Probabilistic solution to a two-dimensional LQG homing problem

• Autorzy: Makasu C. , Lefebvre M.
• Języki publikacji: EN

Abstrakty

EN

Let x_t be an arbitrary one-dimensional diffusion process and y_t be a one-dimensional controlled diffusion process starting from y₀ = y ∈ (a, b). The process is controlled until y_t crosses either y = a or y = b for the first time. Our aim is to find the control u_t that minimizes an expected cost functional with both quadratic control and boundary crossing costs. An explicit form for the optimal control is obtained under certain conditions.

Słowa kluczowe

EN

optimal control; dynamic programming; Whittle's theorem; diffusion process; hitting time

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2012
• Tom: Vol. 41, no. 1
• Strony: 5--12
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Makasu C.

autor

Lefebvre M.

• 1Department of Mathematics and Applied Mathematics University of the Western Cape, Private Bag X17 Bellville 7535, South Africa,

Bibliografia

• Fleming, W.H., Rishel, W.R. (1975) Deterministic and Stochastic Optimal Control. Springer-Verlag, New York.
• Lefebvre, M. (1987) Optimal control of an Ornstein-Uhlenbeck process. Stochastic Process. Appl. 32, 281-287.
• Lefebvre, M. (1991) Forcing a stochastic process to stay in or leave a Niven region. Ann. Appl. Prob. 1, 167-172.
• Lefebvre, M. (1994) LQG problems with a possibly infinite final cost. Optimization 29, 73-79.
• Makasu, C. (2009) Risk-sensitive control for a class of homing problems. Automatica J. IFAC 45, 2454-2455.
• Whittle, P. (1982) Optimization Over Time, Vol. I. Wiley, Chichester.