Polyhedral optimization of second-order discrete and differential inclusions with
delay

Mahmudov, Elimhan; Demir Sağlam, Sevilay

doi:10.3906/mat-2005-50

Polyhedral optimization of second-order discrete and differential inclusions with delay

Sevilay DEMİR SAĞLAM, (İstanbul Üniversitesi, Fen Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Elimhan N. MAHMUDOV (İstanbul Teknik Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2021 Cilt: 45 Sayı: 1 Sayfa Aralığı: 244 - 263 Metin Dili: İngilizce DOI: 10.3906/mat-2005-50 İndeks Tarihi: 05-07-2022

Polyhedral optimization of second-order discrete and differential inclusions with delay

Öz:

The present paper studies the optimal control theory of second-order polyhedral delay discrete and delay differential inclusions with state constraints. We formulate the conditions of optimality for the problems with the secondorder polyhedral delay discrete (P Dd) and the delay differential (P Cd) in terms of the Euler–Lagrange inclusions and the distinctive ”transversality” conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Agarwal RP, Bohner M, Li T, Zhang C. A new approach in the study of oscillatory behavior of even-order neutral delay differential equations. Applied Mathematics and Computation 2013; 225: 787-794.
[2] Aubin JP, Cellina A. Differential Inclusions - Set-Valued Maps and Viability Theory. Grundlehren der mathematischen Wissenschaften, No. 264. Berlin, Germany: Springer-Verlag, 1984.
[3] Azzam DL, Makhlouf A, Thibault L. Existence and relaxation theorem for a second order differential inclusion. Numerical Functional Analysis and Optimization 2010; 31: 1103-1119.
[4] Bohner M, Ding Y, Došly O. Difference Equations, Discrete Dynamical Systems and Applications. Cham, Switzerland: Springer, 2015.
[5] Bohner M, Grace SR, Jadlovská I. Sharp oscillation criteria for second-order neutral delay differential equations. Mathematical Methods in the Applied Sciences 2020; 43: 10041-10053. doi: 10.1002/mma.6677.
[6] Boltyanskii VG. Optimal control of discrete systems. New York, NY, USA: John Wiley, 1978.
[7] Capraru I, Cernea A. On the existence of solutions for nonlinear differential inclusions. Annals of the Alexandru Ioan Cuza University-Mathematics 2015; 61 (1): 195-208.
[8] Cernea A. On the existence of viable solutions for a class of second-order differential inclusions. Discussiones Mathematicae, Differential Inclusions Control and Optimization 2002; 22 (1): 67-78.
[9] Cheng Y, Agarwal RP, O’Regan D. Existence and controllability for nonlinear fractional differential inclusions with nonlocal boundary conditions and time-varying delay. Fractional Calculus and Applied Analysis 2018; 21 (4): 960-980.
[10] Clarke FH. Functional Analysis Calculus of Variations and Optimal Control. Graduate Texts in Mathematics Vol. 264. London, UK: Springer-Verlag, 2013.
[11] Guan X, Chen C, Shi P. On robust stability for uncertain time-delay systems: a polyhedral Lyapunov-Krasovskii approach. Circuits, Systems and Signal Processing 2005; 24: 1-18.
[12] Haddad T, Yarou M. Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space. Electronic Journal of Differential Equations 2006; 33: 1-8.
[13] Hassani S, Mammadov M, Jamshidi M. Optimality conditions via weak subdifferentials in reflexive Banach spaces. Turkish Journal of Mathematics 2017; 41: 1-8.
[14] Koumla S, Precup R, Sene A. Existence results for some neutral functional integrodifferential equations with bounded delay. Turkish Journal of Mathematics 2019; 43: 1809-1822.
[15] Li WS, Chang YK, Nieto JJ. Solvability of impulsive neutral evolution differential inclusions with state-dependent delay. Mathematical and Computer Modelling 2009; 49 (9-10): 1920-1927.
[16] Liu B. Controllability of neutral functional differential and integrodifferential inclusions with infinite delay. Journal of Optimization Theory and Applications 2004; 123: 573-593.
[17] Lombardi W, Olaru S, Lazar M, Bitsoris G, Niculescu SI. On the polyhedral set-invariance conditions for time-delay systems. IFAC Proceedings Volumes 2011; 44 (1): 308-313.
[18] Mahmudov EN. Approximation and Optimization of Discrete and Differential Inclusions. Boston, MA, USA: Elsevier, 2011.
[19] Mahmudov EN, Değer Ö. Optimal control of the elliptic type dierential inclusions with Dirichlet and Neumann boundary conditions. Journal of Dynamical and Control Systems 2011; 17 (2): 163-185.
[20] Mahmudov EN. Optimal control of second order delay-discrete and delay-differential inclusions with state constraints. Evolution Equations & Control Theory 2018; 7: 501-529.
[21] Mahmudov EN. Optimization of second-order discrete approximation inclusions. Numerical Functional Analysis and Optimization 2015; 36 (5): 624-643.
[22] Mahmudov EN. Convex optimization of second-order discrete and differential inclusions with inequality constraints. Journal of Convex Analysis 2018; 25 (1): 293-318.
[23] Mahmudov EN. The optimality principle for discrete and first order partial differential inclusions. Journal of Mathematical Analysis and Applications 2005; 308 (2): 605-619.
[24] Mahmudov EN, Demir S, Değer Ö. Optimization of third-order discrete and differential inclusions described by polyhedral set-valued mappings. Applicable Analysis 2016; 95: 1831-1844.
[25] Mahmudov EN. Necessary and sufficient conditions for discrete and differential inclusions of elliptic type. Journal of Mathematical Analysis and Applications 2006; 323 (2): 768-789.
[26] Mahmudov EN. Optimization of Mayer problem with Sturm-Liouville-type differential inclusions. Journal of Optimization Theory and Applications 2018; 177 (2): 345-375.
[27] Mahmudov EN. Optimal control of higher order differential inclusions with functional constraints. ESAIM: Control, Optimisation and Calculus of Variations 2020; 26: 1-23.
[28] Mahmudov EN. On duality in second-order discrete and differential inclusions with delay. Journal of Dynamical and Control Systems 2020; 26: 733-760. doi:10.1007/s10883-019-09471-4.
[29] Mahmudov EN, Mardanov MJ. On duality in optimal control problems with second-order differential inclusions and initial-point constraints. Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan 2020; 46: 115-128.
[30] Molchanov AP. Lyapunov function for nonlinear discrete-time control systems. Avtomatika i Telemekhanika 1987; 6: 26-35.
[31] Mordukhovich BS. Variational Analysis and Generalized Differentiation, I: Basic Theory; II: Applications. Grundlehren Series (Fundamental Principles of Mathematical Sciences), Vol. 330 and 331. Berlin, Germany: Springer, 2006.
[32] Mordukhovich BS, Wang D, Wang L. Optimal control of delay-differential inclusions with functional endpoint constraints in infinite dimensions. Nonlinear Analysis: Theory, Methods and Applications 2009; 71 (12): 2740-2749.
[33] Mordukhovich BS, Wang L. Optimal control of neutral functional-differential inclusions. SIAM Journal on Control Optimization 2006; 43 (1): 111-136.
[34] Raczynski S. Dynamics of economic growth: uncertainty treatment using differential inclusions. MethodsX 2019; 6: 615-632.
[35] Rubinov AM. Superlinear Multivalued Mappings and Their Applications to Problems in Mathematical Economics. Leningrad, Russia: Nauka, 1980.
[36] Sotskov I. Optimization of models, described by discrete inclusions. Ekonomika i Matematicheskiye Metody 1974; 10 (6).
[37] Smirnov GV. Introduction to the Theory of Differential Inclusions. Providence, RI, USA: American Mathematical Society, 2001.
[38] Tadumadze T. On the existence of an optimal element for a delay control problem. Nonlinear Analysis: Theory, Methods and Applications 2010; 73 (11): 211-220.
[39] Tolstonogov A. Differential Inclusions, Existence of Solutions In Differential Inclusions in a Banach Space, Mathematics and Its Applications, Vol. 524. Dordrecht, Netherlands: Springer, 2000.

APA	Demir Sağlam S, Mahmudov E (2021). Polyhedral optimization of second-order discrete and differential inclusions with delay. , 244 - 263. 10.3906/mat-2005-50
Chicago	Demir Sağlam Sevilay,Mahmudov Elimhan Polyhedral optimization of second-order discrete and differential inclusions with delay. (2021): 244 - 263. 10.3906/mat-2005-50
MLA	Demir Sağlam Sevilay,Mahmudov Elimhan Polyhedral optimization of second-order discrete and differential inclusions with delay. , 2021, ss.244 - 263. 10.3906/mat-2005-50
AMA	Demir Sağlam S,Mahmudov E Polyhedral optimization of second-order discrete and differential inclusions with delay. . 2021; 244 - 263. 10.3906/mat-2005-50
Vancouver	Demir Sağlam S,Mahmudov E Polyhedral optimization of second-order discrete and differential inclusions with delay. . 2021; 244 - 263. 10.3906/mat-2005-50
IEEE	Demir Sağlam S,Mahmudov E "Polyhedral optimization of second-order discrete and differential inclusions with delay." , ss.244 - 263, 2021. 10.3906/mat-2005-50
ISNAD	Demir Sağlam, Sevilay - Mahmudov, Elimhan. "Polyhedral optimization of second-order discrete and differential inclusions with delay". (2021), 244-263. https://doi.org/10.3906/mat-2005-50

APA	Demir Sağlam S, Mahmudov E (2021). Polyhedral optimization of second-order discrete and differential inclusions with delay. Turkish Journal of Mathematics, 45(1), 244 - 263. 10.3906/mat-2005-50
Chicago	Demir Sağlam Sevilay,Mahmudov Elimhan Polyhedral optimization of second-order discrete and differential inclusions with delay. Turkish Journal of Mathematics 45, no.1 (2021): 244 - 263. 10.3906/mat-2005-50
MLA	Demir Sağlam Sevilay,Mahmudov Elimhan Polyhedral optimization of second-order discrete and differential inclusions with delay. Turkish Journal of Mathematics, vol.45, no.1, 2021, ss.244 - 263. 10.3906/mat-2005-50
AMA	Demir Sağlam S,Mahmudov E Polyhedral optimization of second-order discrete and differential inclusions with delay. Turkish Journal of Mathematics. 2021; 45(1): 244 - 263. 10.3906/mat-2005-50
Vancouver	Demir Sağlam S,Mahmudov E Polyhedral optimization of second-order discrete and differential inclusions with delay. Turkish Journal of Mathematics. 2021; 45(1): 244 - 263. 10.3906/mat-2005-50
IEEE	Demir Sağlam S,Mahmudov E "Polyhedral optimization of second-order discrete and differential inclusions with delay." Turkish Journal of Mathematics, 45, ss.244 - 263, 2021. 10.3906/mat-2005-50
ISNAD	Demir Sağlam, Sevilay - Mahmudov, Elimhan. "Polyhedral optimization of second-order discrete and differential inclusions with delay". Turkish Journal of Mathematics 45/1 (2021), 244-263. https://doi.org/10.3906/mat-2005-50