This paper applies nonlinear /spl Hscr//sub /spl infin// control techniques to linear systems with actuator nonlinearities. In our previous paper (1999), this was treated under the certainty equivalence assumption. The control design produces a finite dimensional measurement feedback controller which is computable online provided certain conditions are met. In this paper, we do not use the certainty equivalence theory. Instead, we use the more general theory given by Helton et al. (1999). We design a controller for globally stabilizable linear systems with actuator nonlinearities which is finite dimensional and computable but does not require the onerous certainty equivalence assumption.
{"title":"Measurement feedback nonlinear /spl Hscr//sub /spl infin// control of linear systems with actuator nonlinearities","authors":"P. Dower, J. Helton, M. James","doi":"10.1109/CDC.1999.827939","DOIUrl":"https://doi.org/10.1109/CDC.1999.827939","url":null,"abstract":"This paper applies nonlinear /spl Hscr//sub /spl infin// control techniques to linear systems with actuator nonlinearities. In our previous paper (1999), this was treated under the certainty equivalence assumption. The control design produces a finite dimensional measurement feedback controller which is computable online provided certain conditions are met. In this paper, we do not use the certainty equivalence theory. Instead, we use the more general theory given by Helton et al. (1999). We design a controller for globally stabilizable linear systems with actuator nonlinearities which is finite dimensional and computable but does not require the onerous certainty equivalence assumption.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"53 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":"127108922","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 recognition of the heavy top as an invariant subsystem of the elastic problem, which in turn can be seen as a left-invariant optimal control problem on the group of motions of a Euclidean space E/sup n/ leads to new insights for a large class of Hamiltonian systems on Lie groups and explains the relevance of the classical theory of tops for problems of optimal control. This paper focuses on the issue of integrability. The main import of the paper is to demonstrate that the classical theory of tops, initiated by L. Lagrange, J. Louiville and S. Kowalewski (1889), extends to holomorphic Hamiltonian systems on complex Lie groups SO/sub n/(C), and that complex Lie groups are a natural setting for proper understanding of the basic phenomena.
将重顶视为弹性问题的一个不变子系统，而弹性问题又可视为欧几里德空间E/sup / n/运动群上的左不变最优控制问题，这为李群上的一大类哈密顿系统提供了新的见解，并解释了经典顶理论与最优控制问题的相关性。本文主要研究可积性问题。本文的主要意义在于证明了由L. Lagrange, J. Louiville和S. Kowalewski(1889)提出的经典顶理论，扩展到复李群SO/sub n/(C)上的全纯哈密顿系统，以及复李群是正确理解基本现象的自然环境。
{"title":"Complex Hamiltonians and integrable systems","authors":"V. Jurdjevic","doi":"10.1109/CDC.1999.832812","DOIUrl":"https://doi.org/10.1109/CDC.1999.832812","url":null,"abstract":"The recognition of the heavy top as an invariant subsystem of the elastic problem, which in turn can be seen as a left-invariant optimal control problem on the group of motions of a Euclidean space E/sup n/ leads to new insights for a large class of Hamiltonian systems on Lie groups and explains the relevance of the classical theory of tops for problems of optimal control. This paper focuses on the issue of integrability. The main import of the paper is to demonstrate that the classical theory of tops, initiated by L. Lagrange, J. Louiville and S. Kowalewski (1889), extends to holomorphic Hamiltonian systems on complex Lie groups SO/sub n/(C), and that complex Lie groups are a natural setting for proper understanding of the basic phenomena.","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":"127502937","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 property of input to output stability (IOS) was introduced about 10 years ago (E.D. Sontag, 1989), but most theoretical developments have until now dealt mainly with the special case of input to state stability. The article presents a small-gain theorem for IOS operators, as well as alternative properties and Lyapunov characterizations dealing with the IOS property for state-space systems.
{"title":"Remarks on input to output stability","authors":"B. Ingalls, Eduardo Sontag, Y. Wang","doi":"10.1109/CDC.1999.830099","DOIUrl":"https://doi.org/10.1109/CDC.1999.830099","url":null,"abstract":"The property of input to output stability (IOS) was introduced about 10 years ago (E.D. Sontag, 1989), but most theoretical developments have until now dealt mainly with the special case of input to state stability. The article presents a small-gain theorem for IOS operators, as well as alternative properties and Lyapunov characterizations dealing with the IOS property for state-space systems.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"2014 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":"127504195","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}
Pyragas (1992) proposes a practically useful control method, called delayed feedback control, for control of chaos. Conditions for (local) stabilization by the delayed feedback control, however, are more restricted than those by the Ott-Grebogi-Yorke (1990) method. In order to overcome this problem, we propose a novel control method, called a prediction-based feedback control, for discrete-time chaotic systems. Moreover, we give necessary and sufficient conditions for exponential stabilization of fixed points by the proposed method.
{"title":"Prediction-based control in chaotic discrete-time systems","authors":"T. Ushio, S. Yamamoto","doi":"10.1109/CDC.1999.830942","DOIUrl":"https://doi.org/10.1109/CDC.1999.830942","url":null,"abstract":"Pyragas (1992) proposes a practically useful control method, called delayed feedback control, for control of chaos. Conditions for (local) stabilization by the delayed feedback control, however, are more restricted than those by the Ott-Grebogi-Yorke (1990) method. In order to overcome this problem, we propose a novel control method, called a prediction-based feedback control, for discrete-time chaotic systems. Moreover, we give necessary and sufficient conditions for exponential stabilization of fixed points by the proposed method.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"115 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":"124804615","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 consider the problem of achieving disturbance attenuation in the input-to-state stability (ISS) and integral-ISS sense for nonlinear systems with bounded controls. For the ISS case we derive a "universal" formula which extends an earlier result of Lin and Sontag (1991) to systems with disturbances. For the integral-ISS case we give two constructions, one resulting in a smooth control law and the other in a switching control law. We also briefly discuss some issues related to input-to-state stability of switched and hybrid systems.
{"title":"ISS and integral-ISS disturbance attenuation with bounded controls","authors":"D. Liberzon","doi":"10.1109/CDC.1999.831303","DOIUrl":"https://doi.org/10.1109/CDC.1999.831303","url":null,"abstract":"We consider the problem of achieving disturbance attenuation in the input-to-state stability (ISS) and integral-ISS sense for nonlinear systems with bounded controls. For the ISS case we derive a \"universal\" formula which extends an earlier result of Lin and Sontag (1991) to systems with disturbances. For the integral-ISS case we give two constructions, one resulting in a smooth control law and the other in a switching control law. We also briefly discuss some issues related to input-to-state stability of switched and hybrid systems.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"28 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":"125182423","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}
Deals with the problem of robust stability of linear systems with uncertain real time-varying parameters with magnitudes and rates of change (or variations, in discrete-time) which are confined to a given convex region. A notion of robust stability, referred to as bi-quadratic stability, which is based on a Lyapunov function that depends quadratically on the uncertain parameters is proposed. LMI based sufficient conditions for bi-quadratic stability of continuous- and discrete-time systems are developed. The proposed stability analysis methods have the advantage that they can be used for solving problems of robust control synthesis, including robust stabilization, robust H/sub 2/ control, and robust H/sub /spl infin// control.
{"title":"Bi-quadratic stability of uncertain linear systems","authors":"A. Trofino, C. de Souza","doi":"10.1109/CDC.1999.833343","DOIUrl":"https://doi.org/10.1109/CDC.1999.833343","url":null,"abstract":"Deals with the problem of robust stability of linear systems with uncertain real time-varying parameters with magnitudes and rates of change (or variations, in discrete-time) which are confined to a given convex region. A notion of robust stability, referred to as bi-quadratic stability, which is based on a Lyapunov function that depends quadratically on the uncertain parameters is proposed. LMI based sufficient conditions for bi-quadratic stability of continuous- and discrete-time systems are developed. The proposed stability analysis methods have the advantage that they can be used for solving problems of robust control synthesis, including robust stabilization, robust H/sub 2/ control, and robust H/sub /spl infin// control.","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":"125860310","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 the stability of nonlinear systems subject to generalized disturbances. The first purpose is to give sufficient conditions for the stability of the interconnection of such systems. The second one is to provide a coprime kernel representation for the plant and the controller when both the plant and the controller have right coprime factorization. In this case, the concepts of strong stability and internal stability are equivalent.
{"title":"Kernel representations for nonlinear systems with generalized disturbances: stabilization","authors":"H. Lwafi, T. Zougari, D. Mehdi","doi":"10.1109/CDC.1999.830122","DOIUrl":"https://doi.org/10.1109/CDC.1999.830122","url":null,"abstract":"This paper deals with the stability of nonlinear systems subject to generalized disturbances. The first purpose is to give sufficient conditions for the stability of the interconnection of such systems. The second one is to provide a coprime kernel representation for the plant and the controller when both the plant and the controller have right coprime factorization. In this case, the concepts of strong stability and internal stability are equivalent.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"32 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":"125912471","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}
An optimization problem related to bilinear matrix inequalities (BMIs) is considered. A branch-and-bound type global algorithm is obtained based on a linear matrix inequality (LMI)-relaxation and an upper bound of its worst case performance is derived. Taking account of activities of the relaxed problem, an improved algorithm is also proposed.
{"title":"A branch-and-bound algorithm for solving BMIs taking account of activities of relaxed LMIs","authors":"Hisaya Fujioka","doi":"10.1109/CDC.1999.832926","DOIUrl":"https://doi.org/10.1109/CDC.1999.832926","url":null,"abstract":"An optimization problem related to bilinear matrix inequalities (BMIs) is considered. A branch-and-bound type global algorithm is obtained based on a linear matrix inequality (LMI)-relaxation and an upper bound of its worst case performance is derived. Taking account of activities of the relaxed problem, an improved algorithm is also proposed.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"12 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":"123745519","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 paper deals with the application of the identifiability criteria to mean-value models of turbocharged IC engines. A way of reducing such models to linear regressions using differential-algebraic tools is presented. The conditions of the global identifiability and the persistent excitation are formulated explicitly for a given set of sensors. It is accompanied with an iterative technique of the sensor set reduction. The software tools required are outlined and their complexity is discussed.
{"title":"Structural identifiability: tools and applications","authors":"T. Glad, A. Sokolov","doi":"10.1109/CDC.1999.831285","DOIUrl":"https://doi.org/10.1109/CDC.1999.831285","url":null,"abstract":"The paper deals with the application of the identifiability criteria to mean-value models of turbocharged IC engines. A way of reducing such models to linear regressions using differential-algebraic tools is presented. The conditions of the global identifiability and the persistent excitation are formulated explicitly for a given set of sensors. It is accompanied with an iterative technique of the sensor set reduction. The software tools required are outlined and their complexity is discussed.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"24 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":"123759472","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 class of adaptive control systems which are not only asymptotically stable but also optimal or sub-optimal to some meaningful cost functionals, are derived. By relating Lyapunov functions with solutions of Hamilton-Jacobi (-Isaacs) equations, three types of adaptive optimal control problems are solved (Type 1/spl sim/3), and the adaptive /spl Hscr//sup 2/ (Type 2) and /spl Hscr//sup /spl infin// (Type 1 and 3) optimal (sub-optimal) control systems are constructed for generalized adaptive control problems.
{"title":"Redesign of adaptive control systems based on the notion of optimality","authors":"Y. Miyasato","doi":"10.1109/CDC.1999.827783","DOIUrl":"https://doi.org/10.1109/CDC.1999.827783","url":null,"abstract":"A class of adaptive control systems which are not only asymptotically stable but also optimal or sub-optimal to some meaningful cost functionals, are derived. By relating Lyapunov functions with solutions of Hamilton-Jacobi (-Isaacs) equations, three types of adaptive optimal control problems are solved (Type 1/spl sim/3), and the adaptive /spl Hscr//sup 2/ (Type 2) and /spl Hscr//sup /spl infin// (Type 1 and 3) optimal (sub-optimal) control systems are constructed for generalized adaptive control problems.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"9 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":"123782279","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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