Abstract:
A problem of guaranteed closed-loop control under incomplete information is considered for a linear stochastic differential equation (SDE) from the viewpoint of the method of open-loop control packages worked out earlier for the guidance of a linear control system of ordinary differential equations (ODEs) to a convex target set. The problem consists in designing a deterministic control providing (irrespective of a realized initial state from a given finite set) prescribed properties of the solution (being a random process) at a terminal point in time. It is assumed that a linear signal on some number of realizations is observed. By the equations of the method of moments, the problem for the SDE is reduced to an equivalent problem for systems of ODEs describing the mathematical expectation and covariance matrix of the original process. Solvability conditions for the problems in question are written.
Keywords:
Guidance problem, Guaranteed closed-loop control, Linear stochastic differential equation.
\Bibitem{Roz15}
\by Valeriy~L.~Rozenberg
\paper A guaranteed control problem for a linear stochastic differential equation
\jour Ural Math. J.
\yr 2015
\vol 1
\issue 1
\pages 68--82
\mathnet{http://mi.mathnet.ru/umj7}
\crossref{https://doi.org/10.15826/umj.2015.1.007}
\zmath{https://zbmath.org/?q=an:1396.93064}
\elib{https://elibrary.ru/item.asp?id=25613597}
Linking options:
https://www.mathnet.ru/eng/umj7
https://www.mathnet.ru/eng/umj/v1/i1/p68
This publication is cited in the following 3 articles:
Valeriy Rozenberg, Lecture Notes in Computer Science, 13930, Mathematical Optimization Theory and Operations Research, 2023, 394
V. L. Rozenberg, “Reconstruction problem with incomplete information for a quasilinear stochastic differential equation”, Comput. Math. Math. Phys., 62:11 (2022), 1838–1848
V. L. Rozenberg, “Reconstruction of external actions under incomplete information in a linear stochastic equation”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 196–205
Citation in format AMSBIB
Contact us: