An approximate method of synthesizing statistical optimal control systems

The paper is devoted to an analytical method for synthesizing optimal systems relying on approximate solution of the diffusion Bellman equation. It is proved that if the nonlinear terms of the Bellman equation contain a small parameter, then the resultant suboptimal system does not differ greatly from the optimal one. An example is considered proving that the solution method proposed is an extension of the approximate method to synthesize optimal steady state systems to the nonstationary case.