Advances in optimal control of differential systems with the state suprema
This paper deals with a further development of analytic techniques for Optimal Control Problems (OCPs) involving differential systems with the state suprema. Differential equations evolving with state suprema (maxima) provide a useful modelling framework for various real-world applications, namely,...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
- OAI Identifier:
- oai:repository.udem.edu.co:11407/4886
- Acceso en línea:
- http://hdl.handle.net/11407/4886
- Palabra clave:
- Differential equations
Optimal control systems
Analytic technique
Differential systems
Functional differential equations
Modelling framework
Optimal control problem
Optimal controls
Optimal solutions
State dependent delay
Equations of state
- Rights
- License
- http://purl.org/coar/access_right/c_16ec
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| dc.title.spa.fl_str_mv |
Advances in optimal control of differential systems with the state suprema |
| title |
Advances in optimal control of differential systems with the state suprema |
| spellingShingle |
Advances in optimal control of differential systems with the state suprema Differential equations Optimal control systems Analytic technique Differential systems Functional differential equations Modelling framework Optimal control problem Optimal controls Optimal solutions State dependent delay Equations of state |
| title_short |
Advances in optimal control of differential systems with the state suprema |
| title_full |
Advances in optimal control of differential systems with the state suprema |
| title_fullStr |
Advances in optimal control of differential systems with the state suprema |
| title_full_unstemmed |
Advances in optimal control of differential systems with the state suprema |
| title_sort |
Advances in optimal control of differential systems with the state suprema |
| dc.contributor.affiliation.spa.fl_str_mv |
Verriest, E.I., School of Electrical and Computer Engineering; Georgia Institute of Technology;Azhmyakov, V., Universidad de Medellin |
| dc.subject.spa.fl_str_mv |
Differential equations Optimal control systems Analytic technique Differential systems Functional differential equations Modelling framework Optimal control problem Optimal controls Optimal solutions State dependent delay Equations of state |
| topic |
Differential equations Optimal control systems Analytic technique Differential systems Functional differential equations Modelling framework Optimal control problem Optimal controls Optimal solutions State dependent delay Equations of state |
| description |
This paper deals with a further development of analytic techniques for Optimal Control Problems (OCPs) involving differential systems with the state suprema. Differential equations evolving with state suprema (maxima) provide a useful modelling framework for various real-world applications, namely, in electrical engineering and in biology. The corresponding dynamic models lead to Functional Differential Equations (FDEs) in the presence of state-dependent delays. We study some particular (but important) cases of optimal control processes governed by systems with sup-operator in the right hand sides of the differential equations and obtain constructive characterizations of optimal solutions. The constrained OCPs we examine are formulated assuming the (linear) feedback-type control law. The case study presented in this article constitutes a formal extension of the concept of positive dynamic systems to differential systems with the state suprema. © 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 |
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http://purl.org/coar/resource_type/c_c94f |
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info:eu-repo/semantics/conferenceObject |
| dc.identifier.isbn.none.fl_str_mv |
9781509028733 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/11407/4886 |
| dc.identifier.doi.none.fl_str_mv |
10.1109/CDC.2017.8263748 |
| identifier_str_mv |
9781509028733 10.1109/CDC.2017.8263748 |
| url |
http://hdl.handle.net/11407/4886 |
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eng |
| language |
eng |
| dc.relation.isversionof.spa.fl_str_mv |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85046149590&doi=10.1109%2fCDC.2017.8263748&partnerID=40&md5=15857cd0b8e74fa217c3547b4f941b69 |
| dc.relation.citationvolume.spa.fl_str_mv |
2018-January |
| dc.relation.citationstartpage.spa.fl_str_mv |
739 |
| dc.relation.citationendpage.spa.fl_str_mv |
744 |
| dc.relation.ispartofes.spa.fl_str_mv |
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 |
| dc.relation.references.spa.fl_str_mv |
Ahmed, A., Verriest, E.I., Nonlinear systems evolving with state suprema as multi-mode multi-dimensional systems: Analysis and observation (2015) Proceedings of the 5th IFAC Conference on Analysis and Design of Hybrid Systems, pp. 242-247. , Atlanta, USA;Ahmed, A., Verriest, E.I., Estimator design for a subsonic rocket car (soft landing) based on state-dependent delay measurement (2013) Proceedings of the 52th IEEE Conference on Decision and Control, pp. 5698-5703. , Florence, Italy;Aiello, W.G., Freedman, H.I., Wu, J., Analysis of a model representing stage-structured population growth with state-dependent time delay (1992) SIAM Journal on Applied Mathematics, 52, pp. 855-869;Aliprantis, C.D., Border, K.C., (2006) Infinite Dimensional Analysis, , Springer, Berlin;Angeli, D., Sontag, E.D., Monotone control systems (2003) IEEE Transactions on Automatic Control, 48, pp. 1684-1698;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., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016) Proceedings of the 55th IEEE Conference on Decision and Control, pp. 3617-3623. , Las Vegas, USA;Azhmyakov, V., Juarez, R., A first-order numerical approach to switched-mode systems optimization (2017) Nonlinear Analysis: Hybrid Systems, , to appear;Bainov, D.D., Hristova, S.G., (2011) S.G. 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;Colanery, P., Middleton, R.H., Chen, Z., Caporale, D., Blanchini, F., Convexity of the cost functional in an optimal control problem for a class of positive switched systems (2014) Automatica, 50, pp. 1227-1234;Egerstedt, M., Wardi, Y., Axelsson, H., Transition-time optimization for switched-mode dynamical systems (2006) IEEE Transactions on Automatic Control, 51, pp. 110-115;Farina, L., Rinaldi, S., (2000) Positive Linear Systems: Theory and Applications, , J. Wiley, New York;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;Khalil, H.K., (1996) Nonlinear Systems, , Prentice Hall, Upper Saddle River;Kolesov, A.Yu., Mishchenko, E.F., Rozov, N.Kh., A modification of Hutchinsons equation (1998) Computational Mathematics and Mathematical Physics, 50, pp. 1990-2002;Luenberger, D.G., (1979) Introduction to Dynamic Systems: Theory, Models and Applications, , J. Wiley, New York;Malek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North Holland, Amsterdam;Minc, H., (1988) Nonnegative Matrices, , J. Wiley, New York;Otrocol, D., Rus, I.A., Functional-differential equations with maxima via weakly Picard operators theory (2018) Bull. Math. Soc. Sci. Math., 51, pp. 253-261;Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhäuser, Basel, Switzerland;Rockafellar, T., (1970) Convex Analysis, , Princeton University Press, Princeton;Smith, H.L., Monotone dynamical systems: An introduction to the theory of competetive and cooperative systems (1995) Mathematical Syrveys and Monographs, 41. , AMS;Teo, K.L., Goh, C.J., Wong, K.H., (1991) A Unifed Computational Approach to Optimal Control Problems, , Wiley, New York;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;Walther, H.O., Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays (2010) Journal of Dynamics and Differential Equations, 22, pp. 439-462;Wardi, Y., Optimal control of switched-mode dynamical systems (2012) Proceedings of the 11th International Workshop on Discrete Event Systems, pp. 4-8. , Guadalajara, Mexico |
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http://purl.org/coar/access_right/c_16ec |
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http://purl.org/coar/access_right/c_16ec |
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Institute of Electrical and Electronics Engineers Inc. |
| dc.publisher.program.spa.fl_str_mv |
Ciencias Básicas |
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Facultad de Ciencias Básicas |
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Scopus |
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Universidad de Medellín |
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Repositorio Institucional Universidad de Medellin |
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repositorio@udem.edu.co |
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1814159152535044096 |
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2018-10-31T13:44:21Z2018-10-31T13:44:21Z20189781509028733http://hdl.handle.net/11407/488610.1109/CDC.2017.8263748This paper deals with a further development of analytic techniques for Optimal Control Problems (OCPs) involving differential systems with the state suprema. Differential equations evolving with state suprema (maxima) provide a useful modelling framework for various real-world applications, namely, in electrical engineering and in biology. The corresponding dynamic models lead to Functional Differential Equations (FDEs) in the presence of state-dependent delays. We study some particular (but important) cases of optimal control processes governed by systems with sup-operator in the right hand sides of the differential equations and obtain constructive characterizations of optimal solutions. The constrained OCPs we examine are formulated assuming the (linear) feedback-type control law. The case study presented in this article constitutes a formal extension of the concept of positive dynamic systems to differential systems with the state suprema. © 2017 IEEE.engInstitute of Electrical and Electronics Engineers Inc.Ciencias BásicasFacultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85046149590&doi=10.1109%2fCDC.2017.8263748&partnerID=40&md5=15857cd0b8e74fa217c3547b4f941b692018-January7397442017 IEEE 56th Annual Conference on Decision and Control, CDC 2017Ahmed, A., Verriest, E.I., Nonlinear systems evolving with state suprema as multi-mode multi-dimensional systems: Analysis and observation (2015) Proceedings of the 5th IFAC Conference on Analysis and Design of Hybrid Systems, pp. 242-247. , Atlanta, USA;Ahmed, A., Verriest, E.I., Estimator design for a subsonic rocket car (soft landing) based on state-dependent delay measurement (2013) Proceedings of the 52th IEEE Conference on Decision and Control, pp. 5698-5703. , Florence, Italy;Aiello, W.G., Freedman, H.I., Wu, J., Analysis of a model representing stage-structured population growth with state-dependent time delay (1992) SIAM Journal on Applied Mathematics, 52, pp. 855-869;Aliprantis, C.D., Border, K.C., (2006) Infinite Dimensional Analysis, , Springer, Berlin;Angeli, D., Sontag, E.D., Monotone control systems (2003) IEEE Transactions on Automatic Control, 48, pp. 1684-1698;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., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016) Proceedings of the 55th IEEE Conference on Decision and Control, pp. 3617-3623. , Las Vegas, USA;Azhmyakov, V., Juarez, R., A first-order numerical approach to switched-mode systems optimization (2017) Nonlinear Analysis: Hybrid Systems, , to appear;Bainov, D.D., Hristova, S.G., (2011) S.G. 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;Colanery, P., Middleton, R.H., Chen, Z., Caporale, D., Blanchini, F., Convexity of the cost functional in an optimal control problem for a class of positive switched systems (2014) Automatica, 50, pp. 1227-1234;Egerstedt, M., Wardi, Y., Axelsson, H., Transition-time optimization for switched-mode dynamical systems (2006) IEEE Transactions on Automatic Control, 51, pp. 110-115;Farina, L., Rinaldi, S., (2000) Positive Linear Systems: Theory and Applications, , J. Wiley, New York;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;Khalil, H.K., (1996) Nonlinear Systems, , Prentice Hall, Upper Saddle River;Kolesov, A.Yu., Mishchenko, E.F., Rozov, N.Kh., A modification of Hutchinsons equation (1998) Computational Mathematics and Mathematical Physics, 50, pp. 1990-2002;Luenberger, D.G., (1979) Introduction to Dynamic Systems: Theory, Models and Applications, , J. Wiley, New York;Malek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North Holland, Amsterdam;Minc, H., (1988) Nonnegative Matrices, , J. Wiley, New York;Otrocol, D., Rus, I.A., Functional-differential equations with maxima via weakly Picard operators theory (2018) Bull. Math. Soc. Sci. Math., 51, pp. 253-261;Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhäuser, Basel, Switzerland;Rockafellar, T., (1970) Convex Analysis, , Princeton University Press, Princeton;Smith, H.L., Monotone dynamical systems: An introduction to the theory of competetive and cooperative systems (1995) Mathematical Syrveys and Monographs, 41. , AMS;Teo, K.L., Goh, C.J., Wong, K.H., (1991) A Unifed Computational Approach to Optimal Control Problems, , Wiley, New York;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;Walther, H.O., Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays (2010) Journal of Dynamics and Differential Equations, 22, pp. 439-462;Wardi, Y., Optimal control of switched-mode dynamical systems (2012) Proceedings of the 11th International Workshop on Discrete Event Systems, pp. 4-8. , Guadalajara, MexicoScopusDifferential equationsOptimal control systemsAnalytic techniqueDifferential systemsFunctional differential equationsModelling frameworkOptimal control problemOptimal controlsOptimal solutionsState dependent delayEquations of stateAdvances in optimal control of differential systems with the state supremaConference Paperinfo:eu-repo/semantics/conferenceObjecthttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_c94fVerriest, E.I., School of Electrical and Computer Engineering; Georgia Institute of Technology;Azhmyakov, V., Universidad de MedellinVerriest E.I.Azhmyakov V.http://purl.org/coar/access_right/c_16ec11407/4886oai:repository.udem.edu.co:11407/48862020-05-27 16:34:36.722Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |