On the basis of high-gain observers for perturbed state affine systems, an observer for a class of nonlinear systems satisfying a more general triangular structure is proposed. The design is based on interconnection of subobservers on the one hand, and saturation techniques on the other hand. Exponential convergence of the estimation error is shown under appropriate excitation condition.
{"title":"Further results on high gain observers for nonlinear systems","authors":"G. Besançon","doi":"10.1109/CDC.1999.831376","DOIUrl":"https://doi.org/10.1109/CDC.1999.831376","url":null,"abstract":"On the basis of high-gain observers for perturbed state affine systems, an observer for a class of nonlinear systems satisfying a more general triangular structure is proposed. The design is based on interconnection of subobservers on the one hand, and saturation techniques on the other hand. Exponential convergence of the estimation error is shown under appropriate excitation condition.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115808970","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}
Presents an original method for maximum likelihood parameter estimation in nonlinear dynamical systems with highly correlated residuals. The method relies on an autoregressive representation of the residuals to build an estimate of the inverse of its covariance matrix. Theoretical concepts are developed and we provide a successful application of the method on a two-parameters estimation problem with data collected on a real plant. This experimental study shows that the statistical properties of the estimated parameters are significantly improved with our method in comparison to classical estimation techniques that usually rely on an uncorrelated representation of the residuals. In addition, a far better estimation of the confidence region around the parameter vector is obtained.
{"title":"A maximum likelihood parameter estimation method for nonlinear dynamical systems","authors":"B. David, G. Bastin","doi":"10.1109/CDC.1999.832852","DOIUrl":"https://doi.org/10.1109/CDC.1999.832852","url":null,"abstract":"Presents an original method for maximum likelihood parameter estimation in nonlinear dynamical systems with highly correlated residuals. The method relies on an autoregressive representation of the residuals to build an estimate of the inverse of its covariance matrix. Theoretical concepts are developed and we provide a successful application of the method on a two-parameters estimation problem with data collected on a real plant. This experimental study shows that the statistical properties of the estimated parameters are significantly improved with our method in comparison to classical estimation techniques that usually rely on an uncorrelated representation of the residuals. In addition, a far better estimation of the confidence region around the parameter vector is obtained.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115841285","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 studying the stability of time-delay systems, many published results use a transformation to transform a system with single time-delay to a system with distributed delay. In this article, the inherent limitations of such approaches are studied. Specifically, it is shown that such a transformation incurs additional dynamics which can be characterized by appropriate additional eigenvalues. The critical delay values when such additional eigenvalues cross the imaginary axis can be explicitly calculated. If the smallest of such delays is the smallest of the stability delay limit of the original system, then any stability criteria obtained using such transformation will be conservative. Some examples are also included.
{"title":"Additional dynamics in transformed time-delay systems","authors":"K. Gu, S. Niculescu","doi":"10.1109/CDC.1999.833280","DOIUrl":"https://doi.org/10.1109/CDC.1999.833280","url":null,"abstract":"In studying the stability of time-delay systems, many published results use a transformation to transform a system with single time-delay to a system with distributed delay. In this article, the inherent limitations of such approaches are studied. Specifically, it is shown that such a transformation incurs additional dynamics which can be characterized by appropriate additional eigenvalues. The critical delay values when such additional eigenvalues cross the imaginary axis can be explicitly calculated. If the smallest of such delays is the smallest of the stability delay limit of the original system, then any stability criteria obtained using such transformation will be conservative. Some examples are also included.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124124236","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}
Concerns the decoupling and tracking control for linear time-varying systems, such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain-scheduling control appears to be a focus of the research efforts. The scheduling of a frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and a novel decoupling and tracking control scheme is proposed by using the PD (parallel differential) eigenstructure assignment scheme via the differential Sylvester equation and a CGT (command generator tracker) for linear time-varying systems. The presented method is illustrated by numerical examples.
{"title":"PD-eigenstructure assignment control for decoupling and tracking of linear time-varying systems","authors":"J. Choi, H. Lee","doi":"10.1109/CDC.1999.832917","DOIUrl":"https://doi.org/10.1109/CDC.1999.832917","url":null,"abstract":"Concerns the decoupling and tracking control for linear time-varying systems, such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain-scheduling control appears to be a focus of the research efforts. The scheduling of a frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and a novel decoupling and tracking control scheme is proposed by using the PD (parallel differential) eigenstructure assignment scheme via the differential Sylvester equation and a CGT (command generator tracker) for linear time-varying systems. The presented method is illustrated by numerical examples.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124147969","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}
Proposes an approach to fault detection by a structure of two observers which estimate the plant states decided by the plant input and the states affected by the fault respectively and explicitly. A design example is used to illustrate the proposed fault detection scheme.
{"title":"Fault detection using Luenberger-like observers","authors":"F. W. Poon, D. Gu","doi":"10.1109/CDC.1999.831414","DOIUrl":"https://doi.org/10.1109/CDC.1999.831414","url":null,"abstract":"Proposes an approach to fault detection by a structure of two observers which estimate the plant states decided by the plant input and the states affected by the fault respectively and explicitly. A design example is used to illustrate the proposed fault detection scheme.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"362 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114772013","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 problem of regulating the output voltage of the Boost DC-to-DC power converter has attracted the attention of many control researchers for several years now. Besides its practical relevance, the system is an interesting theoretical case study because it is a switched device whose averaged dynamics are described by a bilinear second order non-minimum phase system with saturated input, partial state measurement and a highly uncertain parameter-the load resistance. In this paper we provide a solution to the problem of designing an output-feedback saturated controller which ensures regulation of the desired output voltage and is, at the same time, insensitive to uncertainty in the load resistance. Furthermore, bounds on this parameter can be used to tune the controller so as to (locally) ensure robust performance, e.g., that the transient has no (under)over-shoot. The controller, which is designed following the energy-balancing methodology recently proposed by Ortega, van der Schaft and Maschke, is a simple static nonlinear output feedback, hence it is computationally less demanding than the industry standard lead-lag filters.
升压型dc - dc功率变换器输出电压的调节问题近年来引起了众多控制研究者的关注。除了具有实际意义外，该系统是一个有趣的理论案例研究，因为它是一个开关器件，其平均动态由双线性二阶非最小相位系统描述，该系统具有饱和输入，部分状态测量和高度不确定参数-负载电阻。本文提出了一种设计输出反馈饱和控制器的解决方案，该控制器既能保证期望输出电压的调节，同时又对负载电阻的不确定性不敏感。此外，该参数的界限可以用来调整控制器，以(本地)确保鲁棒性能，例如，瞬态没有(低于)超调。该控制器是根据Ortega、van der Schaft和Maschke最近提出的能量平衡方法设计的，它是一个简单的静态非线性输出反馈，因此它在计算上的要求比工业标准的超前滞后滤波器要低。
{"title":"A robustly stable output feedback saturated controller for the Boost DC-to-DC converter","authors":"H. Rodríguez, Romeo Ortega, Gerardo Escobar","doi":"10.1109/CDC.1999.831229","DOIUrl":"https://doi.org/10.1109/CDC.1999.831229","url":null,"abstract":"The problem of regulating the output voltage of the Boost DC-to-DC power converter has attracted the attention of many control researchers for several years now. Besides its practical relevance, the system is an interesting theoretical case study because it is a switched device whose averaged dynamics are described by a bilinear second order non-minimum phase system with saturated input, partial state measurement and a highly uncertain parameter-the load resistance. In this paper we provide a solution to the problem of designing an output-feedback saturated controller which ensures regulation of the desired output voltage and is, at the same time, insensitive to uncertainty in the load resistance. Furthermore, bounds on this parameter can be used to tune the controller so as to (locally) ensure robust performance, e.g., that the transient has no (under)over-shoot. The controller, which is designed following the energy-balancing methodology recently proposed by Ortega, van der Schaft and Maschke, is a simple static nonlinear output feedback, hence it is computationally less demanding than the industry standard lead-lag filters.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114944685","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}
Several concepts of controllability for partially observable stochastic systems (complete controllability, approximate controllability, controllability) are discussed. It is shown that complete and approximate controllability notions are equivalent, and in turn they are equivalent to the controllability for linear stochastic systems controlled with Gaussian processes. Necessary and sufficient conditions for these concepts of controllability are derived. These criteria reduce to the well known rank condition.
{"title":"On controllability of linear stochastic systems","authors":"N. Mahmudov","doi":"10.1109/CDC.1999.830193","DOIUrl":"https://doi.org/10.1109/CDC.1999.830193","url":null,"abstract":"Several concepts of controllability for partially observable stochastic systems (complete controllability, approximate controllability, controllability) are discussed. It is shown that complete and approximate controllability notions are equivalent, and in turn they are equivalent to the controllability for linear stochastic systems controlled with Gaussian processes. Necessary and sufficient conditions for these concepts of controllability are derived. These criteria reduce to the well known rank condition.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114986989","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}
We design observers for a class of systems with monotone sector nonlinearities. The resulting nonlinear estimation error system is represented as the feedback interconnection of a linear system and a time-varying multivariable sector nonlinearity. Using LMI software, an observer gain matrix is computed to satisfy the circle criterion and, hence, to drive the estimation error to zero. The new observer is incorporated in output feedback control, as illustrated by an example.
{"title":"Nonlinear observers: a circle criterion design","authors":"M. Arcak, P. Kokotovic","doi":"10.1109/CDC.1999.833315","DOIUrl":"https://doi.org/10.1109/CDC.1999.833315","url":null,"abstract":"We design observers for a class of systems with monotone sector nonlinearities. The resulting nonlinear estimation error system is represented as the feedback interconnection of a linear system and a time-varying multivariable sector nonlinearity. Using LMI software, an observer gain matrix is computed to satisfy the circle criterion and, hence, to drive the estimation error to zero. The new observer is incorporated in output feedback control, as illustrated by an example.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117107651","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}
We show, via an example, a possible way to place the concept of differential flatness into the more general setting of equivalence a la Cartan (1953). In particular we show that a general n-trailer, which is not differentially flat, is anyway equivalent to its differentially flat counterpart, namely the standard n-trailer, along any smooth input trajectory.
通过一个例子，我们展示了一种可能的方法，可以将微分平坦度的概念放入更一般的等价a la Cartan(1953)中。特别地，我们证明了一个一般的n-拖车，它不是微分平坦的，无论如何都等于它的微分平坦的对应物，即标准n-拖车，沿着任何光滑的输入轨迹。
{"title":"General n-trailer, differential flatness and equivalence","authors":"C. Altafini","doi":"10.1109/CDC.1999.831237","DOIUrl":"https://doi.org/10.1109/CDC.1999.831237","url":null,"abstract":"We show, via an example, a possible way to place the concept of differential flatness into the more general setting of equivalence a la Cartan (1953). In particular we show that a general n-trailer, which is not differentially flat, is anyway equivalent to its differentially flat counterpart, namely the standard n-trailer, along any smooth input trajectory.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"98 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116328526","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. Shiriaev, H. Ludvigsen, O. Egeland, A. Pogromsky
The problem of stabilization of the inverted pendulum on a cart is considered. The proposed technique is based on the passivity of the inverted pendulum and reflects its global properties. The new feedback regulators provide that any solution of the closed loop system, except for initial conditions lying on some 2-dimensional manifold, will be in any neighbourhood of the unstable equilibrium with zero displacement of the cart.
{"title":"On global properties of passivity based control of the inverted pendulum","authors":"A. Shiriaev, H. Ludvigsen, O. Egeland, A. Pogromsky","doi":"10.1109/CDC.1999.831305","DOIUrl":"https://doi.org/10.1109/CDC.1999.831305","url":null,"abstract":"The problem of stabilization of the inverted pendulum on a cart is considered. The proposed technique is based on the passivity of the inverted pendulum and reflects its global properties. The new feedback regulators provide that any solution of the closed loop system, except for initial conditions lying on some 2-dimensional manifold, will be in any neighbourhood of the unstable equilibrium with zero displacement of the cart.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123213562","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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