The LQG homing problem for a Wiener process with random infinitesimal parameters

• Autorzy: Lefebvre Mario , Moutassim Abderrazak

Identyfikatory

DOI

10.24425/acs.2019.130198

• Języki publikacji: EN

Abstrakty

EN

The problem of optimally controlling a Wiener process until it leaves an interval (a, b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = -∞, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.

Słowa kluczowe

EN

stochastic optimal control; first-passage time; dynamic programming; Brownian motion

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 3
• Strony: 413--422
• Opis fizyczny: Bibliogr. 5 poz., tab., wykr., wzory

Twórcy

autor

Lefebvre Mario

• Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C. P. 6079, Succursale Centreville, Montréal, Québec, Canada H3C 3A7

autor

Moutassim Abderrazak

• Department of Mathematics and Industrial Engineering, Polytechnique Montréal, C. P. 6079, Succursale Centreville, Montréal, Québec, Canada H3C 3A7

Bibliografia

• [1] J. Kuhn: The risk-sensitive homing problem. Journal of Applied Probability, 22(4), (1985), 796–803.
• [2] M. Lefebvre and A. Moutassim: An optimal control problem for a Wiener process with random infinitesimal mean. Atti della Accademia Peloritana dei Pericolanti – Classe di Scienze Fisiche, Matematiche e Naturali (To appear).
• [3] C. Makasu: Explicit solution for a vector-valued LQG homing problem. Optimization Letters, 7 (2013), 607–612.
• [4] P. Whittle: Optimization over Time, Vol. I. Wiley, Chichester, 1982.
• [5] P. Whittle: Risk-sensitive Optimal Control. Wiley, Chichester, 1990.

Uwagi

EN

1. This work was supported by the Natural Sciences and Engineering Research Council of Canada.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).