Optimization of multi-dimensional stochastic systems and stability of solutions
Two important cases of the problem of optimization of multidimensional stochastic systems are considered. The first case is related to the regulator problem for a stochastic system which describes a regulating nonstochastic and nonstationary device. The second one arises from problems in which some moments must have specified properties. It is shown that the above problems are among the non-well-posed-ones. Hence it is difficult to use experimental data on moments of random processes for the study of an optimization process. The method of synthesis of multi-dimensional systems is proposed and a projection method for the solutions of the exact equation with respect to the impulse response functions is obtained. Theorems on evaluation of the errors of approximate solutions are formulated.