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Conference publicationsAbstractsXX conferenceProgram Control with Probability One for Stochactic SystemsPacific National University, Khabarovsk, Russia, karachanskaya@mail.khstu.ru 1 pp. (accepted)Usually, a program moving is considered as moving on a given manifold. The term "stochastic optimization"\, was actual for stochastic system. Terms "program moving"\, and "program control"\, for stochastic system didn't exist there. There exists a function, which conserves with probability one a constant value for all solutions of stochastic differential equations system, and it is called a first integral of SDE system \cite{D_78,D_02,11_KchUpr}. Then we can set a program control problem with probability one and solve it \cite{11_KchUpr,08_ChContrEn}.
\verb"Definition 1." Let us call \textit{a Program Control with Probability One} (PCP1) as a control in stochastic system, which with probability one provides an insensitivity of this system to random perturbations.
\verb"Definition 2." Let us ${\bf x}(t; {\bf x}_{o},{\bf s};\omega)$ be a solution of a SDE system: \begin{equation}\label{UprPuas2} \begin{array}{c} d {\bf x}(t)= \Bigl[ P(t;{\bf x}(t)) + Q(t;{\bf x}(t)) \cdot {\bf s}(t;{\bf x}(t)) \Bigr] dt + B(t;{\bf x}(t)) d {\bf w}(t) %+ \\ +\displaystyle\int G(t;{\bf x}(t);\gamma)\nu(dt;d\gamma), \end{array} \end{equation} where ${\bf w}(t)$ is a $m$-dimensional Wiener process; $\nu(t;\triangle \gamma)$ is a non-centered Poisson measure. A non-random function is a first integral of SDE system \eqref{UprPuas2} with initial condition ${\bf x}(t;{\bf x}_{o})\bigr|_{t=0}={\bf x}_{o}$. \textit{ A Program Moving of a stochastic system} we will call a solution ${\bf x}(t; {\bf x}_{o},{\bf s};\omega)$, which with a some PCP1 ${\bf s}(t;{\bf x})$ allows this system to remain on the given integral manifold $ u\bigl(t;{\bf x}(t;{\bf x}_{o})\bigr)= u(0;{\bf x}_{o})$ with probability one for any $t$.
\begin{thebibliography}{100} \bibitem{D_78} \textit{Doobko V. A.} A first integral for a stochastic differential equations system (Preprint / Inst. Math. Ac.Sci. USSR) -- Kiev, 1978. 22 p.
\bibitem{D_02} \textit{Doobko V. A.} \textit{Open evolving systems} // I inter. sci.-appl. conf. "Open evolving systems"\, (2002), Kiev, 2002. P. 14--31.
\bibitem{11_KchUpr} \textit{Karachanskaya E. V.} Construction of program control with probability one for a dynamical system with poisson perturbations // \textit{Bulletin of PNU} No 2 (21), 2011. P. 51-60. \bibitem{08_ChContrEn} \textit{Chalykh E.} Constructing the set of program controls with probability 1 for one class of stochastic systems // \textit{Automation and Remote Control} \textbf{70}, No 8, 2009. P. 1364--1375.
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