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


Mahmudov E.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, vol.192, no.1, pp.36-55, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 192 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s10957-021-01936-6
  • Journal Name: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Journal Indexes: 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
  • Page Numbers: pp.36-55
  • Keywords: Discrete-approximate, Euler-Lagrange, Hamiltonian, Differential inclusion, Equivalence, 2ND-ORDER, DISCRETE, CONTROLLABILITY, STABILITY
  • Istanbul Technical University Affiliated: Yes

Abstract

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.