Optimal programmed control of stochastic plants with constraints on the state for each time instant. (English. Russian original) Zbl 0554.93074

Dokuchaev, N. G.; Yakubovich, V. A.

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

Keywords:

stochastic plant; inequality and equality constraints; stochastic maximum principle