Geodesic
Improvement methods for problems of optimal control of multistage processes
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 15-27.

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In this paper, we propose first- and second-order methods of improvement for optimal control problems with non-fixed durations of stages based on the theory of V. F. Krotov. We obtain unimprovability conditions, which are closely related to the necessary and sufficient conditions for a weak local minimum.
Keywords: multistage process, dynamical system, non-fixed time, optimal control, iterative methods. 
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V. A. Baturin; S. Cheremnykh. Improvement methods for problems of optimal control of multistage processes. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 196 (2021), pp. 15-27. http://geodesic.mathdoc.fr/item/INTO_2021_196_a1/

[1] Baturin V. A., Lempert A. A., “Metod uluchsheniya dlya diskretnoi upravlyaemoi sistemy s setevoi strukturoi”, Upravl. bolshimi sist., 30:1 (2010), 11–21

[2] Baturin V. A., Urbanovich D. E., Priblizhennye metody optimalnogo upravleniya, osnovannye na printsipe rasshireniya, Nauka, Novosibirsk, 1997

[3] Gabelko K. N., “Posledovatelnoe uluchshenie mnogoetapnykh protsessov”, Avtomat. telemekh., 1974, no. 12, 72–80

[4] Gurman V. I., Printsip rasshireniya v zadachakh upravleniya, Nauka, M., 1997

[5] Gurman V. I., Orlov A. G., “Dostatochnye usloviya optimalnosti slozhnykh protsessov”, Avtomat. telemekh., 1978, no. 4, 127–134 | MR | Zbl

[6] Gurman V. I., Baturin V. A., Rasina I. V., Priblizhennye metody optimalnogo upravleniya, Izd-vo Irkutsk. un-ta, Irkutsk, 1983

[7] Gurman V. I., Vyrozhdennye zadachi optimalnogo upravleniya, Nauka, M., 1977

[8] Gurman V. I., Rasina I. V., Fesko O. V., Usenko O. V., “Metod uluchsheniya upravleniya dlya ierarkhicheskikh modelei sistem setevoi struktury”, Izv. Irkutsk. gos. un-ta. Ser. Mat., 2014, no. 8, 71–85 | Zbl

[9] Gurman V. I., Rasina I. V., “Dostatochnye usloviya optimalnosti v ierarkhicheskikh modelyakh neodnorodnykh sistem”, Avtomat. telemekh., 2013, no. 12, 15–30 | Zbl

[10] Dmitruk A. V., Kaganovich A. M., “Printsip maksimuma dlya zadach optimalnogo upravleniya s promezhutochnymi ogranicheniyami”, Nelin. dinam. upravl., 2008, no. 6, 101–136

[11] Krotov V. F., Gurman V. I., Metody i zadachi optimalnogo upravleniya, Nauka, M., 1973

[12] Antsaklis P. J., “A brief introduction to the theory and applications of hybrid systems”, Proc. IEEE. Spec. Issue on Hybrid Systems: Theory and Applications, 88:7 (2000), 879–886

[13] Assard R., Montecinob M. A., Maasse A., Sherman D. J., “Modeling acclimatization by hybrid systems: Condition changes alter biological system behavior models”, Biosystems., 121 (2014), 43–53 | DOI

[14] Branicky M. S., “Multiple Lyapunov functions and other analysis tools for switched and hybrid systems”, IEEE Trans. Automat. Contr., 43:4 (1998), 475–482 | DOI | MR | Zbl

[15] Chevalier P.-Y., Hendrickx J. M., Jungers R. M., “Efficient algorithms for the consensus decision problem”, SIAM J. Control Optim., 53:5 (2015), 3104–3119 | DOI | MR | Zbl

[16] Haimovicha H., Seron M. M., “Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations”, Automatica., 49:3 (2013), 748–754 | DOI | MR

[17] Heemels W. P. M. H., De Schutter B., Lunze J., Lazar M., “Stability analysis and controller synthesis for hybrid dynamical systems”, Phil. Trans. Roy. Soc. A., 368 (2010), 4937–4960 | DOI | MR | Zbl

[18] Henrion D., Daafouz J., Claeys M., “Optimal switching control design for polynomial systems: an LMI approach”, Proc. 52nd IEEE Conf. on Decision and Control, 2013, 1349–1354 | DOI

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

[20] Liberzon D., Switching in systems and control, Springer-Verlag, Berlin, 2003 | MR

[21] Lygeros J., Johansson K. H., Simic S. N., Zhang J., Sastry S. S., “Dynamical properties of hybrid automata”, IEEE Trans. Automat. Control., 48:1 (2003), 2–17 | DOI | MR | Zbl

[22] Monovich T., Margaliot M., “Analysis of discrete-time linear switched systems: A variational approach”, SIAM J. Control Optim., 49:2 (2011), 808–829 | DOI | MR | Zbl

[23] Santis E., Benedetto M. D., Gennaro S., Innocenzo A., Pola G., “Critical observability of a class of hybrid systems and application to air trafic management”, Lect. Notes Control Inform. Sci., 337 (2006), 141–170 | DOI | MR | Zbl

[24] Susuki Y., Hikihara T., Predicting voltage instability of power system via hybrid system reachability analysis, Am. Control Conf., New York, 2007