Geodesic
Synthesis of the optimal control of linear logical-dynamical systems under instant multiple switchings of the automaton part
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 36-47 
A. S. Bortakovskii; E. A. Pegachkova. Synthesis of the optimal control of linear logical-dynamical systems under instant multiple switchings of the automaton part. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 36-47. http://geodesic.mathdoc.fr/item/CMFD_2011_42_a4/
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     author = {A. S. Bortakovskii and E. A. Pegachkova},
     title = {Synthesis of the optimal control of linear logical-dynamical systems under instant multiple switchings of the automaton part},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider a dynamic system controlled by an automaton with memory. The continuous part of the system is described by linear differential equations and the logical (automaton) part is described by linear recurrence equations. The moments of the state change of the automaton part are not known in advance and they are determined in the process of optimization. Modes with instant multiple switchings of the automaton part are admitted. Based on sufficient optimality conditions, we develop a technique for the synthesis of a feedback control. The application of the technique is demonstrated in an example.

[1] Boltyanskii V. G., Optimalnoe upravlenie diskretnymi sistemami, Nauka, M., 1973 | MR

[2] Bortakovskii A. S., “Dostatochnye usloviya optimalnosti avtomatnoi chasti logiko-dinamicheskoi sistemy”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2006, no. 6, 77–92 | MR

[3] Bortakovskii A. S., “Neobkhodimye usloviya optimalnosti avtomatnoi chasti logiko-dinamicheskoi sistemy”, Tr. MIAN, 262, 2008, 50–63 | MR | Zbl

[4] Bortakovskii A. S., “Sintez logiko-dinamicheskikh sistem na osnove dostatochnykh uslovii optimalnosti”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2010, no. 2, 54–68 | MR

[5] Bortakovskii A. S., Panteleev A. V., “Dostatochnye usloviya optimalnosti upravleniya nepreryvno-diskretnymi sistemami”, Avtomatika i telemekhanika, 1987, no. 7, 57–66 | MR

[6] Bortakovskii A. S., Pegachkova E. A., “Sintez optimalnogo upravleniya lineinymi logiko-dinamicheskimi sistemami”, Trudy MAI, 27, (25.04.2007) http://www.mai.ru

[7] Vasilev S. N., Zherlov A. K., Fedosov E. A., Fedunov B. E., Intellektnoe upravlenie dinamicheskimi sistemami, Fizmatlit, M., 2000

[8] Gurman V. I., Vyrozhdennye zadachi optimalnogo upravleniya, Nauka, M., 1973 | MR | Zbl

[9] S. V. Emelyanov (red.), Teoriya sistem s peremennoi strukturoi, Nauka, M., 1970 | MR

[10] Krotov V. F., Gurman V. I., Metody i zadachi optimalnogo upravleniya, Nauka, M., 1973 | MR | Zbl

[11] Letov A. M., Dinamika poleta i upravlenie, Nauka, M., 1973

[12] Miller B. M., Rubinovich E. Ya., Optimizatsiya dinamicheskikh sistem s impulsnymi upravleniyami, Nauka, M., 2004

[13] Semenov V. V., “Dinamicheskoe programmirovanie v sinteze logiko-dinamicheskikh sistem”, Priborostroenie, 1984, no. 9, 71–77

[14] Cassandras C. G., Peryne D. L., Wardi Y., “Optimal Control of a class of hybrid systems”, IEEE Trans. Autom. Control., 46:3 (2001), 398–415 | DOI | MR | Zbl

[15] Li Z., Soh Y., Wen C., Switched and impulsive systems: Analysis, design and applications, Springer, Berlin, 2005 | MR

[16] Liberson D., Switching in Systems and Control, Springer, Berlin, 2003

[17] Matveev A. S., Savkin A. V., Qualitative theory of hybrid dynamical systems, Birkhäuser, Boston, 2000 | Zbl

[18] Savkin A. V., Evans R. J., Hybrid dynamical systems: Controller and sensor switching problems, Birkhäuser, Boston, 2002 | MR | Zbl

[19] P. Ahtsaklis, W. Kohn, M. Lemmon, A. Nerode, S. Sastry (eds.), Hybrid Systems V, Lect. Notes Comput. Sci., 1567, Springer, Berlin, 1999 | DOI

[20] R. Alur, T. A. Henzinger, E. D. Sontag (eds.), Hybrid Systems III, Lect. Notes Comput. Sci., 1066, Springer, Berlin, 1996 | DOI

[21] R. L. Grossmann, A. Nerode, A. P. Ravn, H. Rischel (eds.), Hybrid Systems, Lect. Notes Comput. Sci., 736, Springer, Berlin, 1993 | DOI | MR | Zbl

[22] Modelling and analysis of logic controlled dynamic systems, IFAC Workshop, Inst. Syst. Dyn. and Control Theory. Sib. Branch RAS, Irkutsk, 2003