Abstract
This paper deals with the optimal control of a random non-linear sine wave oscillator. It is assumed that the oscillator is subjected to two different kinds of perturbation. The first kind of perturbation is represented by a vector of independent standard Wiener processes and the second kind by a generalized type of a Poisson process. Sufficient conditions on the optimal controls are derived. These conditions are given by a set of two coupled non-linear partial integro-differential equations. A numerical procedure for the solution of these equations is suggested and its efficiency and applicability are demonstrated with examples.
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