ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 49,60,90 Timofeeva Galina, Ural State Academy of Railway Transport, Russia Effective control and observation in the multistage stochastic optimization problem The effective control problem for a multistage system: x_{k+1} = A_{k}x_{k}+b_{k}+ζ_{k}, w_{k+1} = rw_{k}+u_{k}^{T} x_{k}+(u_{k}−u_{k−1})^{T} c_{k} with observation: y_{k+1} = G_{k+1}x_{k+1} + η_{k+1} is considered (k = 0, 1, ⋯, N). Here ζ_{k}, η_{k}, c_{k} are independent Gaussian vectors with known distributions parameters. The effective controls u_{k} are selected by two criteria: the first is maximization of a mean value of the control utility w_{N}, the second is minimization of it’s variance. The connection and separation of the problems of control and observation are studied on the base of theory of control under uncertainty [1]. A notion of a dual stochastic optimization problem is introduced. In case of the linear restrictions on permissible controls an algorithm [2] may be used for the effective controls construction. Reference: [1] A. B. Kurzhanski, Control and observation under uncertainty, Nauka, Moskow(1987) [2]I. Ya. Katz, G. A. Timofeeva Bicriterial problem of stochastic optimization. Avtomatica & Telemech. (Russian) 3(1997),116-123.