Given two "nonlinear filtering problems" described by the processes dx (t)i = fi (xi(t)) dt+gi (xi(t))dwi(t) i=1,2, dx (t)i = hi (xi(t)) dt+dvi(t), we define a notion of strong equivalence relating the solutions to the corresponding Mortensen-Zakai equations dui (t,x) = Lui i(t,x)dt + Li iui (t,x)dyt i, i=1,2, which allows solution of one problem to be obtained easily from solutions of the other. We give a geometric picture of this equivalence as a group of local transformations acting on manifolds of solutions. We then show that by knowing the full invariance group of the time invariant equations dui (t,x) = Lui i (t,x)dt, i=1,2, we can analyze strong equivalence for the filtering problems. In particular if the two time invariant parabolic operators are in the same orbit of the invariance group we can show strong equivalence for the filtering problems. As a result filtering problems are separated into equivalent classes which correspond to orbits of invariance groups of parabolic operators. As specific example we treat V. Bene¿'s case establishing from this point of view the necessity of the Riccati equation.
给定由过程dx (t)i = fi (xi(t)) dt+gi (xi(t))dwi(t) i=1,2, dx (t)i = hi (xi(t)) dt+dvi(t)描述的两个“非线性滤波问题”，我们定义了相应Mortensen-Zakai方程dui (t,x) = Lui (t,x)dt + Li iui (t,x)dyt i, i=1,2的解的强等价概念，使得一个问题的解可以很容易地从另一个问题的解中得到。我们给出了这个等价的几何图像，它是作用于解的流形上的一组局部变换。然后我们证明了通过知道时不变方程dui (t,x) = Lui i (t,x)dt, i=1,2的全不变群，我们可以分析滤波问题的强等价性。特别是当两个时不变抛物算子在不变群的同一轨道上时，我们可以证明滤波问题的强等价性。结果将滤波问题划分为等价类，这些等价类对应于抛物算子不变性群的轨道。作为具体的例子，我们从这一观点出发，讨论了利卡第方程的必要性。
{"title":"Group invariance methods in nonlinear filtering of diffusion processes","authors":"J. Baras","doi":"10.1109/CDC.1980.272022","DOIUrl":"https://doi.org/10.1109/CDC.1980.272022","url":null,"abstract":"Given two \"nonlinear filtering problems\" described by the processes dx (t)i = fi (xi(t)) dt+gi (xi(t))dwi(t) i=1,2, dx (t)i = hi (xi(t)) dt+dvi(t), we define a notion of strong equivalence relating the solutions to the corresponding Mortensen-Zakai equations dui (t,x) = Lui i(t,x)dt + Li iui (t,x)dyt i, i=1,2, which allows solution of one problem to be obtained easily from solutions of the other. We give a geometric picture of this equivalence as a group of local transformations acting on manifolds of solutions. We then show that by knowing the full invariance group of the time invariant equations dui (t,x) = Lui i (t,x)dt, i=1,2, we can analyze strong equivalence for the filtering problems. In particular if the two time invariant parabolic operators are in the same orbit of the invariance group we can show strong equivalence for the filtering problems. As a result filtering problems are separated into equivalent classes which correspond to orbits of invariance groups of parabolic operators. As specific example we treat V. Bene¿'s case establishing from this point of view the necessity of the Riccati equation.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"132 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":"115967764","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}
{"title":"On linear discrete-time deadbeat control","authors":"John B. Lewis, Y. Jan","doi":"10.1109/CDC.1980.271846","DOIUrl":"https://doi.org/10.1109/CDC.1980.271846","url":null,"abstract":"","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"33 32","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114046897","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 "multiple-access" problem in a packet network is considered, where the channel time is slotted and the number of transmitting sources is in general finite. In contrast to most existing studies on similar problems, source queues are allowed. The objective of our efforts is the design of multiple-access protocols which control the queue sizes as well as the per packet delays for all sources, where identical as well as nonidentical sources are considered. The present paper includes only a part of studies, which were pursued in a joint effort with Leonidas Georgiadis and Glenn D. Marcus. The interested reader can find more information on the above studies, in reference [6].
本文研究了分组网络中的“多址”问题，其中信道时间是开槽的，发射源的数量一般是有限的。与大多数关于类似问题的现有研究相比，源队列是允许的。我们努力的目标是设计多址访问协议，控制队列大小以及所有源的每包延迟，其中考虑了相同和非相同源。本文仅包括与Leonidas Georgiadis和Glenn D. Marcus共同进行的部分研究。感兴趣的读者可以在参考文献[6]中找到有关上述研究的更多信息。
{"title":"Multiple access protocols in data transmission","authors":"P. Papantoni-Kazakos","doi":"10.1109/CDC.1980.271875","DOIUrl":"https://doi.org/10.1109/CDC.1980.271875","url":null,"abstract":"In this paper, the \"multiple-access\" problem in a packet network is considered, where the channel time is slotted and the number of transmitting sources is in general finite. In contrast to most existing studies on similar problems, source queues are allowed. The objective of our efforts is the design of multiple-access protocols which control the queue sizes as well as the per packet delays for all sources, where identical as well as nonidentical sources are considered. The present paper includes only a part of studies, which were pursued in a joint effort with Leonidas Georgiadis and Glenn D. Marcus. The interested reader can find more information on the above studies, in reference [6].","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"26 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":"131210340","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}
{"title":"On multivariable regulators: An explicit description","authors":"P. Antsaklis","doi":"10.1109/CDC.1980.271844","DOIUrl":"https://doi.org/10.1109/CDC.1980.271844","url":null,"abstract":"","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"40 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":"133908175","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 use the Hoffman-Wielandt inequalities to solve several minimum norm problems and a matrix minimization problem that arises in determining the maximum power transfer in an electric circuit.
{"title":"Some matrix minimization problems","authors":"E. Barnes","doi":"10.1109/CDC.1980.271790","DOIUrl":"https://doi.org/10.1109/CDC.1980.271790","url":null,"abstract":"We use the Hoffman-Wielandt inequalities to solve several minimum norm problems and a matrix minimization problem that arises in determining the maximum power transfer in an electric circuit.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"104 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":"134405774","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}
Algorithms for the robust detection and estimation of soft failures which have very modest computational requirements are presented. Soft failures are characterized by deviations in the statistical parameters of system inputs and measurement errors. The on-line detection scheme utilizes a single Kalman filter and requires the implementation of Wald Sequential Detectors (WSD). The algorithm consists of repeated application of the Sequential Probability Ratio Test (SPRT) to the filter innovations and use of the sequence of Sample Numbers (SN) for each SPRT termination for the detection of a failure. The proposed scheme for the estimation of a failed parameter consists of a bank of detectors and utilizes the properties of the Average Sample Number (ASN). The capabilities of the scheme, including its robustness for the isolation of single parameter failures, are illustrated via simulation results for a maneuvering target problem.
{"title":"Robust detection and estimation of soft failures in linear systems","authors":"B. Tulpule, C. Knapp","doi":"10.1109/CDC.1980.271955","DOIUrl":"https://doi.org/10.1109/CDC.1980.271955","url":null,"abstract":"Algorithms for the robust detection and estimation of soft failures which have very modest computational requirements are presented. Soft failures are characterized by deviations in the statistical parameters of system inputs and measurement errors. The on-line detection scheme utilizes a single Kalman filter and requires the implementation of Wald Sequential Detectors (WSD). The algorithm consists of repeated application of the Sequential Probability Ratio Test (SPRT) to the filter innovations and use of the sequence of Sample Numbers (SN) for each SPRT termination for the detection of a failure. The proposed scheme for the estimation of a failed parameter consists of a bank of detectors and utilizes the properties of the Average Sample Number (ASN). The capabilities of the scheme, including its robustness for the isolation of single parameter failures, are illustrated via simulation results for a maneuvering target problem.","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":"130390323","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 design of controllers is considered as a parameter optimization problem within the framework of optimal control theory and the calculus of variations. This approach yields a minimum time optimal control problem which is singular. Methods for solving singular optimal control problems are applied to determine optimal parameters for controllers. Examples are presented to illustrate the design of control systems using this approach.
{"title":"Optimization of the parameters of controllers","authors":"Arthur Brummel, B. McInnis","doi":"10.1109/CDC.1980.271969","DOIUrl":"https://doi.org/10.1109/CDC.1980.271969","url":null,"abstract":"The design of controllers is considered as a parameter optimization problem within the framework of optimal control theory and the calculus of variations. This approach yields a minimum time optimal control problem which is singular. Methods for solving singular optimal control problems are applied to determine optimal parameters for controllers. Examples are presented to illustrate the design of control systems using this approach.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"25 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":"115186427","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 the basic problem of using optimization in situations where the quantities involved cannot be evaluated precisely. An example we have considered in the past (see reference [1]) is the circuit design optimization problem. The objective in such a problem is to determine values for certain parameters in the circuits that optimize some measure of circuit performance. This measure or criterion is evaluated by solving a system of nonlinear algebraic and differential equations. These equations can be solved to a specified degree of accuracy, but the cost of a function/ gradient evaluation can increase significantly when the accuracy is increased. In this situation the function and gradient evaluations contain approximately the same percentage errors. Initial tests as represented in [1] indicated that variable metric schemes can be reliable when applied to such problems. Many other applications exist. In this talk we examine this question of computing an 'optimal' solution in the presence of such errors.
{"title":"Use of optimization in applications with errors","authors":"J. Cullum","doi":"10.1109/CDC.1980.271788","DOIUrl":"https://doi.org/10.1109/CDC.1980.271788","url":null,"abstract":"We consider the basic problem of using optimization in situations where the quantities involved cannot be evaluated precisely. An example we have considered in the past (see reference [1]) is the circuit design optimization problem. The objective in such a problem is to determine values for certain parameters in the circuits that optimize some measure of circuit performance. This measure or criterion is evaluated by solving a system of nonlinear algebraic and differential equations. These equations can be solved to a specified degree of accuracy, but the cost of a function/ gradient evaluation can increase significantly when the accuracy is increased. In this situation the function and gradient evaluations contain approximately the same percentage errors. Initial tests as represented in [1] indicated that variable metric schemes can be reliable when applied to such problems. Many other applications exist. In this talk we examine this question of computing an 'optimal' solution in the presence of such errors.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"46 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":"115680193","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 composite control proposed in an earlier paper for a class of singularly perturbed nonlinear systems is now shown to possess properties essential for near-optimal feedback design. It asymptotically stabilizes the desired equilibrium and produces a finite cost which tends to the optimal cost for a slow problem as the singular perturbation parameter tends to zero. Thus the well-posedness of the full regulator problem is established. The stability results are also applicable to two-time scale systems which are not singularly perturbed, and the paper does not assume the knowledge of singular perturbation techniques.
{"title":"A two stage Lyapunov-Bellman feedback design of a class of nonlinear systems","authors":"J. Chow, P. Kokotovic","doi":"10.1109/CDC.1980.271972","DOIUrl":"https://doi.org/10.1109/CDC.1980.271972","url":null,"abstract":"The composite control proposed in an earlier paper for a class of singularly perturbed nonlinear systems is now shown to possess properties essential for near-optimal feedback design. It asymptotically stabilizes the desired equilibrium and produces a finite cost which tends to the optimal cost for a slow problem as the singular perturbation parameter tends to zero. Thus the well-posedness of the full regulator problem is established. The stability results are also applicable to two-time scale systems which are not singularly perturbed, and the paper does not assume the knowledge of singular perturbation techniques.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"11 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":"114417203","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}
Simultaneous control of both species in the Lotka-Volterra prey-predator system model has been previously investigated by Goh, et al. [1], Vincent, et al. [2], Vincent [3], and others. More recently May, et al. [4] using a new model, somewhat akin to the Lotka-Volterra system, examined the consequences of simultaneous constant effort harvesting of both the prey (krill) and the predators (Baleen Whales).
{"title":"Multispaces harvesting of a pery-predator system","authors":"T. Vincent","doi":"10.1109/CDC.1980.271810","DOIUrl":"https://doi.org/10.1109/CDC.1980.271810","url":null,"abstract":"Simultaneous control of both species in the Lotka-Volterra prey-predator system model has been previously investigated by Goh, et al. [1], Vincent, et al. [2], Vincent [3], and others. More recently May, et al. [4] using a new model, somewhat akin to the Lotka-Volterra system, examined the consequences of simultaneous constant effort harvesting of both the prey (krill) and the predators (Baleen Whales).","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"39 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":"123351713","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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