This paper gives a characterization of the smallest upper bound on the norm of the sensitivity matrix over a frequency interval, with the constraint that the norm remain bounded at all frequencies. The matrix Nevanlinna-Pick interpolation theory is applied to give a necessary and sufficient condition for the existence of a sensitivity matrix meeting the upper bound conditions on the j¿-axis, and the matrix Nevanlinna-Pick algorithm is used to compute the bounds. A scalar example is also presented to demonstrate the trade-offs between the bounds inside and outside a given operating frequency band.
{"title":"Sensitivity trade-offs for multivariable plants","authors":"S. O'Young, B. Francis","doi":"10.1109/CDC.1984.272362","DOIUrl":"https://doi.org/10.1109/CDC.1984.272362","url":null,"abstract":"This paper gives a characterization of the smallest upper bound on the norm of the sensitivity matrix over a frequency interval, with the constraint that the norm remain bounded at all frequencies. The matrix Nevanlinna-Pick interpolation theory is applied to give a necessary and sufficient condition for the existence of a sensitivity matrix meeting the upper bound conditions on the j¿-axis, and the matrix Nevanlinna-Pick algorithm is used to compute the bounds. A scalar example is also presented to demonstrate the trade-offs between the bounds inside and outside a given operating frequency band.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124361687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Looze, S. Krolewski, J. Weiss, J. Eterno, S. Gully
This paper presents an approach to the automatic redesign of flight control systems for aircraft that have suffered one or more control element failures. The procedure is based on Linear Quadratic design techniques, and produces a control system that maximizes a measure of feedback system performance subject to a bandwidth constraint.
{"title":"An approach to restructurable control system design","authors":"D. Looze, S. Krolewski, J. Weiss, J. Eterno, S. Gully","doi":"10.1109/CDC.1984.272266","DOIUrl":"https://doi.org/10.1109/CDC.1984.272266","url":null,"abstract":"This paper presents an approach to the automatic redesign of flight control systems for aircraft that have suffered one or more control element failures. The procedure is based on Linear Quadratic design techniques, and produces a control system that maximizes a measure of feedback system performance subject to a bandwidth constraint.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125731720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let Sn be the manifold of linear constant systems over R, with m inputs, p outputs, and n-dimensional state space. In this paper, we are concerned with the subset Sn,l of Sn, consisting in systems whose cyclic structure is l. It is first stated to be a submanifold of Sn, and an atlas is given for it. When l ranges over all cyclic structures, (Sn,l) is a partition of Sn, one element of which is open (and dense), namely the submanifold of cyclic systems. We then introduce special factorizations for transfer functions, which allow us to give another parametrization for Sn,l, in particular, transfer functions of cyclic systems admit a rather simple description. As this paper is a shortened version of [2], most proofs are omitted.
{"title":"On the parametrization of linear systems with given cyclic structure","authors":"L. Baratchart","doi":"10.1109/CDC.1984.272314","DOIUrl":"https://doi.org/10.1109/CDC.1984.272314","url":null,"abstract":"Let Sn be the manifold of linear constant systems over R, with m inputs, p outputs, and n-dimensional state space. In this paper, we are concerned with the subset Sn,l of Sn, consisting in systems whose cyclic structure is l. It is first stated to be a submanifold of Sn, and an atlas is given for it. When l ranges over all cyclic structures, (Sn,l) is a partition of Sn, one element of which is open (and dense), namely the submanifold of cyclic systems. We then introduce special factorizations for transfer functions, which allow us to give another parametrization for Sn,l, in particular, transfer functions of cyclic systems admit a rather simple description. As this paper is a shortened version of [2], most proofs are omitted.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121943246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The extraordinary and little known nonconvex non-linear program solving algorithm of Garcia and Zangwill (G-Z) [8-11] is shown to be suitable for exactly computing the stability margin of diagonally perturbed multivariable feedback systems, even when the number of perturbations exceeds the number three.
Garcia and Zangwill (G-Z)[8-11]的非凡且鲜为人知的非凸非线性规划求解算法被证明适用于精确计算对角摄动多变量反馈系统的稳定余量，即使摄动数超过3。
{"title":"Exact calculation of the multivariable structured-singular-value stability margin","authors":"M. Safonov","doi":"10.1109/CDC.1984.272213","DOIUrl":"https://doi.org/10.1109/CDC.1984.272213","url":null,"abstract":"The extraordinary and little known nonconvex non-linear program solving algorithm of Garcia and Zangwill (G-Z) [8-11] is shown to be suitable for exactly computing the stability margin of diagonally perturbed multivariable feedback systems, even when the number of perturbations exceeds the number three.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122260982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Here we are studying the minimization problem of an integral discounted functional, on a set of non-explosive and non constrained diffusions. The integrand is "weakly coercive", which leads us, using the dynamic programming method, to characterize the optimal cost among the solutions of the solving equation, with radiative conditions expessing the centripetal aspect of the optimal control. The evolution of the problem when the discount vanishes is then considered: the integrand being "strongly coercive" (i.e. its gradient being outward), a limit problem is defined and similarly solved; an inward optimal control exists, which is the limit of the ones of the initial problems. The existence properties are obtained by means of a priori estimates concerning suitable solutions of the solving equations in the whole space.
{"title":"Asymptotic evolution of a stochastic control problem","authors":"R. Tarres","doi":"10.1109/CDC.1984.272443","DOIUrl":"https://doi.org/10.1109/CDC.1984.272443","url":null,"abstract":"Here we are studying the minimization problem of an integral discounted functional, on a set of non-explosive and non constrained diffusions. The integrand is \"weakly coercive\", which leads us, using the dynamic programming method, to characterize the optimal cost among the solutions of the solving equation, with radiative conditions expessing the centripetal aspect of the optimal control. The evolution of the problem when the discount vanishes is then considered: the integrand being \"strongly coercive\" (i.e. its gradient being outward), a limit problem is defined and similarly solved; an inward optimal control exists, which is the limit of the ones of the initial problems. The existence properties are obtained by means of a priori estimates concerning suitable solutions of the solving equations in the whole space.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121729681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper extends the well-known norm-bounded robust stability criteria from strict inequalities that specify open sets to inequalities that specify closed sets. Both the Nyquist and inverse Nyquist type of norm-bounded criteria are considered. The extended criteria form the theoretical basis in the formulation of an iterative procedure for searching the regions of stability for simultaneous gain or phase variations in multivariable feedback systems. The basic idea of the iterative procedure lies in successively perturbing the feedback system from a set of nominal gains or phases that are on the boundary of a previously established region of stability. The iterative procedure is illustrated by a numerical example.
{"title":"Regions of stability for gain or phase variations in multivariable systems","authors":"H. Yeh, S. Banda, D. Ridgely","doi":"10.1109/CDC.1984.272269","DOIUrl":"https://doi.org/10.1109/CDC.1984.272269","url":null,"abstract":"This paper extends the well-known norm-bounded robust stability criteria from strict inequalities that specify open sets to inequalities that specify closed sets. Both the Nyquist and inverse Nyquist type of norm-bounded criteria are considered. The extended criteria form the theoretical basis in the formulation of an iterative procedure for searching the regions of stability for simultaneous gain or phase variations in multivariable feedback systems. The basic idea of the iterative procedure lies in successively perturbing the feedback system from a set of nominal gains or phases that are on the boundary of a previously established region of stability. The iterative procedure is illustrated by a numerical example.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131349901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we develop a state space model for motion of an airfoil in two-dimensional unsteady flow, of an inviscid, incompressible fluid. Then we show that the solution exists, is unique and depends continuously on the initial data. Of particular importance in the context of the present work is the fact that the L-Q-R theory has been extended to such systems and thus may provide appropriate design tools for flutter suppression problems.
{"title":"Modelling and control of aircraft flutter problem","authors":"Shyang Chang","doi":"10.1109/CDC.1984.272198","DOIUrl":"https://doi.org/10.1109/CDC.1984.272198","url":null,"abstract":"In this paper we develop a state space model for motion of an airfoil in two-dimensional unsteady flow, of an inviscid, incompressible fluid. Then we show that the solution exists, is unique and depends continuously on the initial data. Of particular importance in the context of the present work is the fact that the L-Q-R theory has been extended to such systems and thus may provide appropriate design tools for flutter suppression problems.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"515 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132519815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we address the stabilizability of large-scale power systems when in the presence of bounded-but-unknown uncertainty. Test conditions on a system are given such that when satisfied, the system is guaranteed L2-stabilizable via decentralized control. A multi-machine power system model is formulated to which these test conditions can readily be applied. An example is given in which a 9-bus 3-machine system is stabilized with decentralized control when in the presence of structural perturbations.
{"title":"Decentralized stabilizability conditions for large-scale electric power systems","authors":"M. García-Rubio, R. Thomas","doi":"10.1109/CDC.1984.272317","DOIUrl":"https://doi.org/10.1109/CDC.1984.272317","url":null,"abstract":"In this paper, we address the stabilizability of large-scale power systems when in the presence of bounded-but-unknown uncertainty. Test conditions on a system are given such that when satisfied, the system is guaranteed L2-stabilizable via decentralized control. A multi-machine power system model is formulated to which these test conditions can readily be applied. An example is given in which a 9-bus 3-machine system is stabilized with decentralized control when in the presence of structural perturbations.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130136981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper concerns the optimal stopping time problem for a piecewise deterministic process. The associated dynamic programming equation is a variational inequality with integral and first order differential terms Our main results are W1,¿-existence results and probabilistic representations for the solutions of these variational inequalities in bounded domains and in IRn.
{"title":"Optimal stopping time of a piecewise-deterministic process","authors":"S. Lenhart, Y. Liao","doi":"10.1109/CDC.1984.272383","DOIUrl":"https://doi.org/10.1109/CDC.1984.272383","url":null,"abstract":"This paper concerns the optimal stopping time problem for a piecewise deterministic process. The associated dynamic programming equation is a variational inequality with integral and first order differential terms Our main results are W1,¿-existence results and probabilistic representations for the solutions of these variational inequalities in bounded domains and in IRn.","PeriodicalId":269680,"journal":{"name":"The 23rd IEEE Conference on Decision and Control","volume":"63 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1984-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131830062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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