochastic systems with time-varying unknown parameters. It is shown that the plant and measurement control calculations can be separated which simplifies the implementation of the scheme.","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":"130613155","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 problem of dynamic file allocation in a computer network is treated in the case when the time-pattern of the file demand rates is not perfectly known in advance to the designer. Instead, only a prior distribution and a statistical behavior are assumed, and the rates have to be estimated on-line from the incoming requests. We show that these estimates are sufficient statistics for the optimal control and obtain the equation giving the control laws as a function of the current estimates and the present location of the file.
{"title":"Dynamic file assignment in a computer network: Part II: Random rates of demand","authors":"A. Segall","doi":"10.1109/CDC.1975.270669","DOIUrl":"https://doi.org/10.1109/CDC.1975.270669","url":null,"abstract":"The problem of dynamic file allocation in a computer network is treated in the case when the time-pattern of the file demand rates is not perfectly known in advance to the designer. Instead, only a prior distribution and a statistical behavior are assumed, and the rates have to be estimated on-line from the incoming requests. We show that these estimates are sufficient statistics for the optimal control and obtain the equation giving the control laws as a function of the current estimates and the present location of the file.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"15 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":"131968858","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 decision-theoretic formulation is given for the problem of classifying an unknown nonlinear stochastic system into one of M classes when only input-output measurements are available. This leads directly to a pattern recognition solution for the problem, and Bayes-risk theory yields the likelihood-ratio test for class determinations. Parameterizations which yield an implicit description for unknown nonlinear systems are considered, and the theoretical likelihood ratio is related to these parameterizations. The difficult problem of initial feature selection is considered in terms of a parameter vector, and in terms of a quasi-moment expansion, both of which require no a priori knowledge of the system. Experimental results are also cited which show that classification can be accomplished with a low probability of error, and analogies with other classification problems are noted.
{"title":"Feature selection for nonlinear stochastic system classification","authors":"R. Hofstadter, G. Saridis","doi":"10.1109/CDC.1975.270743","DOIUrl":"https://doi.org/10.1109/CDC.1975.270743","url":null,"abstract":"A decision-theoretic formulation is given for the problem of classifying an unknown nonlinear stochastic system into one of M classes when only input-output measurements are available. This leads directly to a pattern recognition solution for the problem, and Bayes-risk theory yields the likelihood-ratio test for class determinations. Parameterizations which yield an implicit description for unknown nonlinear systems are considered, and the theoretical likelihood ratio is related to these parameterizations. The difficult problem of initial feature selection is considered in terms of a parameter vector, and in terms of a quasi-moment expansion, both of which require no a priori knowledge of the system. Experimental results are also cited which show that classification can be accomplished with a low probability of error, and analogies with other classification problems are noted.","PeriodicalId":164707,"journal":{"name":"1975 IEEE Conference on Decision and Control including the 14th Symposium on Adaptive Processes","volume":"11 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":"132037176","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}
Often a mathematical model of a dynamical system requires the consideration of uncertain elements. Historically, emphasis has been placed on studying systems in which disturbances enter additively, but many control problems include disturbances that can be more naturally modeled as uncertain (time-varying) multiplicative gains. If the multiplicative gain is of the white noise type, necessary and sufficient conditions for the stability of many of these systems have been derived previously. In this article, we develop conditions for the stability of some discrete-time systems containing multiplicative colored noise. Discrete-time systems in which the colored noise is generated nonrecursively are studied. Necessary and sufficient conditions for their mean square stability have been obtained, and numerical solutions are provided for cases in which the colored noise parameter is generated recursively.
{"title":"Stability criteria for discrete-time systems with colored multiplicative noise","authors":"David Martin, T. Johnson","doi":"10.1109/CDC.1975.270671","DOIUrl":"https://doi.org/10.1109/CDC.1975.270671","url":null,"abstract":"Often a mathematical model of a dynamical system requires the consideration of uncertain elements. Historically, emphasis has been placed on studying systems in which disturbances enter additively, but many control problems include disturbances that can be more naturally modeled as uncertain (time-varying) multiplicative gains. If the multiplicative gain is of the white noise type, necessary and sufficient conditions for the stability of many of these systems have been derived previously. In this article, we develop conditions for the stability of some discrete-time systems containing multiplicative colored noise. Discrete-time systems in which the colored noise is generated nonrecursively are studied. Necessary and sufficient conditions for their mean square stability have been obtained, and numerical solutions are provided for cases in which the colored noise parameter is generated recursively.","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":"130902781","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}
Effective enforcement of no-parking regulations, an essential operation in urban areas, is labor intensive and thus costly. Efficient, implementable enforcement strategies that can raise and keep compliance at a desired high level are needed. It is the objective of this work to determine such strategies. First a model relating enforcement (input) to compliance (output) was obtained on the basis of experimental data; its form is that of a homogeneous bilinear Markov process. Then several optimization problems that reflect different operating conditions were formulated and the corresponding enforcement strategies were derived. Finally, simulations were used to analyze the practical implications of the results.
{"title":"Optimal stochastic enforcement of parking regulations","authors":"T. Han, A. Levis","doi":"10.1109/CDC.1975.270598","DOIUrl":"https://doi.org/10.1109/CDC.1975.270598","url":null,"abstract":"Effective enforcement of no-parking regulations, an essential operation in urban areas, is labor intensive and thus costly. Efficient, implementable enforcement strategies that can raise and keep compliance at a desired high level are needed. It is the objective of this work to determine such strategies. First a model relating enforcement (input) to compliance (output) was obtained on the basis of experimental data; its form is that of a homogeneous bilinear Markov process. Then several optimization problems that reflect different operating conditions were formulated and the corresponding enforcement strategies were derived. Finally, simulations were used to analyze the practical implications of the results.","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":"130269335","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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