The control laws for the stochastic linear undamped system buried in Gaussian white noise were compared. Consideration was given to the magnitude-bounded and unbounded linear feedback controls. The laws were compared for the purpose of possible replacement by the linear-quadratic procedure of the procedure of determination of the switching lines for the bounded-control law. It is common knowledge that few problems of the optimal stochastic control, including design of the linear stochastic systems with quadratic performance index, have precise solutions. In the rest of the cases where consideration is given to the nonlinear systems or various constraints are imposed on the control action, one has to resort to the approximate methods for solution of the problems of optimal stochastic control such as the dynamic programming method. This method reduces design of the optimal control to solution of the Hamilton-Jacobi-Bellman (HJB) multidimensional partial differential equation.
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