Optimal control of higher order differential inclusions with functional constraints
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 37.

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (P$$); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (P$$). 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 (P$$) 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.

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DOI : 10.1051/cocv/2019018
Classification : 49k20, 49k24, 49J52, 49M25, 90C31
Mots-clés : Higher order differential inclusions, complementary slackness, Euler–Lagrange, approximation, transversality, set-valued 
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     author = {Mahmudov, Elimhan N.},
     title = {Optimal control of higher order differential inclusions with functional constraints},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2019018},
     mrnumber = {4116680},
     zbl = {1447.49039},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv/2019018/}
}
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Mahmudov, Elimhan N. Optimal control of higher order differential inclusions with functional constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 37. doi : 10.1051/cocv/2019018. http://archive.numdam.org/articles/10.1051/cocv/2019018/

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