On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems

This contribution deals with a robust control design for general switched affine control systems. Dynamical models under consideration are described by ordinary differential equations involving a switching mechanism and in the presence of bounded uncertainties. The design procedure we analyse is bas...

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2017
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Universidad de Medellín
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Repositorio UDEM
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eng
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oai:repository.udem.edu.co:11407/6175
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oai_identifier_str oai:repository.udem.edu.co:11407/6175
network_acronym_str REPOUDEM2
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dc.title.none.fl_str_mv On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
title On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
spellingShingle On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
title_short On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
title_full On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
title_fullStr On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
title_full_unstemmed On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
title_sort On the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systems
description This contribution deals with a robust control design for general switched affine control systems. Dynamical models under consideration are described by ordinary differential equations involving a switching mechanism and in the presence of bounded uncertainties. The design procedure we analyse is based on the newly elaborated attractive ellipsoids method ([32]). The stability and robustness of the resulting closed-loop systeminvolves an abstract Clarke stability theoremand a theoretic extension of the celebrated Lyapunov-typemethodology. A short discussion on the obtained analytic results and possible applications and extensions is also included. © 2017 by Nova Science Publishers, Inc. All Rights Reserved.
publishDate 2017
dc.date.accessioned.none.fl_str_mv 2021-02-05T15:00:26Z
dc.date.available.none.fl_str_mv 2021-02-05T15:00:26Z
dc.date.none.fl_str_mv 2017
dc.type.eng.fl_str_mv Book Chapter
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_3248
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.version.none.fl_str_mv info:eu-repo/semantics/bookPart
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/article
dc.identifier.isbn.none.fl_str_mv 9781536108477; 9781536108262
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/6175
identifier_str_mv 9781536108477; 9781536108262
url http://hdl.handle.net/11407/6175
dc.language.iso.none.fl_str_mv eng
language eng
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dc.relation.citationstartpage.none.fl_str_mv 83
dc.relation.citationendpage.none.fl_str_mv 101
dc.relation.references.none.fl_str_mv Alazki, J., Poznyak, A., Robust output stabilization for a class of nonlinear uncertain stochastic systems under multiplicative and additive noises: The attractive ellipsoid method (2016) Journal of Industrial and Management Optimization, 12, pp. 169-186
Azhmyakov, V., On the geometric aspects of the invariant ellipsoid method: Application to the robust control design (2011) Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, pp. 1353-1358. , Orlando, USA
Azhmyakov, V., Poznyak, A., Gonzalez, O., On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach (2013) Journal of Industrial and Management Optimization, 9, pp. 579-593
Azhmyakov, V., Poznyak, A., Juarez, R., On the practical stability of control processes governed by implicit differential equations: The invariant ellipsoid based approach (2013) Journal of The Franklin Institute, 350, pp. 2229-2243
Azhmyakov, V., Basin, M., Reincke-Collon, C., Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs (2014) Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, pp. 6976-6981
Azhmyakov, V., Cabrera Martinez, J., Poznyak, A., Serrezuela, R.R., Optimization of a class of nonlinear switched systems with fixed-levels control inputs Proceedings of the 2015 American Control Conference, pp. 1770-1775. , Chicago, USA
Azhmyakov, V., Juarez, R., On the projected gradient methods for switched-mode systems optimization (2015) IFAC-PapersOnLine, 48, pp. 181-186
Barabanov, A.E., Granichin, O.N., Optimal controller for linear plants with bounded noise (1984) Automation and Remote Control, 45 (5), pp. 39-46
Basin, M., Rodriguez-Gonzalez, J., Fridman, L., Optimal and robust control for linear state-delay systems (2007) Journal of the Franklin Institute, 344 (6), pp. 830-845
Basin, M., Rodriguez-Ramirez, P., Ding, S., Dominic, S., A nonhomogeneous super-twisting algorithm for systems of relative degree more than one (2015) Journal of The Franklin Institute, 352, pp. 1364-1377
Bonilla, M., Malabre, M., Azhmyakov, V., Decoupling of internal variable structure for a class of switched systems (2015) Proceedings of the 2015 European Control Conference, pp. 1890-1895. , Linz, Austria
Bonilla, M., Malabre, M., Azhmyakov, V., An implicit systems characterization of a class of impulsive linear switched control processes (2015) Modeling, Nonlinear Analysis: Hybrid Systems, 15, pp. 157-170
Boyd, S., Ghaoui, E., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities In System And Control Theory, , Philadelphia: SIAM
Clarke, F., (1990) Optimization and Nonsmooth Analysis, , Philadelphia, SIAM
Dahleh, M.A., Pearson, J.B., Boyd, J., Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization (1988) IEEE Transactions on Automatic Control, 33 (8), pp. 722-731
Duncan, G.J., Schweppe, F.C., Control of linear dynamic systems with set constrained disturbances (1971) IEEE Transactions on Automatic Control, AC16, pp. 411-423
Gonzalez, O., Poznyak, A., Azhmyakov, V., On the Robust control design for a class of nonlinear affine control systems: the invariant ellipsoid approach (2009) Proceedings of the 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, pp. 1-6. , Toluca, Mexico
Khalil, H.K., (2002) Nonlinear Systems, , Prentice Hall, Upper Saddle River, NJ, USA
Kurzhanski, A.B., Varaiya, P., Ellipsoidal techniques for reachability under state constraints (2006) SIAM Journal on Control and Optimization, 45 (4), pp. 1369-1394
Kurzhanski, A.B., Veliov, V.M., (1994) Modeling Techniques and Uncertain Systems, , Birkhäuser, New York
Liberzon, D., (2003) Switching in Systems and Control, , Birkhäuser, Boston, USA
Lygeros, J., (2003) Lecture Notes on Hyrid Systems, , Cambridge University Press, Cambridge, UK
Mera, M., Castanos, F., Poznyak, A., Quantised and sampled output feedback for nonlinear systems (2014) International Journal of Control, 87, pp. 2475-2487
Mera, M., Polyakov, A., Perruquetti, W., Zheng, G., Finite-time attractive ellipsoidmethod using implicit Lyapunov functions (2015) Proceedings of the 54th Conference on Decision and Control, pp. 6892-6896. , Osaka, Japan
Michel, A.N., Hou, L., Liu, D., (2007) Stability of Dynamical Systems, , Birkhäuser, New York
Polyak, B.T., Nazin, S.A., Durieu, C., Walter, E., Ellipsoidal parameter or state estimation under model uncertainty (2004) Automatica, 40 (7), pp. 1171-1179
Polyak, T., Suppression of bounded exogeneous disturbances: output control (2008) Automation and Remote Control, 69 (5), pp. 801-818
Polyakov, A., Poznyak, A., Lyapunov function design for finite-time convergence analysis: twisting controller for second-order sliding mode realization (2009) Automatica, 45, pp. 444-448
Polyakov, A., Minimization of disturbances effects in time delay predictor-based sliding mode control systems (2012) Journl of The Franklin institute, 349, pp. 1380-1396
Poznyak, A., (2008) Advanced Mathematical Tools for Automatic Control Engineers:Deterministic Techniques, , Elsevier, Amsterdam
Poznyak, A., Azhmyakov, V., Mera, M., Practical output feedback stabilization for a class of continuous-time dynamic systems under sampledada outputs (2011) International Journal of Control, 84, pp. 1408-1416
Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhäuser, Basel, Switzerland
Poznyak, T., Chairez, I., Poznyak, A., Switching robust control for ozone generators using the attractive ellipsoidmethod (2014) ISA Transactions, 53, pp. 1796-1806
Shaikh, M.S., Caines, P.E., On the hybrid optimal control problem:theory and algorithms (2007) IEEE Transactions on Automatic Control, 52, pp. 1587-1603
Wardi, Y., Egerstedt, M., Twu, P., A controlled precision algorithm for mode-switching optimization (2012) Proceedings of the 51st Conference on Decision and Control, pp. 713-718. , Maui, USA
Zabczyk, J., (1995) Mathematical Control Theory: an Introduction, , Birkhäuser, Boston
Zubov, V.I., (1962) Mathematical Methods for the Study of Automatic Control Systems, , Pergamon Press, New York
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_16ec
rights_invalid_str_mv http://purl.org/coar/access_right/c_16ec
dc.publisher.none.fl_str_mv Nova Science Publishers, Inc.
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
publisher.none.fl_str_mv Nova Science Publishers, Inc.
dc.source.none.fl_str_mv Robust Control: Systems, Theory and Analysis
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
_version_ 1814159205985157120
spelling 20172021-02-05T15:00:26Z2021-02-05T15:00:26Z9781536108477; 9781536108262http://hdl.handle.net/11407/6175This contribution deals with a robust control design for general switched affine control systems. Dynamical models under consideration are described by ordinary differential equations involving a switching mechanism and in the presence of bounded uncertainties. The design procedure we analyse is based on the newly elaborated attractive ellipsoids method ([32]). The stability and robustness of the resulting closed-loop systeminvolves an abstract Clarke stability theoremand a theoretic extension of the celebrated Lyapunov-typemethodology. A short discussion on the obtained analytic results and possible applications and extensions is also included. © 2017 by Nova Science Publishers, Inc. All Rights Reserved.engNova Science Publishers, Inc.Facultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85061655982&partnerID=40&md5=8be272f5c2186f0987d1a74ba8977d8583101Alazki, J., Poznyak, A., Robust output stabilization for a class of nonlinear uncertain stochastic systems under multiplicative and additive noises: The attractive ellipsoid method (2016) Journal of Industrial and Management Optimization, 12, pp. 169-186Azhmyakov, V., On the geometric aspects of the invariant ellipsoid method: Application to the robust control design (2011) Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, pp. 1353-1358. , Orlando, USAAzhmyakov, V., Poznyak, A., Gonzalez, O., On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach (2013) Journal of Industrial and Management Optimization, 9, pp. 579-593Azhmyakov, V., Poznyak, A., Juarez, R., On the practical stability of control processes governed by implicit differential equations: The invariant ellipsoid based approach (2013) Journal of The Franklin Institute, 350, pp. 2229-2243Azhmyakov, V., Basin, M., Reincke-Collon, C., Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs (2014) Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, pp. 6976-6981Azhmyakov, V., Cabrera Martinez, J., Poznyak, A., Serrezuela, R.R., Optimization of a class of nonlinear switched systems with fixed-levels control inputs Proceedings of the 2015 American Control Conference, pp. 1770-1775. , Chicago, USAAzhmyakov, V., Juarez, R., On the projected gradient methods for switched-mode systems optimization (2015) IFAC-PapersOnLine, 48, pp. 181-186Barabanov, A.E., Granichin, O.N., Optimal controller for linear plants with bounded noise (1984) Automation and Remote Control, 45 (5), pp. 39-46Basin, M., Rodriguez-Gonzalez, J., Fridman, L., Optimal and robust control for linear state-delay systems (2007) Journal of the Franklin Institute, 344 (6), pp. 830-845Basin, M., Rodriguez-Ramirez, P., Ding, S., Dominic, S., A nonhomogeneous super-twisting algorithm for systems of relative degree more than one (2015) Journal of The Franklin Institute, 352, pp. 1364-1377Bonilla, M., Malabre, M., Azhmyakov, V., Decoupling of internal variable structure for a class of switched systems (2015) Proceedings of the 2015 European Control Conference, pp. 1890-1895. , Linz, AustriaBonilla, M., Malabre, M., Azhmyakov, V., An implicit systems characterization of a class of impulsive linear switched control processes (2015) Modeling, Nonlinear Analysis: Hybrid Systems, 15, pp. 157-170Boyd, S., Ghaoui, E., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities In System And Control Theory, , Philadelphia: SIAMClarke, F., (1990) Optimization and Nonsmooth Analysis, , Philadelphia, SIAMDahleh, M.A., Pearson, J.B., Boyd, J., Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization (1988) IEEE Transactions on Automatic Control, 33 (8), pp. 722-731Duncan, G.J., Schweppe, F.C., Control of linear dynamic systems with set constrained disturbances (1971) IEEE Transactions on Automatic Control, AC16, pp. 411-423Gonzalez, O., Poznyak, A., Azhmyakov, V., On the Robust control design for a class of nonlinear affine control systems: the invariant ellipsoid approach (2009) Proceedings of the 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, pp. 1-6. , Toluca, MexicoKhalil, H.K., (2002) Nonlinear Systems, , Prentice Hall, Upper Saddle River, NJ, USAKurzhanski, A.B., Varaiya, P., Ellipsoidal techniques for reachability under state constraints (2006) SIAM Journal on Control and Optimization, 45 (4), pp. 1369-1394Kurzhanski, A.B., Veliov, V.M., (1994) Modeling Techniques and Uncertain Systems, , Birkhäuser, New YorkLiberzon, D., (2003) Switching in Systems and Control, , Birkhäuser, Boston, USALygeros, J., (2003) Lecture Notes on Hyrid Systems, , Cambridge University Press, Cambridge, UKMera, M., Castanos, F., Poznyak, A., Quantised and sampled output feedback for nonlinear systems (2014) International Journal of Control, 87, pp. 2475-2487Mera, M., Polyakov, A., Perruquetti, W., Zheng, G., Finite-time attractive ellipsoidmethod using implicit Lyapunov functions (2015) Proceedings of the 54th Conference on Decision and Control, pp. 6892-6896. , Osaka, JapanMichel, A.N., Hou, L., Liu, D., (2007) Stability of Dynamical Systems, , Birkhäuser, New YorkPolyak, B.T., Nazin, S.A., Durieu, C., Walter, E., Ellipsoidal parameter or state estimation under model uncertainty (2004) Automatica, 40 (7), pp. 1171-1179Polyak, T., Suppression of bounded exogeneous disturbances: output control (2008) Automation and Remote Control, 69 (5), pp. 801-818Polyakov, A., Poznyak, A., Lyapunov function design for finite-time convergence analysis: twisting controller for second-order sliding mode realization (2009) Automatica, 45, pp. 444-448Polyakov, A., Minimization of disturbances effects in time delay predictor-based sliding mode control systems (2012) Journl of The Franklin institute, 349, pp. 1380-1396Poznyak, A., (2008) Advanced Mathematical Tools for Automatic Control Engineers:Deterministic Techniques, , Elsevier, AmsterdamPoznyak, A., Azhmyakov, V., Mera, M., Practical output feedback stabilization for a class of continuous-time dynamic systems under sampledada outputs (2011) International Journal of Control, 84, pp. 1408-1416Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhäuser, Basel, SwitzerlandPoznyak, T., Chairez, I., Poznyak, A., Switching robust control for ozone generators using the attractive ellipsoidmethod (2014) ISA Transactions, 53, pp. 1796-1806Shaikh, M.S., Caines, P.E., On the hybrid optimal control problem:theory and algorithms (2007) IEEE Transactions on Automatic Control, 52, pp. 1587-1603Wardi, Y., Egerstedt, M., Twu, P., A controlled precision algorithm for mode-switching optimization (2012) Proceedings of the 51st Conference on Decision and Control, pp. 713-718. , Maui, USAZabczyk, J., (1995) Mathematical Control Theory: an Introduction, , Birkhäuser, BostonZubov, V.I., (1962) Mathematical Methods for the Study of Automatic Control Systems, , Pergamon Press, New YorkRobust Control: Systems, Theory and AnalysisOn the geometry of the attractive ellipsoids method: Applications to the robust control design of switched systemsBook Chapterinfo:eu-repo/semantics/bookPartinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_3248http://purl.org/coar/resource_type/c_2df8fbb1Azhmyakov, V., Department of Basic Sciences, Universidad de Medellin, Medellin, Colombiahttp://purl.org/coar/access_right/c_16ecAzhmyakov V.11407/6175oai:repository.udem.edu.co:11407/61752021-02-05 10:00:26.527Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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