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PROGRAM CONTROL WITH PROBABILITY ONE FOR STOCHACTIC SYSTEMS Karachanskaya E.V. Pacific National University, Khabarovsk, Russia, karachanskaya@mail.khstu.ru

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 [1, 2, 3]. Then we can set a program control problem with probability one and solve it [3, 4]. Definition 1. Let us call 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. Definition 2. Let us x(t ; xo , s; ) be a solution of a SDE system: d x(t ) = P (t ; x(t)) + Q (t; x(t )) · s(t ; x(t )) d t + B(t; x(t ))d w(t ) + G(t ; x(t ); )(d t ; d ), (1) where w(t ) is a m-dimensional Wiener process; (t ; ) is a non-centered Poisson measure. A non-random function is a first integral of SDE system (1) with initial condition x(t ; xo ) t=0 = xo . A Program Moving of a stochastic system we will call a solution x(t ; xo , s; ), which with a some PCP1 s(t; x) allows this system to remain on the given integral manifold u t ; x(t; xo ) = u(0; xo ) with probability one for any t. References. 1. Doobko V. A. A first integral for a stochastic differential equations system (Preprint / Inst. Math. Ac.Sci. USSR) ­ Kiev, 1978. 22 p. 2. Doobko V. A. Open evolving systems // I inter. sci.-appl. conf. "Open evolving systems" (2002), Kiev, 2002. P. 14­31. 3. Karachanskaya E. V. Construction of program control with probability one for a dynamical system with poisson perturbations // Bulletin of PNU No 2 (21), 2011. P. 51-60. 4. Chalykh E. Constructing the set of program controls with probability 1 for one class of stochastic systems // Automation and Remote Control 70, No 8, 2009. P. 1364­1375.