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}
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}
Dynamic suboptimal control of a heat pump/heat storage system, recovering heat from a ground source and supplying it to a building via a storage tank, is investigated when the utilities offer time-of-day energy price incentives. On the basis of the analytical solution to the periodic optimization problem,1 suboptimal trajectories for the general time-varying case are developed and a method for dealing with transition trajectories from one day to the next is given. The transition trajectories are very close to the numerically generated optimal trajectories and are simple enough to be implemented on microprocessors by use of standard PI controllers.
{"title":"Dynamic suboptimal control of a heat pump/heat storage system","authors":"M. Zaheeruddin, V. Gourishankar, R. Rink","doi":"10.1002/OCA.4660090402","DOIUrl":"https://doi.org/10.1002/OCA.4660090402","url":null,"abstract":"Dynamic suboptimal control of a heat pump/heat storage system, recovering heat from a ground source and supplying it to a building via a storage tank, is investigated when the utilities offer time-of-day energy price incentives. On the basis of the analytical solution to the periodic optimization problem,1 suboptimal trajectories for the general time-varying case are developed and a method for dealing with transition trajectories from one day to the next is given. The transition trajectories are very close to the numerically generated optimal trajectories and are simple enough to be implemented on microprocessors by use of standard PI controllers.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"52 1","pages":"341-355"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090402","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031845","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 approximation technique is developed for the steady-state solution of the time-varying matrix Riccati equation. We show how the Newton-type algorithm of Kleinman, developed for computing the steady solution to the algebraic Riccati equation for time-invariant systems, can be extended for time-varying linear systems. The time-varying case is considerably more involved than the time-invariant one. Consider a linear time-varying system x(t) = F(t)x(t) + G(t)u(t). If (F, G) is uniformly completely controllable, we show how one can construct a recursive sequence of matrix functions (using linear techniques) which converge to the steady-state solution of the associated time-varying matrix Riccati equation (a non-linear object). At each successive state, the next approximation is in terms of the steady-state solution to a linear Lyapunov differential equation (which is the extension of the algebraic Lyapunov equations used by Kleinman) for which an explicit expression exists. This provides an approximation technique for obtaining infinite-time, linear-quadratic, optimal controllers and steady-state Kalman—Bucy filters for time-varying systems using purely linear techniques. Thus, we provide new types of suboptimal stabilizing feedback laws for linear time-varying systems.
{"title":"A Newton‐like approximation algorithm for the steady‐state solution of the riccati equation for time‐varying systems","authors":"Erol Emre, G. Knowles","doi":"10.1002/OCA.4660080207","DOIUrl":"https://doi.org/10.1002/OCA.4660080207","url":null,"abstract":"An approximation technique is developed for the steady-state solution of the time-varying matrix Riccati equation. We show how the Newton-type algorithm of Kleinman, developed for computing the steady solution to the algebraic Riccati equation for time-invariant systems, can be extended for time-varying linear systems. The time-varying case is considerably more involved than the time-invariant one. Consider a linear time-varying system x(t) = F(t)x(t) + G(t)u(t). If (F, G) is uniformly completely controllable, we show how one can construct a recursive sequence of matrix functions (using linear techniques) which converge to the steady-state solution of the associated time-varying matrix Riccati equation (a non-linear object). At each successive state, the next approximation is in terms of the steady-state solution to a linear Lyapunov differential equation (which is the extension of the algebraic Lyapunov equations used by Kleinman) for which an explicit expression exists. This provides an approximation technique for obtaining infinite-time, linear-quadratic, optimal controllers and steady-state Kalman—Bucy filters for time-varying systems using purely linear techniques. Thus, we provide new types of suboptimal stabilizing feedback laws for linear time-varying systems.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 1","pages":"191-197"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030591","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":"Advances in Industrial Engineering: Volume 3. Analysis And Design Of Hierarchical Control Systems, With Special Reference to Steel Plant Operations, Theodore J. Williams (ed.), Elsevier Science Publishers, Amsterdam, 1985, ISBN: 044442508‐X, US$59–95/Df1335–00, LXII + 524pp.","authors":"M. Johnson","doi":"10.1002/OCA.4660090212","DOIUrl":"https://doi.org/10.1002/OCA.4660090212","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"224-224"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031193","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 monopolistic firm is considered that can choose between two production activities: a capital-intensive one and a labor-intensive one. The successive stages of evolution of the firm are discussed for several alternative formulations of the objective functional. The effect of a minimum employment constraint is investigated and other sensitivity results are provided.
{"title":"A Dynamic activity analysis for a monopolistic firm","authors":"R. Hartl","doi":"10.1002/OCA.4660090304","DOIUrl":"https://doi.org/10.1002/OCA.4660090304","url":null,"abstract":"A monopolistic firm is considered that can choose between two production activities: a capital-intensive one and a labor-intensive one. The successive stages of evolution of the firm are discussed for several alternative formulations of the objective functional. The effect of a minimum employment constraint is investigated and other sensitivity results are provided.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"253-272"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090304","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031226","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}
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