Polynomial Diophantine equations can be used to solve pole-placement problems and linear quadratic Gaussian (LQG) optimal control problems, for both analogue and digital single-input-single-output (SISO) systems. A description is presented of the how these algorithms are implemented in Program CC, a user-friendly, command driven, computer-aided-control-system-design (CACSD) package.
{"title":"Program CC's implementation of pole‐placement and lqg algorithms using diophantine equations","authors":"P. Thompson","doi":"10.1002/OCA.4660080107","DOIUrl":"https://doi.org/10.1002/OCA.4660080107","url":null,"abstract":"Polynomial Diophantine equations can be used to solve pole-placement problems and linear quadratic Gaussian (LQG) optimal control problems, for both analogue and digital single-input-single-output (SISO) systems. A description is presented of the how these algorithms are implemented in Program CC, a user-friendly, command driven, computer-aided-control-system-design (CACSD) package.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 1","pages":"91-101"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030442","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":"Numerical Analysis, L. W. Johnson and R. Dean Riess, Addison-Wesley, 1982. Price: £16.95 No. of-Dages: 563. ISBN: 0 201 10392–3.","authors":"S. Pulko","doi":"10.1002/OCA.4660080111","DOIUrl":"https://doi.org/10.1002/OCA.4660080111","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 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.4660080111","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030528","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}
We consider a one-reach water quality system subject not only to bounded uncertain disturbances at the input and output levels but also to bounded uncertain variations of the rate coefficients. When the bounds of the time-varying uncertainties are known, two classes of robust controllers, based on the measured state, are proposed to assure some desired performance, including uniform boundedness and uniform ultimate boundedness. If only output rather than full state is available for the control, a class of estimated state-based control is proposed for the desired performance. When the bounds of the uncertainties are not known, we propose a class of controllers which, using the functional properties of the uncertainties, guarantees some desired system properties, one of which is the convergence to zero of all system responses.
{"title":"On the control of an uncertain water quality system","authors":"Y. Chen, C. S. Lee","doi":"10.1002/OCA.4660080309","DOIUrl":"https://doi.org/10.1002/OCA.4660080309","url":null,"abstract":"We consider a one-reach water quality system subject not only to bounded uncertain disturbances at the input and output levels but also to bounded uncertain variations of the rate coefficients. When the bounds of the time-varying uncertainties are known, two classes of robust controllers, based on the measured state, are proposed to assure some desired performance, including uniform boundedness and uniform ultimate boundedness. If only output rather than full state is available for the control, a class of estimated state-based control is proposed for the desired performance. When the bounds of the uncertainties are not known, we propose a class of controllers which, using the functional properties of the uncertainties, guarantees some desired system properties, one of which is the convergence to zero of all system responses.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 1","pages":"279-298"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080309","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030848","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 stochastic (diffusion) sales response model to advertising is postulated. Optimum advertising policies are then found by solving a stochastic control problem with reflecting boundaries. Analytical results are obtained and interpreted to yield insights regarding a firm's risk behaviour and its optimal advertising policy.
{"title":"Risk behaviour and optimum advertising with a stochastic dynamic sales response","authors":"C. Tapiero, J. Eliashberg, Y. Wind","doi":"10.1002/OCA.4660080310","DOIUrl":"https://doi.org/10.1002/OCA.4660080310","url":null,"abstract":"A stochastic (diffusion) sales response model to advertising is postulated. Optimum advertising policies are then found by solving a stochastic control problem with reflecting boundaries. Analytical results are obtained and interpreted to yield insights regarding a firm's risk behaviour and its optimal advertising policy.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"8 1","pages":"299-304"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080310","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030859","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}
M. Bartholomew-Biggs, L. Dixon, S. Hersom, Z. Maany
This paper deals with an approach to the problem of spacecraft trajectory optimization that has been successful on a wide range of practical examples. A particular group of missions involving low-thrust solar-powered vehicles has presented difficulties for the method, however, and these are described and discussed. In particular the problems seem to reveal weaknesses in some current algorithms for constrained minimization, and we therefore consider some new optimization routines. We also derive a new formulation of the problem using eccentricity and momentum vectors as state variables rather than the more usual Cartesian co-ordinates. This reformulation allows us to make some simplifying assumptions which make the problem easier to solve while still furnishing good estimates of the true optimum.
{"title":"The solution of some difficult problems in low-thrust interplanetary trajectory optimization†","authors":"M. Bartholomew-Biggs, L. Dixon, S. Hersom, Z. Maany","doi":"10.1002/OCA.4660090303","DOIUrl":"https://doi.org/10.1002/OCA.4660090303","url":null,"abstract":"This paper deals with an approach to the problem of spacecraft trajectory optimization that has been successful on a wide range of practical examples. A particular group of missions involving low-thrust solar-powered vehicles has presented difficulties for the method, however, and these are described and discussed. In particular the problems seem to reveal weaknesses in some current algorithms for constrained minimization, and we therefore consider some new optimization routines. We also derive a new formulation of the problem using eccentricity and momentum vectors as state variables rather than the more usual Cartesian co-ordinates. This reformulation allows us to make some simplifying assumptions which make the problem easier to solve while still furnishing good estimates of the true optimum.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"229-251"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090303","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031217","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 model for a viscoelastic coating is derived and the coating reflectivity is determined. A coating which minimizes the reflection of sound waves is partly bang-bang and partly singular. A new gradient type algorithm is presented for computing the optimal control. Formulae for the gradient of the cost in optimal control are derived in various settings.
{"title":"Optimal Coatings, Bang-Bang Controls, And Gradient Techniques","authors":"W. Hager, R. Rostamian","doi":"10.1002/OCA.4660080102","DOIUrl":"https://doi.org/10.1002/OCA.4660080102","url":null,"abstract":"A model for a viscoelastic coating is derived and the coating reflectivity is determined. A coating which minimizes the reflection of sound waves is partly bang-bang and partly singular. A new gradient type algorithm is presented for computing the optimal control. Formulae for the gradient of the cost in optimal control are derived in various settings.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"855 1","pages":"1-20"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660080102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51030872","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}
Two non-linear programming algorithms based on the Lagrangian function are compared with respect to their computational efficiency for solving parameterized optimal control problems. If the most efficient, constrained variable metric method together with forward-difference gradients is used, the formulation and implementation of the adjoint variables can be avoided. This is especially convenient in the design phase of large complex systems.
{"title":"Finite-difference gradients versus error-quadrature gradients in the solution of parameterized optimal control problems","authors":"D. Kraft","doi":"10.1002/OCA.4660020207","DOIUrl":"https://doi.org/10.1002/OCA.4660020207","url":null,"abstract":"Two non-linear programming algorithms based on the Lagrangian function are compared with respect to their computational efficiency for solving parameterized optimal control problems. If the most efficient, constrained variable metric method together with forward-difference gradients is used, the formulation and implementation of the adjoint variables can be avoided. This is especially convenient in the design phase of large complex systems.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"191-199"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027579","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":"Memorial for Henry J. Kelley","authors":"E. Cliff","doi":"10.1002/OCA.4660090302","DOIUrl":"https://doi.org/10.1002/OCA.4660090302","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"225-227"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090302","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031203","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 application of a linear quadratic self-tuning control approach to a pulsed liquid-liquid extraction column is described. The control algorithm is derived from the minimization of a quadratic cost function. The resulting Riccati equation is iterated until the closed-loop poles belong to a predefined stability domain included in the unit circle. Based upon the certainty equivalence principle, the adaptive control algorithm involves a parameter identification procedure and a feedback control law which uses the estimated parameters. Several experiments are carried out on a pulsed liquid-liquid extraction column. Such extractors are being increasingly used in several industries because they are not energy-consuming and they lead to high product purity. The column considered has the same dimensions as those currently used in fine chemical processes. The control objective is to optimize the column behaviour. The selected control variables are the pulse frequency and the conductivity measured at the bottom of the column. The experiments have been carried out with a mixture of water and toluene. The physical model developed for the column is too complex to use for control purposes. To represent the complex behaviour of the column, a single-input/single-output discrete-time linear model was adopted. The parameters in the model are estimated on-line with normalized data. The forgetting factor is also adjusted to maintain a constant trace of the estimator gain matix. The results obtained show the ability of this algorithm to improve the efficiency of the process considered. Finally, some details on practical implementation are provided.
{"title":"Linear quadratic self-tuning control of a liquid-liquid extraction column","authors":"K. Najim, H. Youlal, E. Irving, M. Najim","doi":"10.1002/OCA.4660090305","DOIUrl":"https://doi.org/10.1002/OCA.4660090305","url":null,"abstract":"An application of a linear quadratic self-tuning control approach to a pulsed liquid-liquid extraction column is described. The control algorithm is derived from the minimization of a quadratic cost function. The resulting Riccati equation is iterated until the closed-loop poles belong to a predefined stability domain included in the unit circle. Based upon the certainty equivalence principle, the adaptive control algorithm involves a parameter identification procedure and a feedback control law which uses the estimated parameters. \u0000 \u0000 \u0000 \u0000Several experiments are carried out on a pulsed liquid-liquid extraction column. Such extractors are being increasingly used in several industries because they are not energy-consuming and they lead to high product purity. The column considered has the same dimensions as those currently used in fine chemical processes. The control objective is to optimize the column behaviour. The selected control variables are the pulse frequency and the conductivity measured at the bottom of the column. The experiments have been carried out with a mixture of water and toluene. The physical model developed for the column is too complex to use for control purposes. To represent the complex behaviour of the column, a single-input/single-output discrete-time linear model was adopted. The parameters in the model are estimated on-line with normalized data. The forgetting factor is also adjusted to maintain a constant trace of the estimator gain matix. \u0000 \u0000 \u0000 \u0000The results obtained show the ability of this algorithm to improve the efficiency of the process considered. Finally, some details on practical implementation are provided.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"273-284"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090305","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031237","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 is proposed to solve fixed end-point, linear optimal control problems with quadratic cost and singularly perturbed state. After translating the problem into a two-point boundary value problem, we choose two points t1, t2 ϵ [t0, tf] and let τ = (t-t0)/ϵ and σ = (tf-t)/ϵ. The τ-scaled, original and σ-scaled boundary value problems are then solved on the intervals [t0, t1], [t1, t2] and [t2, tf] respectively. A test example is solved to illustrate the method.
{"title":"A Boundary value technique for solving singularly perturbed, fixed end-point optimal control problems","authors":"M. K. Kadalbajoo, Arindama Singh","doi":"10.1002/OCA.4660090407","DOIUrl":"https://doi.org/10.1002/OCA.4660090407","url":null,"abstract":"A method is proposed to solve fixed end-point, linear optimal control problems with quadratic cost and singularly perturbed state. After translating the problem into a two-point boundary value problem, we choose two points t1, t2 ϵ [t0, tf] and let τ = (t-t0)/ϵ and σ = (tf-t)/ϵ. The τ-scaled, original and σ-scaled boundary value problems are then solved on the intervals [t0, t1], [t1, t2] and [t2, tf] respectively. A test example is solved to illustrate the method.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"88 1","pages":"443-448"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031534","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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