Discrete homing problems

• Autorzy: Lefebvre M. , Kounta M
• Języki publikacji: EN

Abstrakty

EN

We consider the so-called homing problem for discrete-time Markov chains. The aim is to optimally control the Markov chain until it hits a given boundary. Depending on a parameter in the cost function, the optimizer either wants to maximize or minimize the time spent by the controlled process in the continuation region. Particular problems are considered and solved explicitly. Both the optimal control and the value function are obtained.

Słowa kluczowe

EN

optimal control; principle of optimality; absorption problems

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2013
• Tom: Vol. 23, no. 1
• Strony: 5--18
• Opis fizyczny: Bibliogr. 6 poz., wzory

Twórcy

autor

Lefebvre M.

• Département de mathématiques et de génie industriel, École Polytechnique, C. P. 6079, Succursale Centre-ville, Montréal, Québec, Canada H3C 3A7

autor

Kounta M

• Département de mathématiques et de statistique, Université de Montréal, C. P. 6128, Succursale Centre-ville, Montréal, Québec, Canada H3C 3J7

Bibliografia

• [1] W. Feller: An Introduction to Probability Theory and its Applications. Vol. I. Wiley, New York, 1968.
• [2] J. Kuhn: The risk-sensitive homing problem. J. Appl. Prob., 22 (1985), 796-803.
• [3] M. Lefebvre: Maximizing the mean exit time of a Brownian motion from an interval. Int. J. Stoch. Anal., vol. 2011, Article ID 296259, 5 pages, 2011. doi: 10.1155/2011/296259
• [4] C. Makasu: Risk-sensitive control for a class of homing problems. Automatica J. IFAC, 45 (2009), 2454-2455.
• [5] P. Whittle: Optimization over Time. Vol. I. Wiley, Chichester, 1982.
• [6] P. Whittle: Risk-sensitive Optimal Control. Wiley, Chichester, 1990.