Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control

This paper studies optimization of dynamic systems described by affine Functional Differential Equations (FDEs) involving a sup-operator. We deal with a class of FDEs-featured Optimal Control Problems (OCPs) in the presence of some additional control constraints. Our aim is to derive the first-order...

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Tipo de recurso:
Fecha de publicación:
2018
Institución:
Universidad de Medellín
Repositorio:
Repositorio UDEM
Idioma:
eng
OAI Identifier:
oai:repository.udem.edu.co:11407/4885
Acceso en línea:
http://hdl.handle.net/11407/4885
Palabra clave:
Automation
Differential equations
Optimal control systems
Process control
Solar energy
Additional control
Computational approach
Effective solution
First-order optimality condition
Functional differential equations
Maximum power point tracking controls
Optimal control problem
Solar energy plants
Maximum power point trackers
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http://purl.org/coar/access_right/c_16ec
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oai_identifier_str oai:repository.udem.edu.co:11407/4885
network_acronym_str REPOUDEM2
network_name_str Repositorio UDEM
repository_id_str
dc.title.spa.fl_str_mv Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
title Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
spellingShingle Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
Automation
Differential equations
Optimal control systems
Process control
Solar energy
Additional control
Computational approach
Effective solution
First-order optimality condition
Functional differential equations
Maximum power point tracking controls
Optimal control problem
Solar energy plants
Maximum power point trackers
title_short Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
title_full Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
title_fullStr Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
title_full_unstemmed Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
title_sort Optimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking control
dc.contributor.affiliation.spa.fl_str_mv Azhmyakov, V., Universidad de Medellin;Vemest, E.I., School of Electrical and Computer Engineering; Georgia Institute of Technology;Trujillo, L.A.G., Universidad de Medellín;Valenzuela, P.A., Universidad Autonoma de Coahuila
dc.subject.spa.fl_str_mv Automation
Differential equations
Optimal control systems
Process control
Solar energy
Additional control
Computational approach
Effective solution
First-order optimality condition
Functional differential equations
Maximum power point tracking controls
Optimal control problem
Solar energy plants
Maximum power point trackers
topic Automation
Differential equations
Optimal control systems
Process control
Solar energy
Additional control
Computational approach
Effective solution
First-order optimality condition
Functional differential equations
Maximum power point tracking controls
Optimal control problem
Solar energy plants
Maximum power point trackers
description This paper studies optimization of dynamic systems described by affine Functional Differential Equations (FDEs) involving a sup-operator. We deal with a class of FDEs-featured Optimal Control Problems (OCPs) in the presence of some additional control constraints. Our aim is to derive the first-order optimality conditions and propose an effective solution algorithm. Moreover, we are interested in applications of the resulting optimal design techniques to the Maximum Power Point Tracking (MPPT) control of solar energy plants. We develop a conceptual computational approach to the specific class of OCPs under consideration and also point possible applications of this new methodology in MPPT control. © 2017 IEEE.
publishDate 2018
dc.date.accessioned.none.fl_str_mv 2018-10-31T13:44:21Z
dc.date.available.none.fl_str_mv 2018-10-31T13:44:21Z
dc.date.created.none.fl_str_mv 2018
dc.type.eng.fl_str_mv Conference Paper
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_c94f
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/conferenceObject
dc.identifier.isbn.none.fl_str_mv 9781538603987
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11407/4885
dc.identifier.doi.none.fl_str_mv 10.1109/CCAC.2017.8276442
identifier_str_mv 9781538603987
10.1109/CCAC.2017.8276442
url http://hdl.handle.net/11407/4885
dc.language.iso.none.fl_str_mv eng
language eng
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dc.relation.citationvolume.spa.fl_str_mv 2018-January
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationendpage.spa.fl_str_mv 7
dc.relation.ispartofes.spa.fl_str_mv 2017 IEEE 3rd Colombian Conference on Automatic Control, CCAC 2017 - Conference Proceedings
dc.relation.references.spa.fl_str_mv Armijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, pp. 1-3;Azhmyakov, V., Boltyanski, V.G., Poznyak, A., Optimal control of impulsive hybrid systems (2008) Nonlinear Analysis: Hybrid Systems, 2, pp. 1089-1097;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, pp. 6976-6981. , Cape Town, South Africa;Azhmyakov, V., Cabrera Martinez, J., Poznyak, A., Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals (2016) Optimal Control Applications and Methods, , to apper in;Azhmyakov, V., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016) Proceedings of the 55th Conference on Decision and Control, pp. 3617-3623. , Las Vegas, USA;Bainov, D.D., Hristova, S.G., (2011) Differential Equations with Maxima, , CRC Press, New York;Basin, M., Optimal control for linear systems with multiple time delays in control input (2006) IEEE Transactions on Automatic Control, 51, pp. 91-97;Betts, J., (2001) Practical Methods for Optimal Control Problems Using Nonlinear Programming, , SIAM, Philadelphia, USA;Bohner, M.J., Georgieva, A.T., Hristova, S.G., Nonlinear differential equations with maxima: Parametric stability in terms of two measures (2013) Applied Mathematics and Information Sciences, 7, pp. 41-48;Desai, H.P., Patel, H.K., Maximum power point algorithm in pv generation: An overview (2007) Power Electronics and Drive Systems, pp. 624-630;Erickson, R.W., Maksimovic, D., (2001) Fundamentals of Power Electronics, , Kluwer, Dordrecht;Fattorini, H.O., (1999) Infinite Dimensional Optimization and Control Theory, , Cambridge University Press, Cambridge;Ghaffari, A., Power optimization for photovoltaic micro-converters using multivariable Newton-based extremum-seeking (2012) Proceedings of the 51st Conference on Decision and Control, pp. 2421-2426. , Maui, USA;Gill, P.E., Murray, W., Wright, M.H., (1981) Practical Optimization, , Academic Press, New York, USA;Goldstein, A.A., Convex programming in Hilbert space (1964) Bulletin of the American Mathematical Society, 70, pp. 709-710;Hale, J.K., Lunel, S.M.V., (1993) Introduction to Functional Differential Equations, , Springer-Verlag, New York;Hartung, F., Pituk, M., (2014) Recent Advances in Delay Differential and Difference Equations, , Springer, Basel;Krstic, M., Performance improvement and limitations in extremum seeking control (2000) Systems and Control Letters, 39, pp. 313-326;Lei, P., Extremum seeking control based integration of MPPT and degradation detection for photovoltaic arrays (2010) Proceedings of the 2010 American Control Conference, pp. 3536-3541. , Sant Louis, USA;Li, X., Li, Y., Seem, J.E., Lei, P., Maximum ower point tracking for photovoltaic systems using adaptive extremum seeking control (2011) Proceedings of the 50th Conference on Decision and Control, pp. 1503-1508. , Orlando, USA;Malek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North Holland, Amsterdam;Polak, E., (1997) Optimization, , Springer, New York;Poznyak, A., (2008) Advanced Mathematical Tools for Automatic Control Engineers, , Elsevier, Amsterdam, The Netherlands;Pytlak, R., (1999) Numerical Methods for Optimal Control Problems with State Constraints, , Springer, Berlin, Germany;Rockafellar, T., (1970) Convex Analysis, , Princeton University Press, Princeton;Roubicek, T., (1997) Relaxation in Optimization Theory and Variational Calculus, , De Gruyter, Berlin;Scott, J.K., Barton, P.I., Convex and concave relaxations for the parametric solutions of semi-explicit index-one differential-algebraic equations (2013) Journal of Optimization Theory and Applications, 156, pp. 617-649;Verriest, E.I., Pseudo-continuous multi-dimensional multi-mode systems (2012) Discrete Event Dynamic Systems, 22, pp. 27-59;Verriest, E.I., Dirr, G., Helmke, U., Mitesser, O., Explicitly solvable bilinear optimal control problems with applications in ecology (2016) Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems, , Minneapolis, MN;Wardi, Y., Optimal control of switched-mode dynamical systems (2012) Proceedings of the 11th International Workshop on Discrete Event Systems, pp. 4-8. , Guadalajara;Zeidler, E., (1990) Nonlinear Functional Analysis and Its Applications, , Springer, 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.spa.fl_str_mv Institute of Electrical and Electronics Engineers Inc.
dc.publisher.program.spa.fl_str_mv Ciencias Básicas
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias Básicas
dc.source.spa.fl_str_mv Scopus
institution Universidad de Medellín
repository.name.fl_str_mv Repositorio Institucional Universidad de Medellin
repository.mail.fl_str_mv repositorio@udem.edu.co
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spelling 2018-10-31T13:44:21Z2018-10-31T13:44:21Z20189781538603987http://hdl.handle.net/11407/488510.1109/CCAC.2017.8276442This paper studies optimization of dynamic systems described by affine Functional Differential Equations (FDEs) involving a sup-operator. We deal with a class of FDEs-featured Optimal Control Problems (OCPs) in the presence of some additional control constraints. Our aim is to derive the first-order optimality conditions and propose an effective solution algorithm. Moreover, we are interested in applications of the resulting optimal design techniques to the Maximum Power Point Tracking (MPPT) control of solar energy plants. We develop a conceptual computational approach to the specific class of OCPs under consideration and also point possible applications of this new methodology in MPPT control. © 2017 IEEE.engInstitute of Electrical and Electronics Engineers Inc.Ciencias BásicasFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85047439048&doi=10.1109%2fCCAC.2017.8276442&partnerID=40&md5=fe30de064581c03a2bc14e18e2d00f062018-January172017 IEEE 3rd Colombian Conference on Automatic Control, CCAC 2017 - Conference ProceedingsArmijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, pp. 1-3;Azhmyakov, V., Boltyanski, V.G., Poznyak, A., Optimal control of impulsive hybrid systems (2008) Nonlinear Analysis: Hybrid Systems, 2, pp. 1089-1097;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, pp. 6976-6981. , Cape Town, South Africa;Azhmyakov, V., Cabrera Martinez, J., Poznyak, A., Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals (2016) Optimal Control Applications and Methods, , to apper in;Azhmyakov, V., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016) Proceedings of the 55th Conference on Decision and Control, pp. 3617-3623. , Las Vegas, USA;Bainov, D.D., Hristova, S.G., (2011) Differential Equations with Maxima, , CRC Press, New York;Basin, M., Optimal control for linear systems with multiple time delays in control input (2006) IEEE Transactions on Automatic Control, 51, pp. 91-97;Betts, J., (2001) Practical Methods for Optimal Control Problems Using Nonlinear Programming, , SIAM, Philadelphia, USA;Bohner, M.J., Georgieva, A.T., Hristova, S.G., Nonlinear differential equations with maxima: Parametric stability in terms of two measures (2013) Applied Mathematics and Information Sciences, 7, pp. 41-48;Desai, H.P., Patel, H.K., Maximum power point algorithm in pv generation: An overview (2007) Power Electronics and Drive Systems, pp. 624-630;Erickson, R.W., Maksimovic, D., (2001) Fundamentals of Power Electronics, , Kluwer, Dordrecht;Fattorini, H.O., (1999) Infinite Dimensional Optimization and Control Theory, , Cambridge University Press, Cambridge;Ghaffari, A., Power optimization for photovoltaic micro-converters using multivariable Newton-based extremum-seeking (2012) Proceedings of the 51st Conference on Decision and Control, pp. 2421-2426. , Maui, USA;Gill, P.E., Murray, W., Wright, M.H., (1981) Practical Optimization, , Academic Press, New York, USA;Goldstein, A.A., Convex programming in Hilbert space (1964) Bulletin of the American Mathematical Society, 70, pp. 709-710;Hale, J.K., Lunel, S.M.V., (1993) Introduction to Functional Differential Equations, , Springer-Verlag, New York;Hartung, F., Pituk, M., (2014) Recent Advances in Delay Differential and Difference Equations, , Springer, Basel;Krstic, M., Performance improvement and limitations in extremum seeking control (2000) Systems and Control Letters, 39, pp. 313-326;Lei, P., Extremum seeking control based integration of MPPT and degradation detection for photovoltaic arrays (2010) Proceedings of the 2010 American Control Conference, pp. 3536-3541. , Sant Louis, USA;Li, X., Li, Y., Seem, J.E., Lei, P., Maximum ower point tracking for photovoltaic systems using adaptive extremum seeking control (2011) Proceedings of the 50th Conference on Decision and Control, pp. 1503-1508. , Orlando, USA;Malek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North Holland, Amsterdam;Polak, E., (1997) Optimization, , Springer, New York;Poznyak, A., (2008) Advanced Mathematical Tools for Automatic Control Engineers, , Elsevier, Amsterdam, The Netherlands;Pytlak, R., (1999) Numerical Methods for Optimal Control Problems with State Constraints, , Springer, Berlin, Germany;Rockafellar, T., (1970) Convex Analysis, , Princeton University Press, Princeton;Roubicek, T., (1997) Relaxation in Optimization Theory and Variational Calculus, , De Gruyter, Berlin;Scott, J.K., Barton, P.I., Convex and concave relaxations for the parametric solutions of semi-explicit index-one differential-algebraic equations (2013) Journal of Optimization Theory and Applications, 156, pp. 617-649;Verriest, E.I., Pseudo-continuous multi-dimensional multi-mode systems (2012) Discrete Event Dynamic Systems, 22, pp. 27-59;Verriest, E.I., Dirr, G., Helmke, U., Mitesser, O., Explicitly solvable bilinear optimal control problems with applications in ecology (2016) Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems, , Minneapolis, MN;Wardi, Y., Optimal control of switched-mode dynamical systems (2012) Proceedings of the 11th International Workshop on Discrete Event Systems, pp. 4-8. , Guadalajara;Zeidler, E., (1990) Nonlinear Functional Analysis and Its Applications, , Springer, New YorkScopusAutomationDifferential equationsOptimal control systemsProcess controlSolar energyAdditional controlComputational approachEffective solutionFirst-order optimality conditionFunctional differential equationsMaximum power point tracking controlsOptimal control problemSolar energy plantsMaximum power point trackersOptimization of affine dynamic systems evolving with state suprema: New perspectives in maximum power point tracking controlConference Paperinfo:eu-repo/semantics/conferenceObjecthttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_c94fAzhmyakov, V., Universidad de Medellin;Vemest, E.I., School of Electrical and Computer Engineering; Georgia Institute of Technology;Trujillo, L.A.G., Universidad de Medellín;Valenzuela, P.A., Universidad Autonoma de CoahuilaAzhmyakov V.Vemest E.I.Trujillo L.A.G.Valenzuela P.A.http://purl.org/coar/access_right/c_16ec11407/4885oai:repository.udem.edu.co:11407/48852020-05-27 16:31:11.218Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co

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