Pub Date : 2004-06-15DOI: 10.1080/00207720410001734192
D. Famularo, P. Pugliese, Y. Sergeyev
A global optimization algorithm is used to solve the fixed-order controller synthesis problem for linear systems. The algorithm, which belongs to the information methods family, is described in some detail and numerical experiments are performed on test problems to show its effectiveness.
{"title":"A global optimization technique for fixed-order control design","authors":"D. Famularo, P. Pugliese, Y. Sergeyev","doi":"10.1080/00207720410001734192","DOIUrl":"https://doi.org/10.1080/00207720410001734192","url":null,"abstract":"A global optimization algorithm is used to solve the fixed-order controller synthesis problem for linear systems. The algorithm, which belongs to the information methods family, is described in some detail and numerical experiments are performed on test problems to show its effectiveness.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125893800","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}
A technique for the bifurcation control of nonlinear systems with periodic coefficients is presented. In such systems, bifurcations occur when one of the Floquet multipliers becomes +1 , -1, or a pair of complex multipliers reaches magnitude 1. The stability of the bifurcated periodic or quasi-periodic orbit is guaranteed by employing a nonlinear state-feedback control. First the Lyapunov-Floquet transformation is applied such that the linear part of system equations becomes time-invariant. Then through an application of the time-periodic center manifold reduction and time-dependent normal form theory one can obtain a completely time-invariant form of the nonlinear equation for codimension one bifurcations. The time-invariant normal form is suitable for the application of control strategies developed for autonomous systems. Then by transforming the results back to the original variables, one obtains the gains for the time-varying controller. The control strategy is illustrated through an example of a parametrically excited simple pendulum undergoing a symmetry breaking bifurcation.
{"title":"Bifurcation control of nonlinear systems with time-periodic coefficients","authors":"A. Dávid, S. Sinha","doi":"10.1109/ACC.1999.782323","DOIUrl":"https://doi.org/10.1109/ACC.1999.782323","url":null,"abstract":"A technique for the bifurcation control of nonlinear systems with periodic coefficients is presented. In such systems, bifurcations occur when one of the Floquet multipliers becomes +1 , -1, or a pair of complex multipliers reaches magnitude 1. The stability of the bifurcated periodic or quasi-periodic orbit is guaranteed by employing a nonlinear state-feedback control. First the Lyapunov-Floquet transformation is applied such that the linear part of system equations becomes time-invariant. Then through an application of the time-periodic center manifold reduction and time-dependent normal form theory one can obtain a completely time-invariant form of the nonlinear equation for codimension one bifurcations. The time-invariant normal form is suitable for the application of control strategies developed for autonomous systems. Then by transforming the results back to the original variables, one obtains the gains for the time-varying controller. The control strategy is illustrated through an example of a parametrically excited simple pendulum undergoing a symmetry breaking bifurcation.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125749658","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}
Some nonlinear minimization problems are proposed for obtaining a solution of the biaffine matrix inequality (BMI) problem. An algorithm is also proposed for solving the nonlinear minimization problems. The algorithm can be easily implemented with the existing convex optimization codes. This nonlinear programming approach can be applied to all multiobjective and structured control problems such as the simultaneous stabilization by static or dynamic output feedback, the mixed H/sub 2//H/sub /spl infin// control, and the decentralized control which can be reduced to BMI problems. The effectiveness is illustrated by numerical examples.
{"title":"Nonlinear programming approach to biaffine matrix inequality problems in multiobjective and structured control","authors":"J. Lee","doi":"10.1109/ACC.1999.786162","DOIUrl":"https://doi.org/10.1109/ACC.1999.786162","url":null,"abstract":"Some nonlinear minimization problems are proposed for obtaining a solution of the biaffine matrix inequality (BMI) problem. An algorithm is also proposed for solving the nonlinear minimization problems. The algorithm can be easily implemented with the existing convex optimization codes. This nonlinear programming approach can be applied to all multiobjective and structured control problems such as the simultaneous stabilization by static or dynamic output feedback, the mixed H/sub 2//H/sub /spl infin// control, and the decentralized control which can be reduced to BMI problems. The effectiveness is illustrated by numerical examples.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127077323","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}
Properties of the optimal stochastic fault detection filter for fault detection and identification are determined. The objective of the filter is to monitor certain faults called target faults and block other faults which are called nuisance faults. This filter is derived by keeping the ratio of the transmission from nuisance fault to the transmission from target fault small. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the ratio of the transmissions is zero, the optimal stochastic fault detection filter is equivalent to the unknown input observer if all invariant zero directions are included with the nuisance fault directions. Detection filter designs can be obtained for both linear time-invariant and time-varying systems.
{"title":"Optimal stochastic fault detection filter","authors":"Robert H. Chen, D. Mingori, J. Speyer","doi":"10.1109/ACC.1999.782746","DOIUrl":"https://doi.org/10.1109/ACC.1999.782746","url":null,"abstract":"Properties of the optimal stochastic fault detection filter for fault detection and identification are determined. The objective of the filter is to monitor certain faults called target faults and block other faults which are called nuisance faults. This filter is derived by keeping the ratio of the transmission from nuisance fault to the transmission from target fault small. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the ratio of the transmissions is zero, the optimal stochastic fault detection filter is equivalent to the unknown input observer if all invariant zero directions are included with the nuisance fault directions. Detection filter designs can be obtained for both linear time-invariant and time-varying systems.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129331895","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}
Considers balanced performance preserving controller reduction with closed-loop system performance-preserving criteria. The two methods proposed are closed loop block balanced truncation and a closed loop structurally balancing method. Due to the introduction of the performance preserving weightings, new methods have improved traditional balanced controller reduction methods in reducing the closed loop H/sub /spl infin// performance degradation.
{"title":"Balanced performance preserving controller reduction","authors":"G. Wang, V. Sreeram, Wanquan Liu","doi":"10.1109/ACC.1999.786283","DOIUrl":"https://doi.org/10.1109/ACC.1999.786283","url":null,"abstract":"Considers balanced performance preserving controller reduction with closed-loop system performance-preserving criteria. The two methods proposed are closed loop block balanced truncation and a closed loop structurally balancing method. Due to the introduction of the performance preserving weightings, new methods have improved traditional balanced controller reduction methods in reducing the closed loop H/sub /spl infin// performance degradation.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"40 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126101295","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 deals with performance enhancement of tracking control systems by multi-rate control. The feedback controller is updated at the same rate as the sampling rate of the output measurements. The feedforward controller processes the desired output signal for high accuracy tracking, and its output is updated at a rate N-times faster than the sampling rate of the output measurements. The discrete time model of the controlled plant may possess unstable zeros, and the zero phase error tracking controller is used as a feedforward controller. Inter-sample behavior of the plant is included in evaluating the tracking performance of the multi-rate system. Illustrative examples are given to show advantages of the proposed multi-rate feedback/feedforward control scheme.
{"title":"Multi-rate feedforward tracking control for plants with nonminimum phase discrete time models","authors":"Yuping Gu, M. Tomizuka","doi":"10.1109/ACC.1999.786375","DOIUrl":"https://doi.org/10.1109/ACC.1999.786375","url":null,"abstract":"This paper deals with performance enhancement of tracking control systems by multi-rate control. The feedback controller is updated at the same rate as the sampling rate of the output measurements. The feedforward controller processes the desired output signal for high accuracy tracking, and its output is updated at a rate N-times faster than the sampling rate of the output measurements. The discrete time model of the controlled plant may possess unstable zeros, and the zero phase error tracking controller is used as a feedforward controller. Inter-sample behavior of the plant is included in evaluating the tracking performance of the multi-rate system. Illustrative examples are given to show advantages of the proposed multi-rate feedback/feedforward control scheme.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128634849","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}
For linear time-varying systems described by the triple (A(t), B(t), C(t)) where A(t), B(t), C(t) are the system, input, and output matrices, respectively, we propose concepts for measures of modal and gross controllability/observability.
{"title":"Measures of modal and gross controllability/observability for linear time-varying systems","authors":"J. W. Choi, H. Lee, J. Zhus","doi":"10.1109/ACC.1999.786147","DOIUrl":"https://doi.org/10.1109/ACC.1999.786147","url":null,"abstract":"For linear time-varying systems described by the triple (A(t), B(t), C(t)) where A(t), B(t), C(t) are the system, input, and output matrices, respectively, we propose concepts for measures of modal and gross controllability/observability.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122905838","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}
A set of integral quadratic constraints (IQC) is derived for a class of "rate limiters", modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework, is expected to be widely useful in nonlinear system analysis. For example, it enables "discrimination" between "saturation-like" and "deadzone-like" nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L/sub 2/ gain of a unity feedback system with a rate limiter in the forward loop cannot exceed /spl radic/2.
{"title":"New IQC for quasi-concave nonlinearities","authors":"A. Megretski","doi":"10.1109/ACC.1999.786471","DOIUrl":"https://doi.org/10.1109/ACC.1999.786471","url":null,"abstract":"A set of integral quadratic constraints (IQC) is derived for a class of \"rate limiters\", modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework, is expected to be widely useful in nonlinear system analysis. For example, it enables \"discrimination\" between \"saturation-like\" and \"deadzone-like\" nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L/sub 2/ gain of a unity feedback system with a rate limiter in the forward loop cannot exceed /spl radic/2.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123348115","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}
Many control techniques employ online optimization in the determination of a control policy. We develop a framework which provides sufficient convex conditions, in the form of linear matrix inequalities, for the analysis of constrained quadratic based optimization schemes. These results encompass standard robustness analysis problems for a wide variety of receding horizon control schemes, including polytopic, structured, and measurement uncertainty for schemes with or without end constraints, observers, or input and output constraints. A simple example illustrates the methodology.
{"title":"The analysis of optimization based controllers","authors":"J. Primbs","doi":"10.1109/ACC.1999.782375","DOIUrl":"https://doi.org/10.1109/ACC.1999.782375","url":null,"abstract":"Many control techniques employ online optimization in the determination of a control policy. We develop a framework which provides sufficient convex conditions, in the form of linear matrix inequalities, for the analysis of constrained quadratic based optimization schemes. These results encompass standard robustness analysis problems for a wide variety of receding horizon control schemes, including polytopic, structured, and measurement uncertainty for schemes with or without end constraints, observers, or input and output constraints. A simple example illustrates the methodology.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126831204","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}
Robust predictive control has been tackled through the use of linear matrix inequalities and ellipsoidal invariant sets. Earlier work in this area restricted the prediction class to state feedback and did not make use of a control horizon, and the computational load in this approach was excessive. Both these problems can be overcome through the use of an autonomous but augmented system for the purposes of prediction. Recent work considered the use of a control horizon and polyhedral sets, and here we extend this approach to the more efficient formulation based on the autonomous system predictions.
{"title":"Linear matrix inequalities and polyhedral invariant sets in constrained robust predictive control","authors":"Y.I. Lee, B. Kouvaritakis","doi":"10.1109/ACC.1999.782910","DOIUrl":"https://doi.org/10.1109/ACC.1999.782910","url":null,"abstract":"Robust predictive control has been tackled through the use of linear matrix inequalities and ellipsoidal invariant sets. Earlier work in this area restricted the prediction class to state feedback and did not make use of a control horizon, and the computational load in this approach was excessive. Both these problems can be overcome through the use of an autonomous but augmented system for the purposes of prediction. Recent work considered the use of a control horizon and polyhedral sets, and here we extend this approach to the more efficient formulation based on the autonomous system predictions.","PeriodicalId":441363,"journal":{"name":"Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251)","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131905567","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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