J. Haslinger, P. Neittaanmäki, T. Tiihonen, A. Kaarna
In the first part we give a general existence theorem and a regularization method for an optimal control problem where the control is a domain in R″ and where the system is governed by a state relation which includes differential equations as well as inequalities. In the second part applications for optimal shape design problems governed by the Dirichlet-Signorini boundary value problem are presented. Several numerical examples are included.
{"title":"Optimal shape design and unilateral boundary value problems: Part II","authors":"J. Haslinger, P. Neittaanmäki, T. Tiihonen, A. Kaarna","doi":"10.1002/OCA.4660090204","DOIUrl":"https://doi.org/10.1002/OCA.4660090204","url":null,"abstract":"In the first part we give a general existence theorem and a regularization method for an optimal control problem where the control is a domain in R″ and where the system is governed by a state relation which includes differential equations as well as inequalities. In the second part applications for optimal shape design problems governed by the Dirichlet-Signorini boundary value problem are presented. Several numerical examples are included.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"145-163"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090204","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On etudie les proprietes de convergence de l'algorithme de calcul des commandes optimales a retard avec contraintes aux limites et on resout 3 problemes de commande optimale hereditaire non lineaire pour illustrer la validite et l'utilite de la technique de calcul
{"title":"A Computational method for time‐lag control problems with control and terminal inequality constraints","authors":"K. Teo, K. Wong","doi":"10.1002/OCA.4660080407","DOIUrl":"https://doi.org/10.1002/OCA.4660080407","url":null,"abstract":"On etudie les proprietes de convergence de l'algorithme de calcul des commandes optimales a retard avec contraintes aux limites et on resout 3 problemes de commande optimale hereditaire non lineaire pour illustrer la validite et l'utilite de la technique de calcul","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 1","pages":"377-395"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dynamic optimization of queueing systems is treated by optimal control theory. This work is based on modelling the queueing problem as a time-varying continuous Markov chain. Necessary and sufficient conditions are given for a broad class of problems which include both scalar and Markovian dynamic programming control structures. Continuity of the switching function is used to characterize optimality near the end points of the horizon. Special properties of the model are exploited to ensure the absence of singular subarcs. Numerical results based on the use of a gradient algorithm report the effect of increasing the system capacity, a comparison of scalar versus Markovian dynamic programming controls, and an application to a multiprogrammed computer system.
{"title":"Optimal control of Markovian queueing systems","authors":"C. F. Klein, W. Gruver","doi":"10.1002/OCA.4660020103","DOIUrl":"https://doi.org/10.1002/OCA.4660020103","url":null,"abstract":"Dynamic optimization of queueing systems is treated by optimal control theory. This work is based on modelling the queueing problem as a time-varying continuous Markov chain. Necessary and sufficient conditions are given for a broad class of problems which include both scalar and Markovian dynamic programming control structures. Continuity of the switching function is used to characterize optimality near the end points of the horizon. Special properties of the model are exploited to ensure the absence of singular subarcs. Numerical results based on the use of a gradient algorithm report the effect of increasing the system capacity, a comparison of scalar versus Markovian dynamic programming controls, and an application to a multiprogrammed computer system.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"23-34"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The optimal management of hydro storage reservoirs is considered. The objective is to minimize thermal power station fuel costs, over a horizon of one or more years, in a mixed hydro-thermal power system. A model of the New Zealand system is developed that is simple enough for computational purposes but nevertheless accounts for all major factors including load diversity and transmission losses. A version of Powell's generalized conjugate-gradient algorithm with Beale restarts is used for the optimization. State and control constraints are enforced by penalty functions and transformations, respectively. Results are presented for a reduced-order model of the New Zealand system.
{"title":"Long-term optimization of hydro-thermal power systems by generalized Conjugate-Gradient Methods","authors":"H. Sirisena, T. Halliburton","doi":"10.1002/OCA.4660020404","DOIUrl":"https://doi.org/10.1002/OCA.4660020404","url":null,"abstract":"The optimal management of hydro storage reservoirs is considered. The objective is to minimize thermal power station fuel costs, over a horizon of one or more years, in a mixed hydro-thermal power system. A model of the New Zealand system is developed that is simple enough for computational purposes but nevertheless accounts for all major factors including load diversity and transmission losses. A version of Powell's generalized conjugate-gradient algorithm with Beale restarts is used for the optimization. State and control constraints are enforced by penalty functions and transformations, respectively. Results are presented for a reduced-order model of the New Zealand system.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"351-364"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020404","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with an optimal advertising model with two state variables. The revenue and efficiency functions are concave. The aim is to choose the rate of advertising expenditures over time in a way that maximizes the present value of net profit streams over an infinite horizon subject to a replenishable budget. It is shown that the optimal advertising expenditures start at a high level and decrease over time if the initial stock of goodwill is low. Low initial budget as well as low initial stock of goodwill can cause shortness of budget. It turns out that, in contrast to comparable linear models, the remaining budget is always positive.
{"title":"Optimal control of non-linear advertising models with replenishable budget","authors":"R. Hartl","doi":"10.1002/OCA.4660030105","DOIUrl":"https://doi.org/10.1002/OCA.4660030105","url":null,"abstract":"This paper deals with an optimal advertising model with two state variables. The revenue and efficiency functions are concave. The aim is to choose the rate of advertising expenditures over time in a way that maximizes the present value of net profit streams over an infinite horizon subject to a replenishable budget. It is shown that the optimal advertising expenditures start at a high level and decrease over time if the initial stock of goodwill is low. Low initial budget as well as low initial stock of goodwill can cause shortness of budget. It turns out that, in contrast to comparable linear models, the remaining budget is always positive.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"3 1","pages":"53-65"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030105","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A finite-element collocation technique is proposed for solving non-linear distributed parameter system (DPS) optimal control problems. On each element, two Gaussian collocation points and Hermite approximation functions are used in the finite-element collocation technique. The numerical experience for two non-linear DPS, one involving distributed control and the other involving spatially-independent control, is reported. Optimal control of DPS can be computed with relatively low-order models when this finite-element collocation technique is used.
{"title":"Optimal control of non‐linear distributed parameter systems by a finite‐element collocation technique","authors":"K. C. Rao, S. Prabhu, S. Mehta","doi":"10.1002/OCA.4660030107","DOIUrl":"https://doi.org/10.1002/OCA.4660030107","url":null,"abstract":"A finite-element collocation technique is proposed for solving non-linear distributed parameter system (DPS) optimal control problems. On each element, two Gaussian collocation points and Hermite approximation functions are used in the finite-element collocation technique. The numerical experience for two non-linear DPS, one involving distributed control and the other involving spatially-independent control, is reported. Optimal control of DPS can be computed with relatively low-order models when this finite-element collocation technique is used.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"3 1","pages":"79-90"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Digital Control Systems: Theory, Hardware, Software, C. H. Houpis and G. B. Lamont, McGraw-Hill, New York, 1985, ISBN 0–07-Y66352–1. £13.50, XIX + 667pp.","authors":"K. Hunt","doi":"10.1002/OCA.4660090211","DOIUrl":"https://doi.org/10.1002/OCA.4660090211","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"223-223"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces novel control schemes to stabilize linear discrete stochastic-parameter systems. It is shown that under some mild conditions, controllers that are optimal in the sense of minimizing a finite sliding-horizon performance index subject to linear stochastic-parameter system constraint are stabilizing for the system in both senses of almost-sure and mean-square asymptotic stability. Moreover, if the uncertainties of stochastic parameters are small enough, the designer can even stabilize these systems by the use of controllers that are designed on the basis of the deterministic equivalent of these systems.
{"title":"Sliding-horizon optimal and certainty-equivalent controllers for stabilizing stochastic-parameter systems","authors":"E. Yaz","doi":"10.1002/OCA.4660080403","DOIUrl":"https://doi.org/10.1002/OCA.4660080403","url":null,"abstract":"This paper introduces novel control schemes to stabilize linear discrete stochastic-parameter systems. It is shown that under some mild conditions, controllers that are optimal in the sense of minimizing a finite sliding-horizon performance index subject to linear stochastic-parameter system constraint are stabilizing for the system in both senses of almost-sure and mean-square asymptotic stability. Moreover, if the uncertainties of stochastic parameters are small enough, the designer can even stabilize these systems by the use of controllers that are designed on the basis of the deterministic equivalent of these systems.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 1","pages":"327-337"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080403","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new method of computing optimal non-linear feedbacks is used for regulating the angular momentum of spacecraft using both reaction jets and flywheels. It is shown that the optimal feedback law satisfies a system of first-order, quasi-linear, partial differential equations. The integration of these equations by the method of characteristics gives the non-linear feedback control. This control reduces the angular velocities of the space vehicle to zero by minimizing the fuel consumption. The optimal regulation, under reaction jet control alone and with the flywheels at fixed angular velocities, is considered. The special case where these velocities are zero leads readily to the known analytical solution of the feedback law, which is linear in the state although the dynamics is non-linear.
{"title":"On Applications of a new method for computing optimal non-linear feedback controls","authors":"H. Bourdache-Siguerdidjane","doi":"10.1002/OCA.4660080408","DOIUrl":"https://doi.org/10.1002/OCA.4660080408","url":null,"abstract":"A new method of computing optimal non-linear feedbacks is used for regulating the angular momentum of spacecraft using both reaction jets and flywheels. It is shown that the optimal feedback law satisfies a system of first-order, quasi-linear, partial differential equations. The integration of these equations by the method of characteristics gives the non-linear feedback control. This control reduces the angular velocities of the space vehicle to zero by minimizing the fuel consumption. \u0000 \u0000 \u0000 \u0000The optimal regulation, under reaction jet control alone and with the flywheels at fixed angular velocities, is considered. The special case where these velocities are zero leads readily to the known analytical solution of the feedback law, which is linear in the state although the dynamics is non-linear.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"76 1","pages":"397-409"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080408","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a recent issue of this Journal, Lin1 analyses a pollution control model that is designed to include adjustment costs, investment, employment and inflation. His analysis of the control theoretic solution appears to contain a number of errors which are pointed out below. Also, the model that he constructs has some awkward features in the view of this analyst. My concerns with the model are outlined in the second section of this comment.
{"title":"The Control of environmental pollution and optimal investment and employment decisions: A Discussion of methodological and modelling issues","authors":"B. A. Forster","doi":"10.1002/OCA.4660090309","DOIUrl":"https://doi.org/10.1002/OCA.4660090309","url":null,"abstract":"In a recent issue of this Journal, Lin1 analyses a pollution control model that is designed to include adjustment costs, investment, employment and inflation. His analysis of the control theoretic solution appears to contain a number of errors which are pointed out below. Also, the model that he constructs has some awkward features in the view of this analyst. My concerns with the model are outlined in the second section of this comment.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"333-336"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090309","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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