RT Journal Article ID 4528db187ea36cbc A1 Mansimov, Kamil Bayramali oglu A1 Mardanov , Misir Jumayil oglu T1 Necessary Conditions of the Optimality of the Second Order in Optimal Control Problems Described by the System of Integrodifferential Equations of the Volterra Type JF Journal of Automation and Information Sciences JO JAI(S) YR 2013 FD 2013-09-05 VO 45 IS 8 SP 59 OP 67 K1 system of integro-differential equations of the Volterra type K1 optimality of the second order K1 necessary conditions K1 Pontryagin maximum principle K1 special control AB An optimal control problem, described by the system of integrodifferential equations of the Volterra type, is considered. Under the assumption of the openness of the controlled field the necessary optimality condition in the form of the Euler equation is derived. Further by examining the second variation of the performance criterion, different necessary conditions of the optimality of the second order have been found, expressed thought the parameters of the posed problem. In particular, the case of degeneration of the analogue of the Legendre−Clebsch condition has been studied. The multi-point necessary optimality conditions of special, in the classical sense, controls were proved. PB Begell House LK https://www.dl.begellhouse.com/journals/2b6239406278e43e,5b5ac16770b645a7,4528db187ea36cbc.html