A numerical algorithm is presented to solve set covering problems using gradient search technique. The method involves a valley seeking point scanning over the polyhedra formed by the constraint hyper surfaces. The concept is illustrated through experimental results.
{"title":"A gradient search algorithm for set covering problems","authors":"N. Ula, A. Nouh","doi":"10.1109/CDC.1980.272017","DOIUrl":"https://doi.org/10.1109/CDC.1980.272017","url":null,"abstract":"A numerical algorithm is presented to solve set covering problems using gradient search technique. The method involves a valley seeking point scanning over the polyhedra formed by the constraint hyper surfaces. The concept is illustrated through experimental results.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"3 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":"125507086","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 stationary conditions of Radner are shown under relaxed conditions to be sufficient for the global optimum of the static team problem with convex cost. This extension of Radner's theorem establishes the global optimality of the optimal affine laws for the exponential of a quadratic performance index. A formulation of the team problem as a constrained parameter optimization problem simplifies the derivation of the necessary conditions for optimal affine team laws. The solution of this constrained problem expresses the optimal decentralized team control law as an explicit projection of the optimal centralized law for both the quadratic and the exponential of a quadratic performance indices.
{"title":"Static decentralized team problems: Sufficient conditions, algorithms, and the exponential cost criterion","authors":"J. Krainak, J. Speyer, S. Marcus","doi":"10.1109/CDC.1980.271991","DOIUrl":"https://doi.org/10.1109/CDC.1980.271991","url":null,"abstract":"The stationary conditions of Radner are shown under relaxed conditions to be sufficient for the global optimum of the static team problem with convex cost. This extension of Radner's theorem establishes the global optimality of the optimal affine laws for the exponential of a quadratic performance index. A formulation of the team problem as a constrained parameter optimization problem simplifies the derivation of the necessary conditions for optimal affine team laws. The solution of this constrained problem expresses the optimal decentralized team control law as an explicit projection of the optimal centralized law for both the quadratic and the exponential of a quadratic performance indices.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"24 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":"114596192","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 group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements. The Dynamic Programming equation is obtained in the framework of the theory of optimal control of Jump processes. A discrete time version of the model is used for the numerical computation of optimal and suboptimal strategies of group preventive replacement. A monotonicity property of the Bellman functional (or cost-to-go function) is stated and serves to reduce the size of the computational problem.
{"title":"Optimal and suboptimal strategies for group preventive replacement","authors":"A. Haurie, P. L'Ecuyer","doi":"10.1109/CDC.1980.271904","DOIUrl":"https://doi.org/10.1109/CDC.1980.271904","url":null,"abstract":"The group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements. The Dynamic Programming equation is obtained in the framework of the theory of optimal control of Jump processes. A discrete time version of the model is used for the numerical computation of optimal and suboptimal strategies of group preventive replacement. A monotonicity property of the Bellman functional (or cost-to-go function) is stated and serves to reduce the size of the computational problem.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"53 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":"117089268","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 unbounded system model is proposed to represent the error behavior inherent in many navigation instruments or associated with their environments. The model consists of an unbounded deterministic part with unknown constant parameters plus a stochastic part with unknown probability distributions. A simple robust strategy is given to identify the unknown parameters and the second-order statistics of the stochastic part from data. The strategy is sequential, i.e., the deterministic part is first identified and then the statistics of the stochastic part are identified from appropriate residuals. Convergence properties, including the rate of convergence, of parameter estimates are given in terms of conditions which can be easily verified in practical applications. An example involving the use of experimental data to identify an error model for a shipboard velocity measuring system is presented to illustrate the technique.
{"title":"On model identification of a class of unbounded systems with application to navigation instrument error modeling","authors":"T. Lee, J. D'appolito","doi":"10.1109/CDC.1980.271861","DOIUrl":"https://doi.org/10.1109/CDC.1980.271861","url":null,"abstract":"An unbounded system model is proposed to represent the error behavior inherent in many navigation instruments or associated with their environments. The model consists of an unbounded deterministic part with unknown constant parameters plus a stochastic part with unknown probability distributions. A simple robust strategy is given to identify the unknown parameters and the second-order statistics of the stochastic part from data. The strategy is sequential, i.e., the deterministic part is first identified and then the statistics of the stochastic part are identified from appropriate residuals. Convergence properties, including the rate of convergence, of parameter estimates are given in terms of conditions which can be easily verified in practical applications. An example involving the use of experimental data to identify an error model for a shipboard velocity measuring system is presented to illustrate the technique.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"160 48 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":"130508394","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 stabilizing feedback controls for Large-Scale Systems often requires the general concepts of decentralization. In this paper, we present a structural framework for the multilevel stabilization problem of Large-Scale Systems. In this context, we address the stabilization of fixed modes via local and global feedback controls and develop a Dynamical Hierarchical approach to stabilization.
{"title":"Structural control of large scale systems","authors":"P. Groumpos, K. Loparo","doi":"10.1109/CDC.1980.271831","DOIUrl":"https://doi.org/10.1109/CDC.1980.271831","url":null,"abstract":"The design of stabilizing feedback controls for Large-Scale Systems often requires the general concepts of decentralization. In this paper, we present a structural framework for the multilevel stabilization problem of Large-Scale Systems. In this context, we address the stabilization of fixed modes via local and global feedback controls and develop a Dynamical Hierarchical approach to stabilization.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"50 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":"121744205","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 relaxed form of Newton's method is analyzed for the problem, min¿F, with ¿ a convex subset of a real Banach space X, and F:X ¿ R1 twice differentiable in Fréchet's sense. Feasible directions are obtained by minimizing local quadratic approximations Q to F, and step lengths are determined by Goldstein's rule. The results established here yield two significant extensions of an earlier theorem of Goldstein for the special case ¿ = X = a Hilbert space. Connections are made with a recently formulated classification scheme for singular and nonsingular extremals.
对于具有实Banach空间X的凸子集，且F:X¿R1在frimcheet意义上可二阶微的min¿F问题，本文分析了牛顿方法的一种松弛形式。通过最小化局部二次逼近Q到F得到可行方向，步长由Goldstein规则确定。这里建立的结果对特殊情况¿= X = a Hilbert空间给出了Goldstein早期定理的两个重要推广。连接与最近制定的奇异和非奇异极值的分类方案。
{"title":"Newton's method and the goldstein step length rule for constrained minimization","authors":"J. Dunn","doi":"10.1109/CDC.1980.272011","DOIUrl":"https://doi.org/10.1109/CDC.1980.272011","url":null,"abstract":"A relaxed form of Newton's method is analyzed for the problem, min¿F, with ¿ a convex subset of a real Banach space X, and F:X ¿ R1 twice differentiable in Fréchet's sense. Feasible directions are obtained by minimizing local quadratic approximations Q to F, and step lengths are determined by Goldstein's rule. The results established here yield two significant extensions of an earlier theorem of Goldstein for the special case ¿ = X = a Hilbert space. Connections are made with a recently formulated classification scheme for singular and nonsingular extremals.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"65 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114002095","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 joint failure detection and estimation problem in linear systems is analyzed and a computationally feasible algorithm is given for the least mean square state estimator by applying the separate-bias estimation results to the parameter adaptive estimation solution.
{"title":"Simultaneous failure detection and estimation in linear systems","authors":"A. Caglayan","doi":"10.1109/CDC.1980.271959","DOIUrl":"https://doi.org/10.1109/CDC.1980.271959","url":null,"abstract":"In this paper, the joint failure detection and estimation problem in linear systems is analyzed and a computationally feasible algorithm is given for the least mean square state estimator by applying the separate-bias estimation results to the parameter adaptive estimation solution.","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":"124466300","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 shows how the design of feedback controllers for nonlinear systems may be formulated as an optimization problem with infinite dimensional constraints for which known algorithms may be employed. An important aspect is a method for reducing the time interval, required to insure stability, to a finite value.
{"title":"Design of nonlinear feedback controllers","authors":"E. Polak, D. Mayne","doi":"10.1109/CDC.1980.271973","DOIUrl":"https://doi.org/10.1109/CDC.1980.271973","url":null,"abstract":"This paper shows how the design of feedback controllers for nonlinear systems may be formulated as an optimization problem with infinite dimensional constraints for which known algorithms may be employed. An important aspect is a method for reducing the time interval, required to insure stability, to a finite value.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"48 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":"124162493","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 a differential encoder for data compression is formulated as a stochastic optimal control problem. The resulting plant to be controlled contains control-dependent noise, but the observation model is noise-free. It is shown that the optimal one-stage control is the prediction error, and therefore, the classical differential pulse code modulation system is optimal for this criterion. The optimal multistage control is shown to include a scaled version of the one-stage control and a weighted sum of the differences between the past inputs and their estimates. Simulation results are presented for a first order differential pulse code modulation system. Four, eight, and twelve level adaptive quantizers are used in the simulations.
{"title":"Differential encoder design using stochastic control theory","authors":"J. Gibson, T. Fischer","doi":"10.1109/CDC.1980.271811","DOIUrl":"https://doi.org/10.1109/CDC.1980.271811","url":null,"abstract":"The design of a differential encoder for data compression is formulated as a stochastic optimal control problem. The resulting plant to be controlled contains control-dependent noise, but the observation model is noise-free. It is shown that the optimal one-stage control is the prediction error, and therefore, the classical differential pulse code modulation system is optimal for this criterion. The optimal multistage control is shown to include a scaled version of the one-stage control and a weighted sum of the differences between the past inputs and their estimates. Simulation results are presented for a first order differential pulse code modulation system. Four, eight, and twelve level adaptive quantizers are used in the simulations.","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":"128047201","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 uniformly balanced realization for time-varying systems is defined. Such a framework has many remarkable properties and leads to a natural setting for performing model reduction. It turns out that in many cases a reduced model preserves the properties of the original model. In this paper stability of the reduced systems is fully explored.
{"title":"Stability of balanced time-variable system approximations","authors":"S. Shokoohi, L. Silverman, P. Dooren","doi":"10.1109/CDC.1980.271847","DOIUrl":"https://doi.org/10.1109/CDC.1980.271847","url":null,"abstract":"A uniformly balanced realization for time-varying systems is defined. Such a framework has many remarkable properties and leads to a natural setting for performing model reduction. It turns out that in many cases a reduced model preserves the properties of the original model. In this paper stability of the reduced systems is fully explored.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"211 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":"132329050","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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