{"title":"Functional Analysis and Linear Control Theory, J. R. Leigh, Academic Press, London, 1980. Price: £12.00. No of pages: 160.","authors":"D. Owens","doi":"10.1002/OCA.4660030209","DOIUrl":"https://doi.org/10.1002/OCA.4660030209","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"3 1","pages":"206-207"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030209","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028001","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":"Optimal resource depletion: Free end time problems","authors":"D. Burghes, S. Lyle, N. Nichols","doi":"10.1002/OCA.4660030306","DOIUrl":"https://doi.org/10.1002/OCA.4660030306","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"18 1","pages":"283-291"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030306","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028084","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}
Using the technique of Wan and Davis, we give an existence theorem for a Nash equilibrium point in N-person non-zero sum stochastic jump differential games. It is shown that if the Nash condition (generalized Isaacs condition) holds there is a Nash equilibrium point in feedback strategies. We extend the results to other solution concepts and discuss applications and extensions.
{"title":"On existence of a Nash equilibrium point in N-person non-zero sum stochastic jump differential games","authors":"B. Wernerfelt","doi":"10.1002/OCA.4660090408","DOIUrl":"https://doi.org/10.1002/OCA.4660090408","url":null,"abstract":"Using the technique of Wan and Davis, we give an existence theorem for a Nash equilibrium point in N-person non-zero sum stochastic jump differential games. It is shown that if the Nash condition (generalized Isaacs condition) holds there is a Nash equilibrium point in feedback strategies. We extend the results to other solution concepts and discuss applications and extensions.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"449-456"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090408","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031599","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 presents a deterministic time-domain approach to z-domain model identification. Coefficients for a discrete transfer function model of specified order are determined by matching the model's impulse response to that of an observed system. Interestingly, the specialized identification equations that result coincide with those from the conventional least-squares theory using regression models and thus provide a link between the deterministic and stochastic theories. The technique is applied to the model reduction problem for discrete linear systems.
{"title":"Impulse response matching for z-Domain identification with application to model order reduction","authors":"David F. Miller","doi":"10.1002/OCA.4660090209","DOIUrl":"https://doi.org/10.1002/OCA.4660090209","url":null,"abstract":"This paper presents a deterministic time-domain approach to z-domain model identification. Coefficients for a discrete transfer function model of specified order are determined by matching the model's impulse response to that of an observed system. Interestingly, the specialized identification equations that result coincide with those from the conventional least-squares theory using regression models and thus provide a link between the deterministic and stochastic theories. The technique is applied to the model reduction problem for discrete linear systems.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"209-214"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090209","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031159","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":"Reviewers for 1979–1980","authors":"B. Pierson","doi":"10.1002/OCA.4660020112","DOIUrl":"https://doi.org/10.1002/OCA.4660020112","url":null,"abstract":"","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"101-105"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020112","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027910","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}
Recent results in design differentiation of structural displacement are used to develop an iterative optimization method that explicitly treats bounds on the maximum displacement of structural elements. Computable design derivative expressions are employed, and a finite-element computational algorithm is presented for obtaining design derivatives needed in structural optimization. A function-space, gradient-projection, optimization technique which uses these derivatives is presented. The method is applied to beam and plate optimization problems to illustrate its use and to evaluate its computational efficiency. Results obtained using this method are compared with solutions reported in the literature. The method is shown to be both generally applicable and numerically efficient.
{"title":"A Numerical method for optimization of distributed parameter structures with displacement constraints","authors":"E. Haug","doi":"10.1002/OCA.4660030305","DOIUrl":"https://doi.org/10.1002/OCA.4660030305","url":null,"abstract":"Recent results in design differentiation of structural displacement are used to develop an iterative optimization method that explicitly treats bounds on the maximum displacement of structural elements. Computable design derivative expressions are employed, and a finite-element computational algorithm is presented for obtaining design derivatives needed in structural optimization. A function-space, gradient-projection, optimization technique which uses these derivatives is presented. The method is applied to beam and plate optimization problems to illustrate its use and to evaluate its computational efficiency. Results obtained using this method are compared with solutions reported in the literature. The method is shown to be both generally applicable and numerically efficient.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"11 1","pages":"269-282"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030305","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028070","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}
Feedback control for systems described by linear parabolic partial differential equations is considered from a time suboptimal point of view. A scalar quadratic function representing the deviation from a desired distribution is first formulated, and the rate of approach to the target is maximized by minimizing this quadratic function at each time step. An orthogonal collocation technique enables an accurate low-order lumped parameter model to be constructed. A direct search optimization can then be used to obtain the optimal quadratic function and, subsequently, the optimal feedback gain matrix for control. The resulting control applied to a diffusion process takes the system to the target rapidly and in a stable manner.
{"title":"Time suboptimal feedback control of systems described by linear parabolic partial differential equations","authors":"Kin Tuck Wong, R. Luus","doi":"10.1002/OCA.4660030206","DOIUrl":"https://doi.org/10.1002/OCA.4660030206","url":null,"abstract":"Feedback control for systems described by linear parabolic partial differential equations is considered from a time suboptimal point of view. A scalar quadratic function representing the deviation from a desired distribution is first formulated, and the rate of approach to the target is maximized by minimizing this quadratic function at each time step. An orthogonal collocation technique enables an accurate low-order lumped parameter model to be constructed. A direct search optimization can then be used to obtain the optimal quadratic function and, subsequently, the optimal feedback gain matrix for control. The resulting control applied to a diffusion process takes the system to the target rapidly and in a stable manner.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"3 1","pages":"177-185"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660030206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51028462","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}
Consideration is given to the lower level of a hierarchical optimization structure for evaluating optimized control schedules for common types of water distribution systems. The structure is presented in Part I. The lower-level optimization problem involves independent optimization of a number of generalized pump stations. This requires minimization of individual pump station consumed power. An algorithm for the pump station power minimization is proposed and its convergence and optimality properties are investigated. The algorithm is tested over a range of physical data. Typical results are presented, which include comparisons with an alternative solution method.
{"title":"A Hierarchical approach to optimized control of water distribution systems: Part II. Lower‐level algorithm","authors":"B. Coulbeck, M. Brdys, C. Orr, J. Rance","doi":"10.1002/OCA.4660090202","DOIUrl":"https://doi.org/10.1002/OCA.4660090202","url":null,"abstract":"Consideration is given to the lower level of a hierarchical optimization structure for evaluating optimized control schedules for common types of water distribution systems. The structure is presented in Part I. The lower-level optimization problem involves independent optimization of a number of generalized pump stations. This requires minimization of individual pump station consumed power. An algorithm for the pump station power minimization is proposed and its convergence and optimality properties are investigated. The algorithm is tested over a range of physical data. Typical results are presented, which include comparisons with an alternative solution method.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"9 1","pages":"109-126"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090202","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031079","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 this paper a control algorithm that minimizes the auxiliary energy consumption in a typical solar cooling system while maintaining appropriate comfortable conditions in the cooled enclosure is devised. A dynamic mathematical model for a lithium bromide-water absorption chiller is developed to be used for deriving the optimal control algorithm. Finally, the results of simulation of the optimal control algorithm indicate that a net reduction of more than 30% in auxiliary energy is possible.
{"title":"Optimal control of solar cooling systems","authors":"M. Salman, S. Kotob, M. Juraidan","doi":"10.1002/OCA.4660090207","DOIUrl":"https://doi.org/10.1002/OCA.4660090207","url":null,"abstract":"In this paper a control algorithm that minimizes the auxiliary energy consumption in a typical solar cooling system while maintaining appropriate comfortable conditions in the cooled enclosure is devised. A dynamic mathematical model for a lithium bromide-water absorption chiller is developed to be used for deriving the optimal control algorithm. Finally, the results of simulation of the optimal control algorithm indicate that a net reduction of more than 30% in auxiliary energy is possible.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"316 1","pages":"187-199"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660090207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51031126","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}
Consider the random motion of two points Me and Mp in an open and bounded domain D0 in the plane. Each of the velocities, u = (u1 u2)T of Me and v = (v1, v2)T of Mp, are perturbed by a corresponding R2-valued Gaussian white noise. Let A and Dc be two disjoint closed subsets of D0. Suppose that at t = 0, Me is in A and Mp is anywhere in D0. Denote by ℰ1 and ℰ2 the following events: ℰ1 = {Mp intercepts Me in A before Me reaches the set Dc and before either Me or Mp has left D0}, and ℰ2 = {Me reaches the set Dc before being intercepted by Mp, while Mp is in A, and before either Mp or Me has left D0}. The problem dealt with here is to find a pair of velocity strategies (u*, v*) such that, in the sense of a Nash equilibrium point, the probabilities Prob(ℰ1) and Prob(ℰ2) will both be maximized on a given class of velocity strategies (u, v). Sufficient conditions on (u*, v*) are derived which require the existence of a smooth solution (V,Q) to a pair of coupled non-linear partial differential equations. A finite-difference scheme for solving these equations is suggested, and two examples are treated in detail.
{"title":"Computation of nash equilibrium pairs of a stochastic differential game","authors":"Y. Yavin, G. Reuter","doi":"10.1002/OCA.4660020303","DOIUrl":"https://doi.org/10.1002/OCA.4660020303","url":null,"abstract":"Consider the random motion of two points Me and Mp in an open and bounded domain D0 in the plane. Each of the velocities, u = (u1 u2)T of Me and v = (v1, v2)T of Mp, are perturbed by a corresponding R2-valued Gaussian white noise. Let A and Dc be two disjoint closed subsets of D0. Suppose that at t = 0, Me is in A and Mp is anywhere in D0. Denote by ℰ1 and ℰ2 the following events: ℰ1 = {Mp intercepts Me in A before Me reaches the set Dc and before either Me or Mp has left D0}, and ℰ2 = {Me reaches the set Dc before being intercepted by Mp, while Mp is in A, and before either Mp or Me has left D0}. \u0000 \u0000 \u0000 \u0000The problem dealt with here is to find a pair of velocity strategies (u*, v*) such that, in the sense of a Nash equilibrium point, the probabilities Prob(ℰ1) and Prob(ℰ2) will both be maximized on a given class of velocity strategies (u, v). Sufficient conditions on (u*, v*) are derived which require the existence of a smooth solution (V,Q) to a pair of coupled non-linear partial differential equations. A finite-difference scheme for solving these equations is suggested, and two examples are treated in detail.","PeriodicalId":54672,"journal":{"name":"Optimal Control Applications & Methods","volume":"2 1","pages":"225-238"},"PeriodicalIF":1.8,"publicationDate":"2007-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/OCA.4660020303","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51027801","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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