|
This article is cited in 2 scientific papers (total in 2 papers)
Stochastic Systems
Probabilistic criterion-based optimal retention of trajectories of a discrete-time stochastic system in a given tube: bilateral estimation of the Bellman function
V. M. Azanov, A. N. Tarasov Moscow Aviation Institute (National Research University), Moscow, Russia
Abstract:
This paper examines an optimal control problem with a probabilistic criterion for retaining the trajectories of a discrete-time stochastic system in given sets. The dynamic programming method is employed for obtaining the isobells of levels 1 and 0 of the Bellman function, two-sided estimates for the right-hand side of the dynamic programming equation, two-sided estimates for the Bellman function, and the optimal-value function of the probabilistic criterion. These results are then used for deriving an approximate formula for the optimal control. As an illustrative example the problem of keeping an inverted pendulum in the neighborhood of an unstable equilibrium is considered.
Keywords:
discrete-time systems, stochastic optimal control, probabilistic criterion, dynamic programming, Bellman function, inverted pendulum.
Citation:
V. M. Azanov, A. N. Tarasov, “Probabilistic criterion-based optimal retention of trajectories of a discrete-time stochastic system in a given tube: bilateral estimation of the Bellman function”, Avtomat. i Telemekh., 2020, no. 10, 93–117; Autom. Remote Control, 81:10 (2020), 1819–1839
Linking options:
https://www.mathnet.ru/eng/at15406 https://www.mathnet.ru/eng/at/y2020/i10/p93
|
Statistics & downloads: |
Abstract page: | 176 | Full-text PDF : | 31 | References: | 28 | First page: | 16 |
|