This paper discusses decentralized parallel distributed compensator design for discrete-time Takagi-Sugeno fuzzy systems by means of overlapping decompositions. The fuzzy system is viewed as an interconnection of subsystems, some of which are strongly connected, while others being weakly connected. The necessary theory is developed so that one can associate this fuzzy system with another one in a higher dimensional, so called expanded space, design decentralized parallel distributed compensators in the expanded space, then contract the solution for implementation on the original fuzzy system. An example is given to illustrate the concepts discussed throughout the paper.
{"title":"Decentralized parallel distributed compensator design for Takagi-Sugeno fuzzy systems","authors":"M. Akar, U. Ozguner","doi":"10.1109/CDC.1999.833308","DOIUrl":"https://doi.org/10.1109/CDC.1999.833308","url":null,"abstract":"This paper discusses decentralized parallel distributed compensator design for discrete-time Takagi-Sugeno fuzzy systems by means of overlapping decompositions. The fuzzy system is viewed as an interconnection of subsystems, some of which are strongly connected, while others being weakly connected. The necessary theory is developed so that one can associate this fuzzy system with another one in a higher dimensional, so called expanded space, design decentralized parallel distributed compensators in the expanded space, then contract the solution for implementation on the original fuzzy system. An example is given to illustrate the concepts discussed throughout the paper.","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":"121857972","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 robust stabilization problem (RSP) associated with a plant family /spl Pscr/(s,/spl delta/_) having a parameter uncertainty /spl delta/_ is considered. An apparent necessary solvability condition is that every element in /spl Pscr/(s,/spl delta/_) is stabilizable. It is shown that this RSP is equivalent to a strong stabilization problem associated with a related plant family /spl Gscr/(s,/spl delta/_), and /spl Pscr/(s,/spl delta/_) is stabilizable if and only if /spl Gscr/(s,/spl delta/_) is as well. Another necessary solvability condition is established in terms of the parity interlacing property of each element in /spl Gscr/(s,/spl delta/_) from the viewpoint of strong stabilization. The concept of the radius of the parity interlacing property is introduced. Some computational aspects of this radius are discussed.
{"title":"On the radius of parity interlacing property of plant family with parameter uncertainty","authors":"W. Wu","doi":"10.1109/CDC.1999.831263","DOIUrl":"https://doi.org/10.1109/CDC.1999.831263","url":null,"abstract":"The robust stabilization problem (RSP) associated with a plant family /spl Pscr/(s,/spl delta/_) having a parameter uncertainty /spl delta/_ is considered. An apparent necessary solvability condition is that every element in /spl Pscr/(s,/spl delta/_) is stabilizable. It is shown that this RSP is equivalent to a strong stabilization problem associated with a related plant family /spl Gscr/(s,/spl delta/_), and /spl Pscr/(s,/spl delta/_) is stabilizable if and only if /spl Gscr/(s,/spl delta/_) is as well. Another necessary solvability condition is established in terms of the parity interlacing property of each element in /spl Gscr/(s,/spl delta/_) from the viewpoint of strong stabilization. The concept of the radius of the parity interlacing property is introduced. Some computational aspects of this radius are discussed.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"58 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":"121747190","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 reformulation of the Witsenhausen counter-example is considered, where the first station is allowed to transmit its information to the second station through a low noise channel. This is in fact a decentralized stochastic system where the communication uncertainty induces a non-classical information pattern. Assuming a small transmission noise intensity, an asymptotic approach is used in order to find an approximated cost. Then, the necessary conditions for asymptotically optimal strategies are obtained using a variational approach. It is shown that the necessary conditions are satisfied by linear strategies with slightly different coefficients than the noiseless transmission case.
{"title":"An asymptotic optimal design for a decentralized system with noisy communication","authors":"K. Shoarinejad, J. Speyer, I. Kanellakopoulos","doi":"10.1109/CDC.1999.833329","DOIUrl":"https://doi.org/10.1109/CDC.1999.833329","url":null,"abstract":"A reformulation of the Witsenhausen counter-example is considered, where the first station is allowed to transmit its information to the second station through a low noise channel. This is in fact a decentralized stochastic system where the communication uncertainty induces a non-classical information pattern. Assuming a small transmission noise intensity, an asymptotic approach is used in order to find an approximated cost. Then, the necessary conditions for asymptotically optimal strategies are obtained using a variational approach. It is shown that the necessary conditions are satisfied by linear strategies with slightly different coefficients than the noiseless transmission case.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"14 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":"121767482","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 stabilization of nonlinear systems in a special normal form as the cascade of a nonlinear subsystem and a linear subsystem. These systems do not possess any particular triangular structure. Despite this fact, we show how a backstepping type procedure applied to these systems naturally leads to a fixed point equation in the control input. We give conditions for well-posedness of these fixed point equations and show how these fixed points called Fixed Point Controllers (FPC) can be used for stabilization of cascade nonlinear systems. As special cases, we apply our results to semiglobal stabilization of two complex under-actuated nonlinear systems, namely the cart-pole system and the rotating pendulum.
{"title":"Fixed point controllers and stabilization of the cart-pole system and the rotating pendulum","authors":"R. Olfati-Saber","doi":"10.1109/CDC.1999.830086","DOIUrl":"https://doi.org/10.1109/CDC.1999.830086","url":null,"abstract":"We consider stabilization of nonlinear systems in a special normal form as the cascade of a nonlinear subsystem and a linear subsystem. These systems do not possess any particular triangular structure. Despite this fact, we show how a backstepping type procedure applied to these systems naturally leads to a fixed point equation in the control input. We give conditions for well-posedness of these fixed point equations and show how these fixed points called Fixed Point Controllers (FPC) can be used for stabilization of cascade nonlinear systems. As special cases, we apply our results to semiglobal stabilization of two complex under-actuated nonlinear systems, namely the cart-pole system and the rotating pendulum.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"105 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":"115843624","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 is based on a new concept for fault-tolerant control systems against sensor failures that the truly important information for control and fault-tolerance should have redundancy. This paper considers redundant observers for information redundancy on the state of a plant and introduces analog vector-valued decision by majority among their estimated states.
{"title":"Reliable observer-based control using vector-valued decision by majority","authors":"K. Suyama","doi":"10.1109/CDC.1999.833248","DOIUrl":"https://doi.org/10.1109/CDC.1999.833248","url":null,"abstract":"This paper is based on a new concept for fault-tolerant control systems against sensor failures that the truly important information for control and fault-tolerance should have redundancy. This paper considers redundant observers for information redundancy on the state of a plant and introduces analog vector-valued decision by majority among their estimated states.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"49 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":"115833052","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 propose a method for joint synthesis of a fault detector and controller based on the free parameters of the fault detector, controller and plant. By using such parametrization, the fault detector design and controller design are merged into one design problem harmoniously, and the plant uncertainty is handled naturally. Since our approach relies on the manipulation of block diagrams, there is a nice physical interpretation of the resulting structure. As an example, this design method is applied to the control of a three mass system.
{"title":"Joint synthesis of fault detector and controller based on structure of two-degree-of-freedom control system","authors":"T. Suzuki, M. Tomizuka","doi":"10.1109/CDC.1999.827911","DOIUrl":"https://doi.org/10.1109/CDC.1999.827911","url":null,"abstract":"We propose a method for joint synthesis of a fault detector and controller based on the free parameters of the fault detector, controller and plant. By using such parametrization, the fault detector design and controller design are merged into one design problem harmoniously, and the plant uncertainty is handled naturally. Since our approach relies on the manipulation of block diagrams, there is a nice physical interpretation of the resulting structure. As an example, this design method is applied to the control of a three mass system.","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":"131350010","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 method for reducing the tracking error due to motion induced vibrations for flexible robots is presented. In order to improve the performances of a feedback controller, the shaping of the reference trajectory is carried out by means of a predictive control scheme, where the online optimization is executed by an evolutionary algorithm. The addition of the feedback estimation error improves the reliability of the prediction, ensuring an adequate robustness despite of uncertainties. The method has been successfully applied by simulation to the tracking error reduction of a flexible link; the computation complexity revealed by simulations allows easy real time implementation.
{"title":"Vibration reduction by predictive evolutionary trajectory shaping","authors":"M. L. Fravolini, A. Ficola, M. La Cava","doi":"10.1109/CDC.1999.833395","DOIUrl":"https://doi.org/10.1109/CDC.1999.833395","url":null,"abstract":"A method for reducing the tracking error due to motion induced vibrations for flexible robots is presented. In order to improve the performances of a feedback controller, the shaping of the reference trajectory is carried out by means of a predictive control scheme, where the online optimization is executed by an evolutionary algorithm. The addition of the feedback estimation error improves the reliability of the prediction, ensuring an adequate robustness despite of uncertainties. The method has been successfully applied by simulation to the tracking error reduction of a flexible link; the computation complexity revealed by simulations allows easy real time implementation.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"56 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":"131969981","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 frequency domain analysis method of a second order iterative learning control (ILC) algorithm is considered. Using the notion of iterative systems bounds for stability are presented in the frequency domain for the second order term. The bounds are found using a geometrical approach based on the special structure of the transfer matrix in the iterative system. Two examples are included showing how the analysis method can be used in an application.
{"title":"A frequency domain analysis of a second order iterative learning control algorithm","authors":"M. Norrlöf, S. Gunnarsson","doi":"10.1109/CDC.1999.830248","DOIUrl":"https://doi.org/10.1109/CDC.1999.830248","url":null,"abstract":"A frequency domain analysis method of a second order iterative learning control (ILC) algorithm is considered. Using the notion of iterative systems bounds for stability are presented in the frequency domain for the second order term. The bounds are found using a geometrical approach based on the special structure of the transfer matrix in the iterative system. Two examples are included showing how the analysis method can be used in an application.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"341 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":"134201966","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}
Two approaches for robustness analysis of linear periodically time-varying systems are presented. In the first approach the state space matrices of the nominal system are expanded in Fourier series. The system can then be represented as an interconnection of a linear time-invariant system and an uncertainty that contains all harmonic functions in the Fourier series. Integral quadratic constraints (IQCs) can then be used to derive robustness conditions, which are equivalent to several linear matrix inequalities. In the second approach, instead of being factorized out, the harmonic terms are kept in the nominal system. Periodic IQCs are then used to characterize the uncertainties. This generally gives a lower dimensional optimization problem but with added complexity due to the fact that the system matrices are periodic.
{"title":"Robustness analysis of periodic systems","authors":"U. Jonsson, Chung-Yao Kao, A. Megretski","doi":"10.1109/CDC.1999.830901","DOIUrl":"https://doi.org/10.1109/CDC.1999.830901","url":null,"abstract":"Two approaches for robustness analysis of linear periodically time-varying systems are presented. In the first approach the state space matrices of the nominal system are expanded in Fourier series. The system can then be represented as an interconnection of a linear time-invariant system and an uncertainty that contains all harmonic functions in the Fourier series. Integral quadratic constraints (IQCs) can then be used to derive robustness conditions, which are equivalent to several linear matrix inequalities. In the second approach, instead of being factorized out, the harmonic terms are kept in the nominal system. Periodic IQCs are then used to characterize the uncertainties. This generally gives a lower dimensional optimization problem but with added complexity due to the fact that the system matrices are periodic.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"47 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":"134417775","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 state-dependent scaling approach to robust backstepping is proposed for global robust stabilization of nonlinear systems via output feedback. The design procedure handles output-feedback stabilization of strict-feedback systems with various kinds of uncertainty structures in a unified way. The backstepping is ready for numerical computation. The paper shows a condition of allowable uncertainty size under which an uncertain system is globally robustly stabilized by output feedback. A special class of systems is shown to be always globally stabilizable for arbitrarily large nonlinear size of uncertainties. The design procedure is developed by using the Schur complements instead of Young's inequality. A recursive procedure of robust observer design is proposed.
{"title":"Recursive state-dependent scaling design of robust output feedback control for global stabilization","authors":"H. Ito, M. Krstić","doi":"10.1109/CDC.1999.832896","DOIUrl":"https://doi.org/10.1109/CDC.1999.832896","url":null,"abstract":"A state-dependent scaling approach to robust backstepping is proposed for global robust stabilization of nonlinear systems via output feedback. The design procedure handles output-feedback stabilization of strict-feedback systems with various kinds of uncertainty structures in a unified way. The backstepping is ready for numerical computation. The paper shows a condition of allowable uncertainty size under which an uncertain system is globally robustly stabilized by output feedback. A special class of systems is shown to be always globally stabilizable for arbitrarily large nonlinear size of uncertainties. The design procedure is developed by using the Schur complements instead of Young's inequality. A recursive procedure of robust observer design is proposed.","PeriodicalId":137513,"journal":{"name":"Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)","volume":"282 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":"133924785","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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