Stochastic differential system output control by the quadratic criterion. II. Dynamic programming equations numerical solution

The second part of the optimal control problem investigation for the Ito diffusion process and the controlled linear output is presented. Optimal control for output $dz_t= a_t y_t \,dt+b_t z_t \,dt+ c_t u_t\,dt+\sigma_t \,dw_t$ of the stochastic differential system $dy_t= A_t(y_t)\,dt +\Sigma_t (y_t) \,dv_t$ and quadratic quality criterion defined by Bellman function having form $V_t(y,z)= \alpha_t z^2+\beta_t(y) z+\gamma_t(y)$ is determined numerically by an approximate solution to*the grid methods of differential equations for the coefficients $\alpha_t$, $\beta_t(y)$, and $\gamma_t(y)$. A model experiment based on a simple differential presentation for the RTT (Round-Trip Time) parameter of the TCP (Transmission Control Protocol) network protocol is considered in detail. The results of numerical simulation are given and allow one to assess the difficulties in the practical implementation of the optimal solution and define the tasks of further research.