Approximate design of some stochastic control systems with random parameters

The paper is concerned with design of controllable dynamic systems that are disturbed by white noise and whose differential equations contain multiplicative random parameters. The a priori uncertainty of parameters is assumed to be a small quantity in a certain sense. For design of quasioptimal control the method of successive approximations is suggested where the zero approximation is a solution to the optimal control problem with the values of all parameters known precisely. For the first two approximations performance estimates are given of approximate design. An example is given.