Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H/sup /spl infin// constraint on disturbance attenuation are developed. The H/sup /spl infin// constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H/sup 2/ performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H/sup 2/ performance. The algorithms are based on a minimal parameter formulation: Ly-Bryson-Cannon's 2/spl times/2 block parametrization. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H/sup 2//H/sup /spl infin// synthesis. The nonmonotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary.<>
{"title":"Probability-one homotopy algorithms for full and reduced order H/sup 2//H/sup /spl infin// controller synthesis","authors":"Y. Ge, L. Watson, E. Collins, D. Bernstein","doi":"10.1109/CDC.1994.411301","DOIUrl":"https://doi.org/10.1109/CDC.1994.411301","url":null,"abstract":"Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H/sup /spl infin// constraint on disturbance attenuation are developed. The H/sup /spl infin// constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper bound on H/sup 2/ performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H/sup 2/ performance. The algorithms are based on a minimal parameter formulation: Ly-Bryson-Cannon's 2/spl times/2 block parametrization. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H/sup 2//H/sup /spl infin// synthesis. The nonmonotonicity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated than standard continuation are necessary.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115953517","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 biaffine matrix inequality (BMI) is a potentially very flexible new framework for approaching complex robust control system synthesis problems with multiple plants, multiple objectives and controller order constraints. The BMI problem may be viewed as the nondifferentiable biconvex programming problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices. The BMI problem is non-local-global in general, i.e. there may exist local minima which are not global minima. While local optimization techniques sometimes yield good results, global optimization procedures need to be considered for the complete solution of the BMI problem. In this paper, we present a global optimization algorithm for the BMI based on the branch and bound approach. A simple numerical example is included.<>
{"title":"A global optimization approach for the BMI problem","authors":"K. Goh, M. Safonov, G. Papavassilopoulos","doi":"10.1109/CDC.1994.411445","DOIUrl":"https://doi.org/10.1109/CDC.1994.411445","url":null,"abstract":"The biaffine matrix inequality (BMI) is a potentially very flexible new framework for approaching complex robust control system synthesis problems with multiple plants, multiple objectives and controller order constraints. The BMI problem may be viewed as the nondifferentiable biconvex programming problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices. The BMI problem is non-local-global in general, i.e. there may exist local minima which are not global minima. While local optimization techniques sometimes yield good results, global optimization procedures need to be considered for the complete solution of the BMI problem. In this paper, we present a global optimization algorithm for the BMI based on the branch and bound approach. A simple numerical example is included.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115980662","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}
It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims, at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the lattice objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propagation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.<>
{"title":"On passivity-based output feedback global stabilization of Euler-Lagrange systems","authors":"R. Ortega, A. Loría, R. Kelly, L. Praly","doi":"10.1109/CDC.1994.410898","DOIUrl":"https://doi.org/10.1109/CDC.1994.410898","url":null,"abstract":"It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims, at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the lattice objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propagation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"407 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131935483","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 a solution to the singular H/sub /spl infin// control problem via state feedback for a class of nonlinear systems. It is shown that the problem of almost disturbance decoupling with stability plays a fundamental role in the solution of the considered problem. The author also points out when the singular problem can be reduced to a regular one or solved via standard H/sub /spl infin// technique. The author stresses that the solution of the singular problem is obtained without making any approximation of it by regular problems, i.e. via the so called cheap control. The latter is used to provide a solution to the general H/sub /spl infin// control problem, i.e. when no assumptions are made on the zero dynamic of the system.<>
{"title":"Singular H/sub /spl infin// control","authors":"A. Astolfi","doi":"10.1109/CDC.1994.411527","DOIUrl":"https://doi.org/10.1109/CDC.1994.411527","url":null,"abstract":"Presents a solution to the singular H/sub /spl infin// control problem via state feedback for a class of nonlinear systems. It is shown that the problem of almost disturbance decoupling with stability plays a fundamental role in the solution of the considered problem. The author also points out when the singular problem can be reduced to a regular one or solved via standard H/sub /spl infin// technique. The author stresses that the solution of the singular problem is obtained without making any approximation of it by regular problems, i.e. via the so called cheap control. The latter is used to provide a solution to the general H/sub /spl infin// control problem, i.e. when no assumptions are made on the zero dynamic of the system.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132363313","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 first present a few definitions of frequency response arcs and their argument increase and convexity properties. These definitions are based on the original definitions introduced by Hamann and Barmish (1993). We then reformulate argument increase and arc convexity in terms of certain inner products, which we interpret as first and second angular derivatives. The resulting formulation resembles the first and second derivative test for increase and convexity of real valued functions.<>
{"title":"Convexity of a frequency response arc associated with a stable quasi-polynomial","authors":"N. Cohen, J. Kogan","doi":"10.1109/CDC.1994.411298","DOIUrl":"https://doi.org/10.1109/CDC.1994.411298","url":null,"abstract":"We first present a few definitions of frequency response arcs and their argument increase and convexity properties. These definitions are based on the original definitions introduced by Hamann and Barmish (1993). We then reformulate argument increase and arc convexity in terms of certain inner products, which we interpret as first and second angular derivatives. The resulting formulation resembles the first and second derivative test for increase and convexity of real valued functions.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134285242","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}
Mobile robots with non-holonomic kinematics have three degrees of freedom for planar motion, but there are only two control inputs available. The stabilization problem for such robots is known not to be solvable via smooth time-invariant feedback. The authors propose to utilize a Lyapunov function to prescribe a set of desired trajectories to navigate the robot to a specified configuration. Ideal tracking of the prescribed trajectories is achieved by exploiting the invariance property and the order reduction property of sliding mode control. The mobile robot is shown to be exponentially stabilizable for a class of quadratic Lyapunov functions.<>
{"title":"Stabilization of non-holonomic mobile robots using Lyapunov functions for navigation and sliding mode control","authors":"J. Guldner, V. Utkin","doi":"10.1109/CDC.1994.411340","DOIUrl":"https://doi.org/10.1109/CDC.1994.411340","url":null,"abstract":"Mobile robots with non-holonomic kinematics have three degrees of freedom for planar motion, but there are only two control inputs available. The stabilization problem for such robots is known not to be solvable via smooth time-invariant feedback. The authors propose to utilize a Lyapunov function to prescribe a set of desired trajectories to navigate the robot to a specified configuration. Ideal tracking of the prescribed trajectories is achieved by exploiting the invariance property and the order reduction property of sliding mode control. The mobile robot is shown to be exponentially stabilizable for a class of quadratic Lyapunov functions.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131833672","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}
M. Sampath, Raja Sengupta, S. Lafortune, K. Sinnamohideen, D. Teneketzis
We propose a discrete event systems (DES) approach to the failure diagnosis problem. We present a methodology for modeling physical systems in a DES framework. We discuss the notion of diagnosability and present the construction procedure of the diagnoser. Finally, we illustrate our approach using a heating, ventilation and air conditioning (HVAC) system.<>
{"title":"Failure diagnosis using discrete event models","authors":"M. Sampath, Raja Sengupta, S. Lafortune, K. Sinnamohideen, D. Teneketzis","doi":"10.1109/CDC.1994.411307","DOIUrl":"https://doi.org/10.1109/CDC.1994.411307","url":null,"abstract":"We propose a discrete event systems (DES) approach to the failure diagnosis problem. We present a methodology for modeling physical systems in a DES framework. We discuss the notion of diagnosability and present the construction procedure of the diagnoser. Finally, we illustrate our approach using a heating, ventilation and air conditioning (HVAC) system.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131838726","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, the method of exterior differential systems for analyzing nonlinear systems is presented. Conditions are given for converting Pfaffian systems into Goursat normal form, and for converting control systems into Brunovsky form. All of the existing results on feedback linearization for control systems can be restated in the language of Pfaffian systems, and in addition, new conditions for linearizing control systems using dynamic extension are given.<>
{"title":"On Goursat normal forms, prolongations, and control systems","authors":"D. Tilbury, S. Sastry","doi":"10.1109/CDC.1994.411123","DOIUrl":"https://doi.org/10.1109/CDC.1994.411123","url":null,"abstract":"In this paper, the method of exterior differential systems for analyzing nonlinear systems is presented. Conditions are given for converting Pfaffian systems into Goursat normal form, and for converting control systems into Brunovsky form. All of the existing results on feedback linearization for control systems can be restated in the language of Pfaffian systems, and in addition, new conditions for linearizing control systems using dynamic extension are given.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132788597","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 parameters of fixed structure PID controller are difficult to determine, especially for non-minimum phase system. Recently, there has been significant progress in combining adaptive technology with PID controller. Most of them use pole assignment method, but the choosing closed-loop system poles and solving equation online restrict their development. The self-tuning PID controller can overcome this problems, but the stability analysis of closed loop system is difficult and global convergence of the algorithm cannot be established. This paper presents a new self-tuning feedforward controller and solves the above problems. The controller proposed is based on the generalised minimum variance control strategy.<>
{"title":"Self-tuning feedforward PID controller","authors":"Wen-Shyong Yu, T. Chai, X. Gu","doi":"10.1109/CDC.1994.411402","DOIUrl":"https://doi.org/10.1109/CDC.1994.411402","url":null,"abstract":"The parameters of fixed structure PID controller are difficult to determine, especially for non-minimum phase system. Recently, there has been significant progress in combining adaptive technology with PID controller. Most of them use pole assignment method, but the choosing closed-loop system poles and solving equation online restrict their development. The self-tuning PID controller can overcome this problems, but the stability analysis of closed loop system is difficult and global convergence of the algorithm cannot be established. This paper presents a new self-tuning feedforward controller and solves the above problems. The controller proposed is based on the generalised minimum variance control strategy.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131068656","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}
M. Bonilla, O. M. Améstegui, I. Siller-Alcalá, R. Galindo
We consider a control scheme of a squared-cage-induction-machine, which maximize the power factor and control the angular position. An adaptive control is developed since the parameters of the motor (inductances l/sub s/ and I/sub r/ and in particular the rotor resistance R/sub r/) change greatly with temperature and/or magnetic saturation as well as uncertainty in the measurement of any of the parameters.<>
考虑了一种能最大限度地提高功率因数和控制电机角位置的方形感应电机控制方案。由于电机参数(电感l/sub s/和I/sub r/，特别是转子电阻r/ sub r/)随温度和/或磁饱和以及测量任何参数的不确定性而变化很大，因此开发了自适应控制。
{"title":"Angular position adaptive control of a squirrel-cage-induction-machine","authors":"M. Bonilla, O. M. Améstegui, I. Siller-Alcalá, R. Galindo","doi":"10.1109/CDC.1994.410873","DOIUrl":"https://doi.org/10.1109/CDC.1994.410873","url":null,"abstract":"We consider a control scheme of a squared-cage-induction-machine, which maximize the power factor and control the angular position. An adaptive control is developed since the parameters of the motor (inductances l/sub s/ and I/sub r/ and in particular the rotor resistance R/sub r/) change greatly with temperature and/or magnetic saturation as well as uncertainty in the measurement of any of the parameters.<<ETX>>","PeriodicalId":355623,"journal":{"name":"Proceedings of 1994 33rd IEEE Conference on Decision and Control","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131251177","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：