M. Velasco-Villa, E. Aranda-Bricaire, H. Rodríguez-Cortés, J. González-Sierra
The trajectory tracking problem for a wheeled mobile robot is addressed and solved by means of a partial state feedback strategy based on measurements from an indoor vision based absolute positioning system. The Cartesian coordinates provided by the localization system are fed to the proposed observer in order to estimate the orientation of the vehicle. It is shown that the combination of a classical dynamic full information controller with an asymptotically convergent vehicle attitude observer, designed using the immersion and invariance technique, yields a locally asymptotically stable closed-loop system. Real time experiments show the performance of the proposed control scheme.
{"title":"Trajectory Tracking for a Wheeled Mobile Robot Using a Vision Based Positioning System and an Attitude Observer","authors":"M. Velasco-Villa, E. Aranda-Bricaire, H. Rodríguez-Cortés, J. González-Sierra","doi":"10.3166/ejc.18.348-355","DOIUrl":"https://doi.org/10.3166/ejc.18.348-355","url":null,"abstract":"The trajectory tracking problem for a wheeled mobile robot is addressed and solved by means of a partial state feedback strategy based on measurements from an indoor vision based absolute positioning system. The Cartesian coordinates provided by the localization system are fed to the proposed observer in order to estimate the orientation of the vehicle. It is shown that the combination of a classical dynamic full information controller with an asymptotically convergent vehicle attitude observer, designed using the immersion and invariance technique, yields a locally asymptotically stable closed-loop system. Real time experiments show the performance of the proposed control scheme.","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79121005","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}
Pub Date : 2012-01-01DOI: 10.1016/S0947-3580(12)70562-9
Yingxin Guo
{"title":"Discussion on: \"Transfer Matrices and Advanced Statistical Analysis of Digital Controlled Continuous-Time Periodic Processes with Delay\"","authors":"Yingxin Guo","doi":"10.1016/S0947-3580(12)70562-9","DOIUrl":"https://doi.org/10.1016/S0947-3580(12)70562-9","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78182625","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}
Pub Date : 2010-01-01DOI: 10.1016/S0947-3580(10)70694-4
F. Castaños
{"title":"Discussion on: \"Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs\"","authors":"F. Castaños","doi":"10.1016/S0947-3580(10)70694-4","DOIUrl":"https://doi.org/10.1016/S0947-3580(10)70694-4","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73975096","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 port-Hamiltonian systems with dissipation (PHSD) whose underlying geometric structure is represented as the composition of a Dirac and a resistive structure. We show how the choice of a new passive input-output pair for a PHSD is reflected in a new Dirac structure. We define a general class of new passive inputoutput pairs for a PHSD and subsequently compute (in a constructive manner) the resulting new Dirac structure and examine the achievable Casimirs for this new Dirac structure. We focus on the special case where only the passive output is changed (while retaining the original input) and subsequently define a general class of new passive outputs for the PHSD. We then identify (on the basis of the achievable Casimirs) the precise form of the so-called dissipation obstacle, and how this obstacle may be removed by changing the passive output.We also review the “swapping the damping” procedure for computing a new passive output, and show how this can be obtained as a special case within our approach. We finally consider the examples of the RLC-circuit and MEMS optical switch to investigate the role played by the new class of passive outputs in shaping the system's energy.
{"title":"Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs","authors":"A. Venkatraman, A. Schaft","doi":"10.3166/ejc.16.665-677","DOIUrl":"https://doi.org/10.3166/ejc.16.665-677","url":null,"abstract":"We consider port-Hamiltonian systems with dissipation (PHSD) whose underlying geometric structure is represented as the composition of a Dirac and a resistive structure. We show how the choice of a new passive input-output pair for a PHSD is reflected in a new Dirac structure. We define a general class of new passive inputoutput pairs for a PHSD and subsequently compute (in a constructive manner) the resulting new Dirac structure and examine the achievable Casimirs for this new Dirac structure. We focus on the special case where only the passive output is changed (while retaining the original input) and subsequently define a general class of new passive outputs for the PHSD. We then identify (on the basis of the achievable Casimirs) the precise form of the so-called dissipation obstacle, and how this obstacle may be removed by changing the passive output.We also review the “swapping the damping” procedure for computing a new passive output, and show how this can be obtained as a special case within our approach. We finally consider the examples of the RLC-circuit and MEMS optical switch to investigate the role played by the new class of passive outputs in shaping the system's energy.","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75473760","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 biological research, experimental data analysis plays an important role since it enables quantitative understanding of biochemical processes. On the other hand, today's measurement techniques, in continuous development, generally allow measuring a subset of the major system's variables. Such major issue can be tackled by relying on a system's and mathematical approach. For instance, first principles modelling of metabolic or signal transduction networks typically leads to a set of nonlinear differential equations. In this paper, we devise a nonlinear observer specifically suited for models of biochemical reaction networks. We show that the observer is locally convergent under certain observability conditions which can be inferred by elementary network analysis. The applicability and performance of the outlined observer are shown considering the state estimation problem for a benchmark biochemical reaction network.
{"title":"An Observer for Mass-action Chemical Reaction Networks","authors":"M. Farina, S. Bittanti","doi":"10.3166/ejc.15.578-593","DOIUrl":"https://doi.org/10.3166/ejc.15.578-593","url":null,"abstract":"In biological research, experimental data analysis plays an important role since it enables quantitative understanding of biochemical processes. On the other hand, today's measurement techniques, in continuous development, generally allow measuring a subset of the major system's variables. Such major issue can be tackled by relying on a system's and mathematical approach. For instance, first principles modelling of metabolic or signal transduction networks typically leads to a set of nonlinear differential equations. In this paper, we devise a nonlinear observer specifically suited for models of biochemical reaction networks. We show that the observer is locally convergent under certain observability conditions which can be inferred by elementary network analysis. The applicability and performance of the outlined observer are shown considering the state estimation problem for a benchmark biochemical reaction network.","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89308834","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 investigates the problem of asymptotic state observation for analytic nonlinear discrete-time systems. A new technique for the observer construction, based on the Taylor polynomial approximation of the inverse of the observability map, is presented and discussed. The degree chosen for the approximation is the most important design parameter of the observer, in that it can be chosen such to ensure the convergence of the observation error at any desired exponential rate, in any prescribed convergence region (semiglobal exponential convergence).
{"title":"A Discrete-time Observer Based on the Polynomial Approximation of the Inverse Observability Map","authors":"A. Germani, C. Manes","doi":"10.3166/ejc.15.143156","DOIUrl":"https://doi.org/10.3166/ejc.15.143156","url":null,"abstract":"This paper investigates the problem of asymptotic state observation for analytic nonlinear discrete-time systems. A new technique for the observer construction, based on the Taylor polynomial approximation of the inverse of the observability map, is presented and discussed. The degree chosen for the approximation is the most important design parameter of the observer, in that it can be chosen such to ensure the convergence of the observation error at any desired exponential rate, in any prescribed convergence region (semiglobal exponential convergence).","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87265666","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}
Pub Date : 2009-01-01DOI: 10.1016/S0947-3580(09)70704-6
J. Maciejowski
{"title":"Discussion on: \"Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability\"","authors":"J. Maciejowski","doi":"10.1016/S0947-3580(09)70704-6","DOIUrl":"https://doi.org/10.1016/S0947-3580(09)70704-6","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73404899","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}
New magnitude bounds of the frequency response functions for the Nonlinear AutoRegressive model with eXogenous input (NARX) are investigated by exploiting the symmetry of the nth-order generalized frequency response function (GFRF) in its n frequency variables. The new magnitude bound of the nth-order symmetric GFRF is frequency-dependent, and is a polynomial function of the magnitude of the first order GFRF. The coefficients of this polynomial function are functions of model parameters. Based on this result, the system output spectrum can also be bounded by an analytical polynomial function of the magnitude of the first order GFRF. The conservatism in the bound evaluations is reduced compared with previous results. Several examples and necessary discussions illustrate the potential application and effectiveness of the new results.
{"title":"Frequency-Dependent Magnitude Bounds of the Generalized Frequency Response Functions for NARX Model","authors":"X. Jing, Z. Lang, S. Billings","doi":"10.3166/ejc.15.68-83","DOIUrl":"https://doi.org/10.3166/ejc.15.68-83","url":null,"abstract":"New magnitude bounds of the frequency response functions for the Nonlinear AutoRegressive model with eXogenous input (NARX) are investigated by exploiting the symmetry of the nth-order generalized frequency response function (GFRF) in its n frequency variables. The new magnitude bound of the nth-order symmetric GFRF is frequency-dependent, and is a polynomial function of the magnitude of the first order GFRF. The coefficients of this polynomial function are functions of model parameters. Based on this result, the system output spectrum can also be bounded by an analytical polynomial function of the magnitude of the first order GFRF. The conservatism in the bound evaluations is reduced compared with previous results. Several examples and necessary discussions illustrate the potential application and effectiveness of the new results.","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88238442","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}
D. Raimondo, D. Limón, M. Lazar, L. Magni, E. Camacho
Min-max model predictive control (MPC) is one of the few techniques suitable for robust stabilization of uncertain nonlinear systems subject to constraints. Stability issues as well as robustness have been recently studied and some novel contributions on this topic have appeared in the literature. In this survey, we distill from an extensive literature a general framework for synthesizing min-max MPC schemes with ana priori robust stability guarantee. First, we introduce a general predictionmodel that covers a wide class of uncertainties, which includes bounded disturbances as well as state and input dependent disturbances (uncertainties). Second, we extend the notion of regional input-to-state stability (ISS) in order to fit the considered class of uncertainties. Then, we establish that the standard min-max approach can only guarantee practical stability. We concentrate our attention on two different solutions for solving this problem. The first one is based on a particular design of the stage cost of the performance index, which leads to aH∞ strategy, while the second one is based on a dual-mode strategy. Under fairly mild assumptions both controllers guarantee ISS of the resulting closed-loop system.Moreover, it is shown that the nonlinear auxiliary control law introduced in [29] to solve theH∞ problem can be used, for nonlinear systems affine in control, in all the proposed min-max schemes and also in presence of state-independent disturbances. A simulation example illustrates the techniques surveyed in this article.
{"title":"Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability","authors":"D. Raimondo, D. Limón, M. Lazar, L. Magni, E. Camacho","doi":"10.3166/ejc.15.5-21","DOIUrl":"https://doi.org/10.3166/ejc.15.5-21","url":null,"abstract":"Min-max model predictive control (MPC) is one of the few techniques suitable for robust stabilization of uncertain nonlinear systems subject to constraints. Stability issues as well as robustness have been recently studied and some novel contributions on this topic have appeared in the literature. In this survey, we distill from an extensive literature a general framework for synthesizing min-max MPC schemes with ana priori robust stability guarantee. First, we introduce a general predictionmodel that covers a wide class of uncertainties, which includes bounded disturbances as well as state and input dependent disturbances (uncertainties). Second, we extend the notion of regional input-to-state stability (ISS) in order to fit the considered class of uncertainties. Then, we establish that the standard min-max approach can only guarantee practical stability. We concentrate our attention on two different solutions for solving this problem. The first one is based on a particular design of the stage cost of the performance index, which leads to aH∞ strategy, while the second one is based on a dual-mode strategy. Under fairly mild assumptions both controllers guarantee ISS of the resulting closed-loop system.Moreover, it is shown that the nonlinear auxiliary control law introduced in [29] to solve theH∞ problem can be used, for nonlinear systems affine in control, in all the proposed min-max schemes and also in presence of state-independent disturbances. A simulation example illustrates the techniques surveyed in this article.","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72916069","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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