Suboptimal controls of a second-order system subjected to discontinuous random perturbations

Abstract

This paper doala with tho suboptimal control of a stochastic second-order system. It is assumed that the system is subjected to two different kinds of perturbation. The first kind of perturbation is represented by the standard Wiener process and tho second kind by a homogeneous process with independent increments, finite second-order moments, mean zero and no continuous sample paths. The stochastic system is approximated by a diffusion type system, and the optimal feedback control laws for the diffusion type system are chosen as the suboptimal controls for the given system. It is shown that in order to construct tho suboptimal controls, a non-linear partial differential equation and a linear partial integro-difforontial equation, have to be solved. A finite difference algorithm for the solution of these equations is proposed, and its efficiency and applicability are demonstrated with examples.