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Risk-sensitive control for a class of homing problems. (English) Zbl 1183.93128
Summary: A result of {\it M. Lefebvre} [Syst. Control Lett. 42, No. 5, 347--352 (2001; Zbl 0974.93071)] is here extended to a two-dimensional homing problem with a risk-sensitive cost criterion. It is shown that the optimal control is given explicitly, and moreover, the optimal value function has a simple probabilistic representation associated with a backward stochastic differential equation with a random terminal time.

93E20Optimal stochastic control (systems)
60H10Stochastic ordinary differential equations
Full Text: DOI
[1] Kuhn, J.: The risk-sensitive homing problem, Journal of applied probability 22, 796-803 (1985) · Zbl 0607.93065 · doi:10.2307/3213947
[2] Lefebvre, M.: A different class of homing problems, Systems & control letters 42, 347-352 (2001) · Zbl 0974.93071 · doi:10.1016/S0167-6911(00)00107-9
[3] Pardoux, E.; Peng, S.: Adapted solution of a backward stochastic differential equation, Systems & control letters 14, 55-61 (1990) · Zbl 0692.93064
[4] Rishel, R.: Controlled wear process: modeling optimal control, IEEE transactions on automatic control 36, 1100-1102 (1991)
[5] Whittle, P.: Risk-sensitive optimal control, (1990) · Zbl 0718.93068