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Optimal programmed control of stochastic plants with constraints on the state for each time instant. (English. Russian original) Zbl 0554.93074
Autom. Remote Control 45, 859-866 (1984); translation from Avtom. Telemekh. 1984, No. 7, 49-57 (1984).
A stochastic plant is described by means of the differential equation $$(dx/dt)=f(x(t),u(t),t,\omega)$$, $$0\leq t\leq T$$, $$x(0)=a(\omega)$$, where x(t) is the random state n-vector, u(t) is a deterministic control m- vector, $$\omega$$ is a random parameter and a($$\omega)$$ is the random initial state. Furthermore, the control u($$\cdot)$$ is a piecewise continuous function from [0,T] into a bounded subset $$\Delta$$ of $${\mathbb{R}}^ m$$. There are inequality and equality constraints for the plant connecting the means of certain functions of (x(t),u(t),t,$$\omega)$$, $$0\leq t\leq T$$. The cost function $$\phi =\phi (u(\cdot),T)$$ to be minimized subject to u($$\cdot)$$ and T involves again means of some functions of (x(t),u(t),t,$$\omega)$$, $$0\leq t\leq T$$. Necessary optimality conditions are given by means of a ”stochastic maximum principle”.
Reviewer: K.Marti
##### MSC:
 93E20 Optimal stochastic control 49K45 Optimality conditions for problems involving randomness 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations 34F05 Ordinary differential equations and systems with randomness