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İntegrallenebilir Yörüngeleri ve Kontrol Kaynakları Kısıtlı olan Kontrol Sistemin Yörüngeler Kümesinin Özellikleri Üzerine

Yıl 2023, Cilt: 16 Sayı: 1, 24 - 29, 12.10.2023
https://doi.org/10.58688/kujs.1289473

Öz

Bu çalışmada, davranışı Urysohn tür integral denklem ile verilen ve kontrol fonksiyonları üzerinde integral kısıt olan kontrol sistem incelenmektedir. Mümkün kontrol fonksiyonlar L_p (E;R^m ) (p>1) uzayının merkezi orijinde olan r yarıçaplı kapalı yuvarından seçilmektedir. Sistemin yörüngesi verilen denklemi hemen hemen her yerde sağlayan çok değişkenli integrallenebilir fonksiyon olarak tanımlanmaktadır. Yörüngeler kümesinin çapı için bir üst sınır elde edilmiş, yörüngeler kümesinin r ‘ye göre Lipschitz sürekli olduğu kanıtlanmıştır.

Kaynakça

  • Brauer, F. (1975). On a nonlinear integral equation for population growth problems. SIAM J. Math. Anal., 6(2), 312-317.
  • Conti, R. (1974). Problemi di controllo e di controllo ottimale. UTET, Torino.
  • Deimling, K. (1992). Multivalued differential equations. Walter de Gruyter, Berlin.
  • Guseinov, K. G., & Nazlipinar, A. S. (2007). On the continuity property of L_p balls and an application. J. Math. Anal. Appl., 335(2), 1347-1359.
  • Gusev, M. I., & Zykov, I. V. (2017). On extremal properties of the boundary points of reachable sets for control systems with integral constraints. Tr. Inst. Math. Mekh. UrO RAN, 23(1), 103-115.
  • Hu, S., & Papageorgiou, N. S. (1997). Handbook of multivlued analysis. Vol. I: Theory. Kluwer, Dordrecht.
  • Huseyin, N., Guseinov, K. G., & Ushakov, V. N. (2015). Approximate construction of the set of trajectories of the control system described by a Volterra integral equation. Math. Nachr., 288(16), 1891-1899.
  • Huseyin, N., Huseyin, A., & Guseinov, K. G. (2018). Approxmation of the set of trajectories of the nonlinear control system with limited control resources. Math. Model. Anal., 23(1), 152-166.
  • Huseyin, N. (2020). On the properties of the set of p-integrable trajectories of the control system with limited control resources. Internat. J. Control, 93(8), 1810-1816.
  • Huseyin, A. (2022). On the p-integrable trajectories of the nonlinear control system described by the Urysohn-type integral equation. Open Math., 20(1), 1101-1111.
  • Ibragimov, G., Ferrara, M., Ruziboev, M., & Pansera, B. A. (2021). Linear evasion differential game of one evader and several pursuers with integral constraints. Int. J. Game Theory, 50, 729–750.
  • Kalman, R. E. (1963). Mathematical description of linear dynamical systems. J. SIAM Control, Ser. A, 1, 152-192.
  • Kelley, J. L. (1975). General topology. Springer, New York.
  • Krasovskii, N. N. (1968). Theory of control of motion: Linear systems. Nauka, Moscow.
  • Krasovskii, N. N., & Subbotin, A. I. (1988). Game-theoretical control problems. Springer, New York.
  • Krasnoselskii, M. A., & Krein, S. G. (1955). On the principle of averaging in nonlinear mechanics. Uspekhi Mat. Nauk. 10(3), 147-153.
  • Kostousova, E. K. (2020). On the polyhedral estimation of reachable sets in the "extended'' space for multistage systems with uncertain matrices and integral constraints. Tr. Inst. Mat. Mekh. UrO RAN, 26(1), 141-155.
  • Polyanin, A. D., & Manzhirov, A. V. (1998). Handbook of integral equations. CRC Press, Boca Raton.
  • Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1962). The mathematical theory of optimal processes. John Wiley & Sons, New York.
  • Subbotin, A. I, & Ushakov, V. N. (1975). Alternative for an encounter-evasion differential game with integral constraints on the players' controls. J. Appl. Math. Mech., 39(3), 367-375.
  • Subbotina, N. N., & Subbotin, A. I. (1975). Alternative for the encounter-evasion differential game with constraints on the momenta of the players controls. J. Appl. Math. Mech., 39(3), 376-385.
  • Ukhobotov, V. I., & Izmest’ev, I. V. (2018). Impulse differential game with a mixed constraint on the choice of the control of the first player. Tr. Inst. Math. Mekh. UrO RAN, 24(1), 209-222.
  • Urysohn, P. S. (1923). On a type of nonlinear integral equation. Mat. Sb., 31(2), 236-255.

On the Properties of the Set of Trajectories of the Control System with Integrable Trajectories and Limited Control Resources

Yıl 2023, Cilt: 16 Sayı: 1, 24 - 29, 12.10.2023
https://doi.org/10.58688/kujs.1289473

Öz

In this paper the control system given by Urysohn type integral equation with integral constraint on the control functions is studied. The admissible control functions are chosen from the closed ball of the space L_p (E;R^m ) (p>1) centered at the origin with radius r. The trajectory of the system is defined as a multivariable integrable function which satisfies the system’s equation almost everywhere. An upper evaluation for diameter of the set of trajectories is obtained and it is proved that the set of trajectories is Lipschitz continuous with respect to r.

Kaynakça

  • Brauer, F. (1975). On a nonlinear integral equation for population growth problems. SIAM J. Math. Anal., 6(2), 312-317.
  • Conti, R. (1974). Problemi di controllo e di controllo ottimale. UTET, Torino.
  • Deimling, K. (1992). Multivalued differential equations. Walter de Gruyter, Berlin.
  • Guseinov, K. G., & Nazlipinar, A. S. (2007). On the continuity property of L_p balls and an application. J. Math. Anal. Appl., 335(2), 1347-1359.
  • Gusev, M. I., & Zykov, I. V. (2017). On extremal properties of the boundary points of reachable sets for control systems with integral constraints. Tr. Inst. Math. Mekh. UrO RAN, 23(1), 103-115.
  • Hu, S., & Papageorgiou, N. S. (1997). Handbook of multivlued analysis. Vol. I: Theory. Kluwer, Dordrecht.
  • Huseyin, N., Guseinov, K. G., & Ushakov, V. N. (2015). Approximate construction of the set of trajectories of the control system described by a Volterra integral equation. Math. Nachr., 288(16), 1891-1899.
  • Huseyin, N., Huseyin, A., & Guseinov, K. G. (2018). Approxmation of the set of trajectories of the nonlinear control system with limited control resources. Math. Model. Anal., 23(1), 152-166.
  • Huseyin, N. (2020). On the properties of the set of p-integrable trajectories of the control system with limited control resources. Internat. J. Control, 93(8), 1810-1816.
  • Huseyin, A. (2022). On the p-integrable trajectories of the nonlinear control system described by the Urysohn-type integral equation. Open Math., 20(1), 1101-1111.
  • Ibragimov, G., Ferrara, M., Ruziboev, M., & Pansera, B. A. (2021). Linear evasion differential game of one evader and several pursuers with integral constraints. Int. J. Game Theory, 50, 729–750.
  • Kalman, R. E. (1963). Mathematical description of linear dynamical systems. J. SIAM Control, Ser. A, 1, 152-192.
  • Kelley, J. L. (1975). General topology. Springer, New York.
  • Krasovskii, N. N. (1968). Theory of control of motion: Linear systems. Nauka, Moscow.
  • Krasovskii, N. N., & Subbotin, A. I. (1988). Game-theoretical control problems. Springer, New York.
  • Krasnoselskii, M. A., & Krein, S. G. (1955). On the principle of averaging in nonlinear mechanics. Uspekhi Mat. Nauk. 10(3), 147-153.
  • Kostousova, E. K. (2020). On the polyhedral estimation of reachable sets in the "extended'' space for multistage systems with uncertain matrices and integral constraints. Tr. Inst. Mat. Mekh. UrO RAN, 26(1), 141-155.
  • Polyanin, A. D., & Manzhirov, A. V. (1998). Handbook of integral equations. CRC Press, Boca Raton.
  • Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1962). The mathematical theory of optimal processes. John Wiley & Sons, New York.
  • Subbotin, A. I, & Ushakov, V. N. (1975). Alternative for an encounter-evasion differential game with integral constraints on the players' controls. J. Appl. Math. Mech., 39(3), 367-375.
  • Subbotina, N. N., & Subbotin, A. I. (1975). Alternative for the encounter-evasion differential game with constraints on the momenta of the players controls. J. Appl. Math. Mech., 39(3), 376-385.
  • Ukhobotov, V. I., & Izmest’ev, I. V. (2018). Impulse differential game with a mixed constraint on the choice of the control of the first player. Tr. Inst. Math. Mekh. UrO RAN, 24(1), 209-222.
  • Urysohn, P. S. (1923). On a type of nonlinear integral equation. Mat. Sb., 31(2), 236-255.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Anar Huseyin 0000-0002-3911-2304

Yayımlanma Tarihi 12 Ekim 2023
Gönderilme Tarihi 3 Mayıs 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 16 Sayı: 1

Kaynak Göster

APA Huseyin, A. (2023). İntegrallenebilir Yörüngeleri ve Kontrol Kaynakları Kısıtlı olan Kontrol Sistemin Yörüngeler Kümesinin Özellikleri Üzerine. Kafkas Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 16(1), 24-29. https://doi.org/10.58688/kujs.1289473