The problem of adjustment time in neoclassical monetary growth models is examined. Comparisons are made with the neoclassical growth model without money. Discretionary monetary and fiscal policies of a ‘bang-bang’ type based upon Pontryagin's minimum principle and the ‘minimum-time’ problem are derived by computer simulation since the models are non-linear and except in trivial cases cannot be solved analytically. The effectiveness of policies in reducing adjustment time between equilibria is explored. These policies provide for increased confidence in the relevance of comparative static predictions derived from the type of models studied.
{"title":"Adjustment time and optimal control of neoclassical monetary growth models","authors":"Stephen D. Lewis","doi":"10.1002/OCA.4660020305","DOIUrl":"https://doi.org/10.1002/OCA.4660020305","url":null,"abstract":"The problem of adjustment time in neoclassical monetary growth models is examined. Comparisons are made with the neoclassical growth model without money. Discretionary monetary and fiscal policies of a ‘bang-bang’ type based upon Pontryagin's minimum principle and the ‘minimum-time’ problem are derived by computer simulation since the models are non-linear and except in trivial cases cannot be solved analytically. The effectiveness of policies in reducing adjustment time between equilibria is explored. These policies provide for increased confidence in the relevance of comparative static predictions derived from the type of models studied.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"251-267"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020305","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027850","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}
An optimal control theory for a class of non-linear distributed parameter control systems in the general setting involving more than one spatial co-ordinate is developed for use on control of a typical soaking pit in a steel industry. The system is described by a set of non-linear partial differential equations in multidimensional spatial co-ordinates and non-linear boundary conditions with time-dependent boundary controls as well as a spatially independent parameter vector which is governed by its own set of dynamic equations. The set of necessary conditions for optimality obtained from the theoretical development is directly applied to the optimal heating control of the soaking pit with rectangular ingots. The numerical solution by iterations demonstrates the success of the technique and the algorithm leading to the optimal policy for heating control of a typical soaking pit with minimum fuel consumption.
{"title":"Optimal control of temperature and fuel consumption for soaking pits in a steel plant—a distributed parameter approach","authors":"D. R. Yang, F. Y. Wang, K. Chang, Won-Kyoo Lee","doi":"10.1002/OCA.4660090406","DOIUrl":"https://doi.org/10.1002/OCA.4660090406","url":null,"abstract":"An optimal control theory for a class of non-linear distributed parameter control systems in the general setting involving more than one spatial co-ordinate is developed for use on control of a typical soaking pit in a steel industry. The system is described by a set of non-linear partial differential equations in multidimensional spatial co-ordinates and non-linear boundary conditions with time-dependent boundary controls as well as a spatially independent parameter vector which is governed by its own set of dynamic equations. The set of necessary conditions for optimality obtained from the theoretical development is directly applied to the optimal heating control of the soaking pit with rectangular ingots. The numerical solution by iterations demonstrates the success of the technique and the algorithm leading to the optimal policy for heating control of a typical soaking pit with minimum fuel consumption.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"417-442"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090406","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031509","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":"Control System Design: An Introduction To State-Space Methods, Bernard Friedland, McGraw-Hill (UK), 1986. ISBN: 07–022441–2. Price: £41.95","authors":"M. Johnson","doi":"10.1002/OCA.4660090111","DOIUrl":"https://doi.org/10.1002/OCA.4660090111","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"107-107"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090111","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031053","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 method of optimal design of damped structures under dynamic loads is developed, and several illustrative problems for minimum-weight design of planar frame structures under impulsive external forces or ground accelerations are studied. In order to analyse dynamic structures, the finite element method and modal analysis technique are used, and structural damping is included in terms of modal damping ratios. For numerical optimization, a gradient-type algorithm based on the state-space approach in optimal control is utilized.
{"title":"Optimal design of damped dynamic structures","authors":"Seung Woo Kimf, B. Kwak","doi":"10.1002/OCA.4660020403","DOIUrl":"https://doi.org/10.1002/OCA.4660020403","url":null,"abstract":"A method of optimal design of damped structures under dynamic loads is developed, and several illustrative problems for minimum-weight design of planar frame structures under impulsive external forces or ground accelerations are studied. In order to analyse dynamic structures, the finite element method and modal analysis technique are used, and structural damping is included in terms of modal damping ratios. For numerical optimization, a gradient-type algorithm based on the state-space approach in optimal control is utilized.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"335-350"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020403","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028093","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}
For certain types of elliptic boundary control problems, the boundary element method has considerable advantage over the traditional finite element or finite difference methods because of the reduction of dimensionality in computations. In this paper we examine a variant of such boundary integral methods based on Cauchy integrals. The cost functional here contains only finitely many quadratic terms related to sensory data at those finite interior points. We see that the numerical efficiency of this approach hinges largely on the complexity of the inverse of a certain boundary integral operator. In the case of a circle, such an inverse is readily obtainable and entire computations require only a small effort to yield useful numerical information about the optimal control. Other general situations are also discussed.
{"title":"A boundary element method based on Cauchy integrals for some linear quadratic boundary control problems on a circle","authors":"Goong Chen, Chiang-Pu Chen, I. Aronov","doi":"10.1002/OCA.4660090109","DOIUrl":"https://doi.org/10.1002/OCA.4660090109","url":null,"abstract":"For certain types of elliptic boundary control problems, the boundary element method has considerable advantage over the traditional finite element or finite difference methods because of the reduction of dimensionality in computations. In this paper we examine a variant of such boundary integral methods based on Cauchy integrals. The cost functional here contains only finitely many quadratic terms related to sensory data at those finite interior points. We see that the numerical efficiency of this approach hinges largely on the complexity of the inverse of a certain boundary integral operator. In the case of a circle, such an inverse is readily obtainable and entire computations require only a small effort to yield useful numerical information about the optimal control. Other general situations are also discussed.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"93-100"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090109","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031031","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 control of a gas compressor station is required which minimizes the costs of powering the compressors. An algorithm is developed which has a two-level structure: an optimization level and a control/adjustment level. The former minimizes the engine fuel consumption with the use of measured values of flow through the station together with suction and discharge pressure. The latter level ensures proper operating conditions for the compressors and thereby reduces the cost of maintenance and repairs. The proposed procedure is illustrated by an example, and the results show that the method can lead to a significant saving in fuel consumption.
{"title":"A Local optimization procedure for a gas compressor station","authors":"A. Osiadacz, D. Bell","doi":"10.1002/OCA.4660020304","DOIUrl":"https://doi.org/10.1002/OCA.4660020304","url":null,"abstract":"The optimal control of a gas compressor station is required which minimizes the costs of powering the compressors. An algorithm is developed which has a two-level structure: an optimization level and a control/adjustment level. The former minimizes the engine fuel consumption with the use of measured values of flow through the station together with suction and discharge pressure. The latter level ensures proper operating conditions for the compressors and thereby reduces the cost of maintenance and repairs. The proposed procedure is illustrated by an example, and the results show that the method can lead to a significant saving in fuel consumption.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"44 1","pages":"239-250"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020304","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027841","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}
Models of optimal control of two-species ecological systems are considered on an infinite time horizon. Conditions are obtained under which the optimal exploitation of the system is stabilizing. Thus, a stationary state toward which all optimal trajectories must converge is defined. This extends to this class of models, the co-called turnpike property of optimal economic growth models.
{"title":"Stability and optimal exploitation over an infinite time horizon of interacting populations","authors":"A. Haurie","doi":"10.1002/OCA.4660030303","DOIUrl":"https://doi.org/10.1002/OCA.4660030303","url":null,"abstract":"Models of optimal control of two-species ecological systems are considered on an infinite time horizon. Conditions are obtained under which the optimal exploitation of the system is stabilizing. Thus, a stationary state toward which all optimal trajectories must converge is defined. This extends to this class of models, the co-called turnpike property of optimal economic growth models.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"3 1","pages":"241-256"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030303","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028053","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":"Computational Techniques In Operations Research, A. M. Andrew, Abacus Press, 1985. No. of pages: 201. Price: £14.95. ISBN: 0 85626 425 3","authors":"D. S. Butler","doi":"10.1002/OCA.4660080110","DOIUrl":"https://doi.org/10.1002/OCA.4660080110","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"58 1","pages":"105-105"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080110","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030518","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}
Optimal control of a composite rectangular plate on an elastic foundation is studied with the objective of minimizing its dynamic response in a given period of time with the minimum possible expenditure of force. The plate undergoes transient vibrations starting from specified initial displacement and velocity distributions, and the control is exercised by optimally determining the transverse distributed force. The multiple objectives of the problem are taken into account by adopting a vector performance criterion comprising quadratic functional of the deflection, velocity and distributed force. The sufficiency condition of optimality is derived using control theory results which lead to an analytic solution of the problem. Numerical results are given for simply supported plates made of specially orthotropic layers of boron-fibre-reinforced plastic material. It is demonstrated that the effectiveness of the proposed control depends on the lamination order, foundation modulus, viscous damping, aspect ratio and terminal time as well as on the weight factors attached to various cost functionals.
{"title":"Distributed control of layered orthotropic plates with damping","authors":"S. Adali, I. Sadek, J. Sloss, J. Bruch","doi":"10.1002/OCA.4660090102","DOIUrl":"https://doi.org/10.1002/OCA.4660090102","url":null,"abstract":"Optimal control of a composite rectangular plate on an elastic foundation is studied with the objective of minimizing its dynamic response in a given period of time with the minimum possible expenditure of force. The plate undergoes transient vibrations starting from specified initial displacement and velocity distributions, and the control is exercised by optimally determining the transverse distributed force. The multiple objectives of the problem are taken into account by adopting a vector performance criterion comprising quadratic functional of the deflection, velocity and distributed force. The sufficiency condition of optimality is derived using control theory results which lead to an analytic solution of the problem. Numerical results are given for simply supported plates made of specially orthotropic layers of boron-fibre-reinforced plastic material. It is demonstrated that the effectiveness of the proposed control depends on the lamination order, foundation modulus, viscous damping, aspect ratio and terminal time as well as on the weight factors attached to various cost functionals.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"1-17"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030946","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 zero-sum differential game model is presented for two players who are both transmitting information and jamming their opponent at the same time, under channel capacity constraints. The problem for each player is to find an optimal policy for allocating this capacity over the duration of the game. Given a cost function for the game, conditions are determined under which equilibrium strategies exist. These (pure) strategies are found to be of the bang-bang variety and depend on game parameters such as the channel capacity and jamming effectiveness of the players, as well as the duration of the game.
{"title":"Optimal transmission and jamming strategies in a communication channel","authors":"C. Cassandras","doi":"10.1002/OCA.4660090103","DOIUrl":"https://doi.org/10.1002/OCA.4660090103","url":null,"abstract":"A zero-sum differential game model is presented for two players who are both transmitting information and jamming their opponent at the same time, under channel capacity constraints. The problem for each player is to find an optimal policy for allocating this capacity over the duration of the game. Given a cost function for the game, conditions are determined under which equilibrium strategies exist. These (pure) strategies are found to be of the bang-bang variety and depend on game parameters such as the channel capacity and jamming effectiveness of the players, as well as the duration of the game.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"19-36"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030965","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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