Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays
Our contribution deals with a class of Optimal Control Problems (OCPs) of dynamic systems with randomly varying time delays. We study the minimax-type OCPs associated with a family of delayed differential equations. The presented minimax dynamic optimization has a natural interpretation as a robustn...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
- OAI Identifier:
- oai:repository.udem.edu.co:11407/6162
- Acceso en línea:
- http://hdl.handle.net/11407/6162
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- http://purl.org/coar/access_right/c_16ec
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Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| title |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| spellingShingle |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| title_short |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| title_full |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| title_fullStr |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| title_full_unstemmed |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| title_sort |
Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays |
| description |
Our contribution deals with a class of Optimal Control Problems (OCPs) of dynamic systems with randomly varying time delays. We study the minimax-type OCPs associated with a family of delayed differential equations. The presented minimax dynamic optimization has a natural interpretation as a robustness (in optimization) with respect to the possible delays in control system under consideration. A specific structure of a delayed model makes it possible to reduce the originally given sophisticated OCP to an equivalent convex program in an Euclidean space. This analytic transformation implies a possibility to derive the necessary and sufficient optimality conditions for the original OCP. Moreover, it also allows consideration of the wide range of effective numerical procedures for the constructive treatment of the obtained convex-like OCP. The concrete computational methodology we follow in this paper involves a gradient projected algorithm. We give a rigorous formal analysis of the proposed solution approach and establish the necessary numerical consistence properties of the resulting robust optimization algorithm. © 2018 |
| publishDate |
2018 |
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2021-02-05T15:00:18Z |
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2021-02-05T15:00:18Z |
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2018 |
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Article |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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24058963 |
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http://hdl.handle.net/11407/6162 |
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10.1016/j.ifacol.2018.11.075 |
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24058963 10.1016/j.ifacol.2018.11.075 |
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http://hdl.handle.net/11407/6162 |
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eng |
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eng |
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https://www.scopus.com/inward/record.uri?eid=2-s2.0-85056875837&doi=10.1016%2fj.ifacol.2018.11.075&partnerID=40&md5=01af086b50be515b647c1572a27850c1 |
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51 |
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25 |
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Ahmed, A., Verriest, E.I., Estimator design for a subsonic rocket car (soft landing) based on state-dependent delay measurement (2013), pp. 5698-5703. , Proceedings of the 52th IEEE Conference on Decision and Control, 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 Armijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, p. 13 Azhmyakov, V., Raisch, J., Convex control systems and convex optimal control problems with constraints (2008) IEEE Transactions on Automatic Control, 53, pp. 993-998 Azhmyakov, V., Basin, M., Raisch, J., A Proximal point based approach to optimal control of affine switched systems (2012) Discrete Event Dynamic Systems, 22 (1), pp. 61-81 Azhmyakov, V., Basin, M., Reincke-Collon, C., Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs (2014), pp. 6976-6981. , Proceedings of the 19th IFAC World Congress, 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, 37 (5), pp. 1035-1055 Azhmyakov, V., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016), pp. 3617-3623. , Proceedings of the 55th IEEE Conference on Decision and Control, Las Vegas, USA Azhmyakov, V., Juarez, R., A first-order numerical approach to switched-mode systems optimization (2017) Nonlinear Analysis: Hybrid Systems, 25 (1), pp. 126-137 Azhmyakov, V., (2018) A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems, , Elsevier Massachusetts, USA to appear in Basin, M., Optimal control for linear systems with multiple time delays in control input (2006) IEEE Transactions on Automatic Control, 51, pp. 91-97 BelloCruz, J.Y., de Oliveira, C.W., (2014), pp. 1-18. , On weak and strong convergence of the projected gradient method for convex optimization in Hilbert spaces, arXiv Bertsekas, D., (1995) Nonlinear Programming, , Athena Scientific Belmont, USA Betts, J., (2001) Practical Methods for Optimal Control Problems Using Nonlinear Programming, , SIAM Philadelphia, USA Boltyanski, V., Martini, H., Soltan, V., (1999) Geometric Methods and Optimization Problems, , Kluver Academic Publishers Dordrecht Bryson, A.E., Ho, Y.-C., Applied Optimal Control: Optimization (1975) Estimation and Control, , CRC Press New York Diekmann, O., van, S.A., Gils, S.M., Lunel, V., Walther, H.O., (1995) Delay Equations: Functional-, Complex-, and Nonlinear Analysis, , Springer New York 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 Egerstedt, M., Martin, C., (2009) Control Theoretic Splines: Optimal Control, Statistics, and Path Planning, , Princeton University Press Princeton, USA Goldstein, A.A., Convex programming in Hilbert space (1964) Bulletin of the American Mathematical Society, 70, pp. 709-710 Gomez, M.M., Sadeghpour, M., Bennett, M.R., Orosz, G., Murray, R.M., Stability of systems with stochastic delays and applications to genetic regulatory networks (2016) SIAM Journal of Applied Dynamic Systems, 15 (4). , pp 1844 – 1873 Hadeler, K.P., (1979) Delay Equations in Biology, , Springer 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 Hiriart-Urruty, J.B., Lemarchal, C., (1996) Convex Analysis and Minimization Algorithms, , Springer Berlin, Germany vol. 305 and 306 Ioffe, A.D., Tichomirov, V.M., (1979) Theory of Extremal Problems, , North Holland Amsterdam Malek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North Holland Amsterdam Otrocol, D., Rus, I.A., Functional-differential equations with maxima via weakly Picard operators theory (2008) Bull. Math. Soc. Sci. Math., 51, pp. 253-261 Polak, E., (1997) Optimization, , Springer-Verlag New York, USA Poznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhäuser Basel, Switzerland Pytlak, R., (1999) Numerical Methods for Optimal Control Problems with State Constraints, , Springer Berlin, Germany Rockafellar, T., (1970) Convex Analysis, , Princeton University Press Princeton Teo, K.L., Goh, C.J., Wong, K.H., (1991) A Unifed Computational Approach to Optimal Control Problems, , Wiley New York Thitsa, M., Williams, S., Verriest, E., Formal power series method for nonlinear time delay systems with analytic initial data (2015), pp. 6478-6483. , Proceedings of the 54rd IEEE Conference on Decision and Control, Kita-KuOsaka, Japan 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 Verriest, E.I., Dirr, G., Helmke, U., Delayed resource allocation optimization with applications in population dynamics (2016) IFAC-PapersOnline, 49 (10), pp. 1-6 Verriest, E.I., Azhmyakov, Advances in optimal control of differential systems with state suprema (2017), pp. 739-744. , Proceedings of the 56th IEEE Conference on Decision and Control, Melbourne, Australia 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., (2012), pp. 4-8. , Optimal control of switched-mode dynamical systems, in: Proceedings of the 11th International Workshop on Discrete Event Systems, Guadalajara, Mexico |
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Elsevier B.V. |
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Facultad de Ciencias Básicas |
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Elsevier B.V. |
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IFAC-PapersOnLine |
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Repositorio Institucional Universidad de Medellin |
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1814159157242101760 |
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20182021-02-05T15:00:18Z2021-02-05T15:00:18Z24058963http://hdl.handle.net/11407/616210.1016/j.ifacol.2018.11.075Our contribution deals with a class of Optimal Control Problems (OCPs) of dynamic systems with randomly varying time delays. We study the minimax-type OCPs associated with a family of delayed differential equations. The presented minimax dynamic optimization has a natural interpretation as a robustness (in optimization) with respect to the possible delays in control system under consideration. A specific structure of a delayed model makes it possible to reduce the originally given sophisticated OCP to an equivalent convex program in an Euclidean space. This analytic transformation implies a possibility to derive the necessary and sufficient optimality conditions for the original OCP. Moreover, it also allows consideration of the wide range of effective numerical procedures for the constructive treatment of the obtained convex-like OCP. The concrete computational methodology we follow in this paper involves a gradient projected algorithm. We give a rigorous formal analysis of the proposed solution approach and establish the necessary numerical consistence properties of the resulting robust optimization algorithm. © 2018engElsevier B.V.Facultad de Ciencias Básicashttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85056875837&doi=10.1016%2fj.ifacol.2018.11.075&partnerID=40&md5=01af086b50be515b647c1572a27850c151251823Ahmed, A., Verriest, E.I., Estimator design for a subsonic rocket car (soft landing) based on state-dependent delay measurement (2013), pp. 5698-5703. , Proceedings of the 52th IEEE Conference on Decision and Control, Florence, ItalyAiello, 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. 855-869Aliprantis, C.D., Border, K.C., (2006) Infinite Dimensional Analysis, , Springer BerlinArmijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, p. 13Azhmyakov, V., Raisch, J., Convex control systems and convex optimal control problems with constraints (2008) IEEE Transactions on Automatic Control, 53, pp. 993-998Azhmyakov, V., Basin, M., Raisch, J., A Proximal point based approach to optimal control of affine switched systems (2012) Discrete Event Dynamic Systems, 22 (1), pp. 61-81Azhmyakov, V., Basin, M., Reincke-Collon, C., Optimal LQ-type switched control design for a class of linear systems with piecewise constant inputs (2014), pp. 6976-6981. , Proceedings of the 19th IFAC World Congress, Cape Town, South AfricaAzhmyakov, V., Cabrera Martinez, J., Poznyak, A., Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals (2016) Optimal Control Applications and Methods, 37 (5), pp. 1035-1055Azhmyakov, V., Ahmed, A., Verriest, E.I., On the optimal control of systems evolving with state suprema (2016), pp. 3617-3623. , Proceedings of the 55th IEEE Conference on Decision and Control, Las Vegas, USAAzhmyakov, V., Juarez, R., A first-order numerical approach to switched-mode systems optimization (2017) Nonlinear Analysis: Hybrid Systems, 25 (1), pp. 126-137Azhmyakov, V., (2018) A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems, , Elsevier Massachusetts, USA to appear inBasin, M., Optimal control for linear systems with multiple time delays in control input (2006) IEEE Transactions on Automatic Control, 51, pp. 91-97BelloCruz, J.Y., de Oliveira, C.W., (2014), pp. 1-18. , On weak and strong convergence of the projected gradient method for convex optimization in Hilbert spaces, arXivBertsekas, D., (1995) Nonlinear Programming, , Athena Scientific Belmont, USABetts, J., (2001) Practical Methods for Optimal Control Problems Using Nonlinear Programming, , SIAM Philadelphia, USABoltyanski, V., Martini, H., Soltan, V., (1999) Geometric Methods and Optimization Problems, , Kluver Academic Publishers DordrechtBryson, A.E., Ho, Y.-C., Applied Optimal Control: Optimization (1975) Estimation and Control, , CRC Press New YorkDiekmann, O., van, S.A., Gils, S.M., Lunel, V., Walther, H.O., (1995) Delay Equations: Functional-, Complex-, and Nonlinear Analysis, , Springer New YorkColanery, 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. 1227-1234Egerstedt, M., Wardi, Y., Axelsson, H., Transition-time optimization for switched-mode dynamical systems (2006) IEEE Transactions on Automatic Control, 51, pp. 110-115Egerstedt, M., Martin, C., (2009) Control Theoretic Splines: Optimal Control, Statistics, and Path Planning, , Princeton University Press Princeton, USAGoldstein, A.A., Convex programming in Hilbert space (1964) Bulletin of the American Mathematical Society, 70, pp. 709-710Gomez, M.M., Sadeghpour, M., Bennett, M.R., Orosz, G., Murray, R.M., Stability of systems with stochastic delays and applications to genetic regulatory networks (2016) SIAM Journal of Applied Dynamic Systems, 15 (4). , pp 1844 – 1873Hadeler, K.P., (1979) Delay Equations in Biology, , Springer New YorkHale, J.K., Lunel, S.M.V., (1993) Introduction to Functional Differential Equations, , Springer-Verlag New YorkHartung, F., Pituk, M., (2014) Recent Advances in Delay Differential and Difference Equations, , Springer BaselHiriart-Urruty, J.B., Lemarchal, C., (1996) Convex Analysis and Minimization Algorithms, , Springer Berlin, Germany vol. 305 and 306Ioffe, A.D., Tichomirov, V.M., (1979) Theory of Extremal Problems, , North Holland AmsterdamMalek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North Holland AmsterdamOtrocol, D., Rus, I.A., Functional-differential equations with maxima via weakly Picard operators theory (2008) Bull. Math. Soc. Sci. Math., 51, pp. 253-261Polak, E., (1997) Optimization, , Springer-Verlag New York, USAPoznyak, A., Polyakov, A., Azhmyakov, V., (2014) Attractive Ellipsoids in Robust Control, , Birkhäuser Basel, SwitzerlandPytlak, R., (1999) Numerical Methods for Optimal Control Problems with State Constraints, , Springer Berlin, GermanyRockafellar, T., (1970) Convex Analysis, , Princeton University Press PrincetonTeo, K.L., Goh, C.J., Wong, K.H., (1991) A Unifed Computational Approach to Optimal Control Problems, , Wiley New YorkThitsa, M., Williams, S., Verriest, E., Formal power series method for nonlinear time delay systems with analytic initial data (2015), pp. 6478-6483. , Proceedings of the 54rd IEEE Conference on Decision and Control, Kita-KuOsaka, JapanVerriest, E.I., Pseudo-continuous multi-dimensional multi-mode systems (2012) Discrete Event Dynamic Systems, 22, pp. 27-59Verriest, 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, MNVerriest, E.I., Dirr, G., Helmke, U., Delayed resource allocation optimization with applications in population dynamics (2016) IFAC-PapersOnline, 49 (10), pp. 1-6Verriest, E.I., Azhmyakov, Advances in optimal control of differential systems with state suprema (2017), pp. 739-744. , Proceedings of the 56th IEEE Conference on Decision and Control, Melbourne, AustraliaWalther, 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. 439-462Wardi, Y., (2012), pp. 4-8. , Optimal control of switched-mode dynamical systems, in: Proceedings of the 11th International Workshop on Discrete Event Systems, Guadalajara, MexicoIFAC-PapersOnLineRobust Optimal Control of Linear-Type Dynamic Systems with Random DelaysArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Azhmyakov, V., Department of Basic Sciences, Universidad de Medellin, Medellin, ColombiaVerriest, E.I., School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United StatesGuzman Trujillo, L.A., Department of Basic Sciences, Universidad de Medellin, Medellin, Colombia, School for Engineers in Sciences and Technology, University of Angers, Angers, FranceLahaye, S., School for Engineers in Sciences and Technology, University of Angers, Angers, FranceDelanoue, N., School for Engineers in Sciences and Technology, University of Angers, Angers, Francehttp://purl.org/coar/access_right/c_16ecAzhmyakov V.Verriest E.I.Guzman Trujillo L.A.Lahaye S.Delanoue N.11407/6162oai:repository.udem.edu.co:11407/61622021-02-05 10:00:18.265Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |