Refined Euler-Lagrange inclusion for an optimal control problem with discontinuous integrand. (English. Russian original) Zbl 1481.49020

Proc. Steklov Inst. Math. 315, No. 1, 27-55 (2021); translation from Tr. Mat. Inst. Steklova 315, 34-63 (2021).
Summary: We study a free-time optimal control problem for a differential inclusion with mixed-type functional in which the integral term contains the characteristic function of a given open set of “undesirable” states of the system. The statement of this problem can be viewed as a weakening of the statement of the classical optimal control problem with state constraints. Using the approximation method, we obtain first-order necessary optimality conditions in the form of the refined Euler-Lagrange inclusion. We also present sufficient conditions for their nondegeneracy and pointwise nontriviality and give an illustrative example.


49K15 Optimality conditions for problems involving ordinary differential equations
93C20 Control/observation systems governed by partial differential equations
Full Text: DOI


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