Affiliation:
1. Polytechnique Montreal, Montreal, Canada
Abstract
The problem of minimizing or maximizing the time spent by a controlled
diffusion process in a given interval is known as LQG homing. The optimal control,
when it is possible to obtain an explicit solution to such a problem, is often expressed
as special functions. Here, the inverse problem is considered: we determine, under certain
assumptions, the processes for which the optimal control is a simple power function.
Moreover, the problem is extended to the case of jump-diffusion processes.
Publisher
National Academy of Sciences of the Republic of Armenia
Reference9 articles.
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2. J. Kuhn, “The risk-sensitive homing problem,” J. Appl. Probab., 22, 796 – 803 (1985). https://doi.org/10.2307/3213947
3. M. Lefebvre, “Optimally ending an epidemic”, Optimization, 67 (3), 399 – 407 (2018). https://doi.org/10.1080/02331934.2017.1397147
4. M. Lefebvre, “Optimal control of a stochastic system related to the Kermack-McKendrick model”, Bul. Acad. ¸Stiin¸te Repub. Mold., Mat., 3 (91), 60 – 64 (2019).
5. M. Lefebvre, “Minimizing the time spent in an interval by a Wiener process with uniform jumps”, Control Cybern., 48 (3), 407 – 415 (2019).