Geodesic
Optimal Control of Second Order Sweeping Processes with Discrete and Differential Inclusions
Journal of convex analysis, Tome 29 (2022) no. 1, pp. 269-29
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We discuss the problem of optimal control theory given by second order sweeping processes with discrete and differential inclusions. The main problem is to derive sufficient optimality conditions for second-order sweeping processes with differential inclusions. By using first and second order difference operators in a continuous problem we associate the second order sweeping processes with a discrete-approximate problem. On the basis of the discretization method in the form of Euler-Lagrange inclusions, optimality conditions for discrete approximate inclusions and transversality conditions are obtained. The establishment of Euler-Lagrange type adjoint inclusions is based on the presence of equivalence relations for locally adjoint mappings. To demonstrate the results obtained, a second-order sweeping process with a "linear" differential inclusion is considered.
Classification : 49K24, 34A60, 34A40, 26D10
Mots-clés : Euler-Lagrange inclusions, adjoint mappings, set-valued map, approximation, second order, sweeping, transversality 
@article{JCA_2022_29_1_JCA_2022_29_1_a16,
     author = {E. N. Mahmudov},
     title = {Optimal {Control} of {Second} {Order} {Sweeping} {Processes} with {Discrete} and {Differential} {Inclusions}},
     journal = {Journal of convex analysis},
     pages = {269--29},
     year = {2022},
     volume = {29},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a16/}
}
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E. N. Mahmudov. Optimal Control of Second Order Sweeping Processes with Discrete and Differential Inclusions. Journal of convex analysis, Tome 29 (2022) no. 1, pp. 269-29. http://geodesic.mathdoc.fr/item/JCA_2022_29_1_JCA_2022_29_1_a16/