Abstract
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.
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© 1972 Springer-Verlag
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Solodovnikov, V.V., Biriukov, V.F. (1972). Optimization of multi-dimensional stochastic systems and stability of solutions. In: Stability of Stochastic Dynamical Systems. Lecture Notes in Mathematics, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064953
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DOI: https://doi.org/10.1007/BFb0064953
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06050-5
Online ISBN: 978-3-540-38000-9
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