Optimal control of higher order differential inclusions with functional constraints

Elimhan N. Mahmudov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler-Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Original languageEnglish
Article number37
JournalESAIM - Control, Optimisation and Calculus of Variations
Publication statusPublished - 2020

Bibliographical note

Publisher Copyright:
© EDP Sciences, SMAI 2020.


  • Approximation
  • Complementary slackness
  • Euler-Lagrange
  • Higher order differential inclusions
  • Set-valued
  • Transversality


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