Optimality Conditions in One Stochastic Control Problem

Öz

For one stochastic optimal control problem described by a linear Ito stochastic equation and linear quality functional a necessary and sufficient optimality condition form of the Pontryagin maximum principle is obtained. In the case of convexity of the nonlinear quality functional, a sufficient optimality condition is obtained. In the deterministic case, many authors have studied such problems using the increment method. The considered work using a stochastic analogue of the increment method necessary and sufficient conditions for optimality as well as sufficient conditions are established.

Anahtar Kelimeler

• Ito equations
• optimal control
• optimality conditions

Kaynakça

1. 1 I. I. Gikhman, A.V. Skorokhod, Introduction to the theory of random processes, Dover Books on Mathematics, Mineola, New York, 1996, 544 pp.
2. 2 I. I. Gikhman, A. V. Skorokhod, Stochastic Differential Equations and their Applications, Nauka dumka, Kiev, 1982,612 pp.
3. 3 H. J. Kushner, F. C. Schweppe, A maximum principle for stochastic control problems, J. math. Appl. (1964), 287- 302.
4. 4 H. J. Kushner, On the stochastic maximum principle: Fixed time of control, J. Math. Anal. Appl. V.(11) (1965), 78-92.
5. 5 Y. M. Kabanov, On Pontryagin’s maximum principle for linear stochastic differential equations, in the collection M: AN SSSR, (1978), 85-94.
6. 6 R. Gabasov, F. M. Kirillova, The maximum principle in optimal control theory, Moscow URSS. (2011), 272.