Öz
Teşekkür
Ön izleme aşamasında, "Ek Bilgiler" bölümünde kendi ülkenizden iki, yurt dışından iki hakemi aşağıdaki şekilde önermelisiniz/ uyarısı yapılmaktadır, ancak Ek Bilgiler bölümde hakem önerilerini yazabileceğim uygun alt-bölüm bulamamam sebebiyle bu bölümde belirtmek istedim: bu önerilerimiz aşağıdaki gibidir. Teşekkürler, İyi çalışmalar. Özkan DEĞER, Türkiye, İstanbul Üniversitesi, ozdeger@istanbul.edu.tr; Gülçin DİNÇ YALÇIN, Türkiye, Eskişehir Teknik Üniversitesi, gdinc@eskisehir.edu.tr; Ali Hakan TOR, Türkiye, Abdullah Gül Üniversitesi, hakan.tor@agu.edu.tr; Savin TREANTA, Romania, Polytechnic University of Bucharest, Romanya, savin_treanta@yahoo.com; Basil KOKKİNİS, Greece, National Technical University of Athens, bkok@math.ntua.gr
Kaynakça
- Agarwal, R., Hristova, S., Strict stability in terms of two measures for impulsive differential equations with ‘supremum’, Appl. Anal., 91(7)(2012), 1379–1392.
- Aliprantis, C.D., Border, K.C., Infinite Dimensional Analysis A Hitchhiker’s Guide, 3nd ed., Springer-Verlag, Berlin, 2007.
- Bainov, D., Hristova, S., Differential Equations with Maxima, Taylor and Francis, 2011.
- Bantsur, N.R., Trofimchuk, O.P., On the existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima, Ukrainian Mathematical Journal, 50(6)(1998), 747–754.
- Brogliato, B., Nonsmooth Mechanics: Models, Dynamics and Control, Springer-Verlag, London, 1999.
- Clarke, F.H., Generalized gradients and applications, Trans. Amer. Math. Soc., 205(1975), 247–262.
- Clarke, F.H., The Maximum Principle under minimal hypotheses, SIAM J. Control and Optimization, 14(6)(1976), 1078–1091.
- Clarke, F.H., Optimization and Nonsmooth Analysis, SIAM Classics in Applied Mathematics, Philadelphia, 1990.
- Demyanov, V.F., Rubinov, A.M., Quasidifferential Calculus, Optimization Software, Inc. Publications Division, New York, 1986.
- Geiger, T., Wachsmuth, D., Wachsmuth, G. Optimal control of ODEs with state suprema, Mathematical Control and Related Fields, 11(3)(2021), 555–578.
- Giorgi, G., Guerraggio, A., Thierfelder, J., Mathematics of Optimization: Smooth and Nonsmooth Case, Elsevier Science, 2004.
- Hristova, S., Golev, A., Stefanova, K., Approximate method for boundary value problems of anti-periodic type for differential equations with maxima, Boundary Value Problems, 1(2013), 12.
- Ilter, S., Weak maximum principle for optimal control problems of nonsmooth systems, Applied Mathematics and Computation, 218(3)(2011), 805–808.
- Jankovski, T., Systems of differential equations with maxima, Doklady Akademii Nauk, 8(1997), 57–60.
- McClamroch, N.H., State Models of Dynamic Systems, Springer-Verlag, New York-Heidelberg-Berlin, 1980.
- Otrocol, D., Systems of functional differential equations with maxima, of mixed type, Electron. J. Qual. Theory Differ. Equ., 5(2014), 1–9.
- Popov, E., Automatic Regulation and Control, Nauka, Moscow, 1966.Roberts, A.W., Varberg, D.E., Convex Functions, Academic Press, New York-London, 1973.
- Roberts, A.W., Varberg, D.E., Convex Functions, Academic Press, New York-London, 1973.
- Rockafellar, R.T., Convex Analysis, Princeton University, New Jersey, 1970.
- Shpakovich, V.P., Muntyan, V.I., Method of averaging for differential equations with maxima, Ukrainian Mathematical Journal, 39(5)(1987), 543–545.
- Vinter, R.B., Optimal Control, Birkh¨auser, Boston, 2000.
Öz
In this paper, we consider optimal control systems with continuous-time which is governed by systems
of ordinary differential equation including max-type functions. We derive some properties concerning nonsmooth concepts, and a special form of adjoint condition involved in the maximum principle giving necessary conditions of optimality for optimal control problems of these systems.
Anahtar Kelimeler
Optimal control problems nonsmooth analysis max-type functions
Kaynakça
- Agarwal, R., Hristova, S., Strict stability in terms of two measures for impulsive differential equations with ‘supremum’, Appl. Anal., 91(7)(2012), 1379–1392.
- Aliprantis, C.D., Border, K.C., Infinite Dimensional Analysis A Hitchhiker’s Guide, 3nd ed., Springer-Verlag, Berlin, 2007.
- Bainov, D., Hristova, S., Differential Equations with Maxima, Taylor and Francis, 2011.
- Bantsur, N.R., Trofimchuk, O.P., On the existence and stability of periodic and almost periodic solutions of quasilinear equations with maxima, Ukrainian Mathematical Journal, 50(6)(1998), 747–754.
- Brogliato, B., Nonsmooth Mechanics: Models, Dynamics and Control, Springer-Verlag, London, 1999.
- Clarke, F.H., Generalized gradients and applications, Trans. Amer. Math. Soc., 205(1975), 247–262.
- Clarke, F.H., The Maximum Principle under minimal hypotheses, SIAM J. Control and Optimization, 14(6)(1976), 1078–1091.
- Clarke, F.H., Optimization and Nonsmooth Analysis, SIAM Classics in Applied Mathematics, Philadelphia, 1990.
- Demyanov, V.F., Rubinov, A.M., Quasidifferential Calculus, Optimization Software, Inc. Publications Division, New York, 1986.
- Geiger, T., Wachsmuth, D., Wachsmuth, G. Optimal control of ODEs with state suprema, Mathematical Control and Related Fields, 11(3)(2021), 555–578.
- Giorgi, G., Guerraggio, A., Thierfelder, J., Mathematics of Optimization: Smooth and Nonsmooth Case, Elsevier Science, 2004.
- Hristova, S., Golev, A., Stefanova, K., Approximate method for boundary value problems of anti-periodic type for differential equations with maxima, Boundary Value Problems, 1(2013), 12.
- Ilter, S., Weak maximum principle for optimal control problems of nonsmooth systems, Applied Mathematics and Computation, 218(3)(2011), 805–808.
- Jankovski, T., Systems of differential equations with maxima, Doklady Akademii Nauk, 8(1997), 57–60.
- McClamroch, N.H., State Models of Dynamic Systems, Springer-Verlag, New York-Heidelberg-Berlin, 1980.
- Otrocol, D., Systems of functional differential equations with maxima, of mixed type, Electron. J. Qual. Theory Differ. Equ., 5(2014), 1–9.
- Popov, E., Automatic Regulation and Control, Nauka, Moscow, 1966.Roberts, A.W., Varberg, D.E., Convex Functions, Academic Press, New York-London, 1973.
- Roberts, A.W., Varberg, D.E., Convex Functions, Academic Press, New York-London, 1973.
- Rockafellar, R.T., Convex Analysis, Princeton University, New Jersey, 1970.
- Shpakovich, V.P., Muntyan, V.I., Method of averaging for differential equations with maxima, Ukrainian Mathematical Journal, 39(5)(1987), 543–545.
- Vinter, R.B., Optimal Control, Birkh¨auser, Boston, 2000.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Varyasyon Hesabı, Sistem Teorisinin Matematiksel Yönleri ve Kontrol Teorisi |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 16 Sayı: 1 |