Several direct optimization algorithms for dynamic non-linear optimal control problems with bounded control inputs are reviewed. The algorithms are based on well-known conjugate gradient and variable metric methods for unconstrained optimization. Scaling is shown to improve the algorithms' performance considerably. Comparison of the algorithms is provided for a real-life example of sewer network flow control.
{"title":"Comparison of direct optimization algorithms for dynamic network flow control","authors":"M. Papageorgiou, R. Mayr","doi":"10.1002/OCA.4660090206","DOIUrl":"https://doi.org/10.1002/OCA.4660090206","url":null,"abstract":"Several direct optimization algorithms for dynamic non-linear optimal control problems with bounded control inputs are reviewed. The algorithms are based on well-known conjugate gradient and variable metric methods for unconstrained optimization. Scaling is shown to improve the algorithms' performance considerably. Comparison of the algorithms is provided for a real-life example of sewer network flow control.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"175-185"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031116","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 path of an industrial manipulator in a crowded workspace generally consists of a set of Cartesian straight-line segments connecting a set of two adjacent points. To achieve the Cartesian straight-line path (segment) is, however, a non-trivial task, and an alternative approach is to place enough intermediate points along a desired path and linearly interpolate between these points in the joint space. A method is developed that determines the subtravelling and transition times such that the total travelling time for this path is minimized subject to the maximum joint velocity and acceleration constraints. These results are simulated on a digital computer using a six-joint revolute manipulator to show their applications.
{"title":"Optimal time joint‐trajectory planning for an industrial manipulator using linear interpolation","authors":"H. Jeon, M. Eslami","doi":"10.1002/OCA.4660090210","DOIUrl":"https://doi.org/10.1002/OCA.4660090210","url":null,"abstract":"The path of an industrial manipulator in a crowded workspace generally consists of a set of Cartesian straight-line segments connecting a set of two adjacent points. To achieve the Cartesian straight-line path (segment) is, however, a non-trivial task, and an alternative approach is to place enough intermediate points along a desired path and linearly interpolate between these points in the joint space. A method is developed that determines the subtravelling and transition times such that the total travelling time for this path is minimized subject to the maximum joint velocity and acceleration constraints. These results are simulated on a digital computer using a six-joint revolute manipulator to show their applications.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"215-221"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090210","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031170","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":"The control of environmental pollution and optimal investment and employment decisions: a comment","authors":"R. Hartl","doi":"10.1002/OCA.4660090310","DOIUrl":"https://doi.org/10.1002/OCA.4660090310","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"337-339"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090310","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031416","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 well known problem of the optimal control of a stochastic discrete linear system with independent parameters and with a quadratic objective functional is generalized to the case where the parameters of the system constitute a first-order Markov chain. The solution to this more general problem is obtained by the principles of stochastic dynamic programming, and the ‘bi-feedback’ nature of the optimal controls is explained. The results are applied to the solution of a 25-period stochastic pension funding problem where it is assumed that the market returns constitute a first-order Markov chain.
{"title":"Stochastic control of a pension fund model with first‐order Markov‐dependent parameters","authors":"M. Parlar","doi":"10.1002/OCA.4660020206","DOIUrl":"https://doi.org/10.1002/OCA.4660020206","url":null,"abstract":"The well known problem of the optimal control of a stochastic discrete linear system with independent parameters and with a quadratic objective functional is generalized to the case where the parameters of the system constitute a first-order Markov chain. The solution to this more general problem is obtained by the principles of stochastic dynamic programming, and the ‘bi-feedback’ nature of the optimal controls is explained. The results are applied to the solution of a 25-period stochastic pension funding problem where it is assumed that the market returns constitute a first-order Markov chain.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"175-189"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027567","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 direct method for solving optimal control problems by parameterizing state variables is developed. This state parameterization (SP) procedure is first formulated for a general class of problem. Next, a simpler and more efficient alternative version of the SP algorithm is developed for an important special class of problems, namely those involving systems that can be cast into a multivariable non-linear phase-variable form. The modified SP algorithm in particular avoids explicit integration of the system state and costate differential equations. The algorithm is tested on two problems which are parameterized in terms of cubic splines.
{"title":"State parameterization approach to the solution of optimal control problems","authors":"H. Sirisena, F. Chou","doi":"10.1002/OCA.4660020307","DOIUrl":"https://doi.org/10.1002/OCA.4660020307","url":null,"abstract":"A direct method for solving optimal control problems by parameterizing state variables is developed. This state parameterization (SP) procedure is first formulated for a general class of problem. Next, a simpler and more efficient alternative version of the SP algorithm is developed for an important special class of problems, namely those involving systems that can be cast into a multivariable non-linear phase-variable form. The modified SP algorithm in particular avoids explicit integration of the system state and costate differential equations. The algorithm is tested on two problems which are parameterized in terms of cubic splines.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"289-298"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020307","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027874","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":"Applied Optimal Design: Mechanical and Structural Systems, Ed Ward J. Haug and Jasbir S. Arora, Wiley-Interscience, New York, 1979. No. of pages: 506. Price: $28.50.","authors":"I. Ebcioǧlu, W. Boykin","doi":"10.1002/OCA.4660020110","DOIUrl":"https://doi.org/10.1002/OCA.4660020110","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"95-96"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020110","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027900","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 addresses the problem of parameter sensitivity reduction in linear regulators. It is shown that the minimization of a modified performance index which includes a quadratic term of trajectory sensitivity (state, output, or control) subject to the augmented sensitivity system dynamics causes reduction not only in trajectory sensitivity but also in cost sensitivity. Inclusion of both state sensitivity and control sensitivity terms in the cost functional reduces cost sensitivity and facilitates the unification of two approaches previously treated independently: ‘trajectory sensitivity reduction’ and ‘cost sensitivity reduction’. Two control design methods, one based on a linear formulation and the other on a non-linear formulation, are given for both deterministic and stochastic systems. The improvement of these methods over existing methods is illustrated by examples.
{"title":"Controller design for parameter sensitivity reduction in linear regulators","authors":"R. Yedavalli, R. Skelton","doi":"10.1002/OCA.4660030302","DOIUrl":"https://doi.org/10.1002/OCA.4660030302","url":null,"abstract":"This paper addresses the problem of parameter sensitivity reduction in linear regulators. It is shown that the minimization of a modified performance index which includes a quadratic term of trajectory sensitivity (state, output, or control) subject to the augmented sensitivity system dynamics causes reduction not only in trajectory sensitivity but also in cost sensitivity. Inclusion of both state sensitivity and control sensitivity terms in the cost functional reduces cost sensitivity and facilitates the unification of two approaches previously treated independently: ‘trajectory sensitivity reduction’ and ‘cost sensitivity reduction’. Two control design methods, one based on a linear formulation and the other on a non-linear formulation, are given for both deterministic and stochastic systems. The improvement of these methods over existing methods is illustrated by examples.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"90 1","pages":"221-240"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030302","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028041","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":"Oracls: A Design system for linear multivariable control, Ernest S. Armstrong, Volume 10, Control and Systems Theory, Marcel Dekker Inc., New York, 1980. No. of pages: ix + 244. Price: 114 Sw. Fr. ISBN 08247 12390.","authors":"M. Johnson","doi":"10.1002/OCA.4660030310","DOIUrl":"https://doi.org/10.1002/OCA.4660030310","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"22 1","pages":"301-301"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030310","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028213","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 develops an optimal control model for the firm's decision-making concerning pollution control spending, employment and investment. The model explicitly considers the impact of adjustment costs of changing the level of the pollution stock and involves three state variables and two control variables. Necessary conditions are derived by the maximum principle. The results include an optimal employment-investment-pollution abatement programme, an optimal pollution control decision rule, the equilibrium optimal pollution control and spending plan, and the equilibrium employment-investment decision.
{"title":"The control of environmental pollution and optimal investment and employment decisions","authors":"Winston T. Lin","doi":"10.1002/OCA.4660080103","DOIUrl":"https://doi.org/10.1002/OCA.4660080103","url":null,"abstract":"This paper develops an optimal control model for the firm's decision-making concerning pollution control spending, employment and investment. The model explicitly considers the impact of adjustment costs of changing the level of the pollution stock and involves three state variables and two control variables. Necessary conditions are derived by the maximum principle. The results include an optimal employment-investment-pollution abatement programme, an optimal pollution control decision rule, the equilibrium optimal pollution control and spending plan, and the equilibrium employment-investment decision.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"248 1","pages":"21-36"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030881","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 problem of optimal freeways traffic control is described by a detailed non-linear discrete-time model. A four-level hierarchical algorithm is developed to compute the optimal control strategies. Simulation results indicate the efficiency of the developed algorithm in bringing congested traffic flow back to normal operation.
{"title":"Optimization of freeway traffic control problems","authors":"M. S. Mahmoud, S. Eid","doi":"10.1002/OCA.4660090104","DOIUrl":"https://doi.org/10.1002/OCA.4660090104","url":null,"abstract":"The problem of optimal freeways traffic control is described by a detailed non-linear discrete-time model. A four-level hierarchical algorithm is developed to compute the optimal control strategies. Simulation results indicate the efficiency of the developed algorithm in bringing congested traffic flow back to normal operation.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"37-49"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090104","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030978","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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