arXiv subjects
Publications and source records attributed to I. P. Smirnov.
The conjugate problem in stochastic optimal control can be formulated in terms of operators conjugated to the operators of stochastic integration [1, 2, 3]. In this paper we study some of such operators acting on the spaces of progressively measurable random functions.
The solution of the Helmholtz equation in optical semiclassic approximation is associated with the calculation of ray paths and matrices of variations. The transformation rules for elements of matrices on the boundaries of the waveguide are obtained.
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a given set in the phase space is considered. Necessary conditions of optimality (of the Pontryagin maximum principle form) and existence theorems are developed. The initial control problem was trasformed to an auxiliary deterministic problem, the differentiability of the auxiliary functional was discussed.