Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions

Mahmudov E.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, cilt.192, sa.1, ss.36-55, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 192 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10957-021-01936-6
  • Dergi Adı: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.36-55
  • Anahtar Kelimeler: Discrete-approximate, Euler-Lagrange, Hamiltonian, Differential inclusion, Equivalence, 2ND-ORDER, DISCRETE, CONTROLLABILITY, STABILITY
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

The paper is devoted to Lagrange problem of optimal control theory with higher-order differential inclusions (HODI) and special boundary conditions. Optimality conditions are derived for HODIs, as well as for their discrete analogy. In this case, discretization method of the second-order differential inclusion is used to form sufficient optimality conditions for HODIs and periodic boundary conditions, the so-called transversality conditions. And to construct an Euler-Lagrange-type inclusion, a locally adjoint mapping is used, which is closely related to the coderivative concept of Mordukhovich. In turn, this approach requires several important equivalence results concerning LAMs to the discrete and discrete-approximate problems. The results obtained are demonstrated by the optimization of some "linear" optimal control problems, for which the Weierstrass-Pontryagin maximum principle and transversality conditions are formulated.