Optimal Control of a Discrete-Time Stochastic System with a Probabilistic Criterion and a Non-fixed Terminal Time

This paper considers an optimal control problem for a discrete-time stochastic system with the probability of first reaching the boundaries of a given domain as the optimality criterion. Dynamic programming-based sufficient conditions of optimality are formulated and proved. The isobells of levels 1...

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Bibliographic Details
Published inAutomation and remote control Vol. 81; no. 12; pp. 2143 - 2159
Main Author Azanov, V. M.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2020
Springer Nature B.V
Subjects
639/301/1034/1035
639/925/357/995
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Computer-Aided Engineering (CAD
Control
Control systems
Discrete time systems
Dynamic programming
Estimates
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Optimal control
Optimality criteria
Optimization
Probability theory
Robotics
Statistical analysis
Stochastic systems
Systems Theory
Topical Issue
stochastic optimal control
dynamic programming
discrete-time systems
Bellman function
probabilistic criterion
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Summary:This paper considers an optimal control problem for a discrete-time stochastic system with the probability of first reaching the boundaries of a given domain as the optimality criterion. Dynamic programming-based sufficient conditions of optimality are formulated and proved. The isobells of levels 1 and 0 of the Bellman function are used for obtaining two-sided estimates of the right-hand side of the dynamic programming equation, two-sided estimates of the Bellman function, and two-sided estimates of the optimal-value function of the probabilistic criterion. A suboptimal control design method is proposed. The conditions of equivalence to an optimal control problem with a probabilistic terminal criterion are established. An illustrative example is given.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117920120012