Risk-sensitive control for a class of homing problems

Makasu, Cloud

doi:10.1016/j.automatica.2009.06.015

Cited by 21 publications

(7 citation statements)

References 4 publications

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“…Emails: mario.lefebvre@polymtl.ca, mlefebvre@polymtl.ca Lefebvre has written a series of papers on LQG homing problems; see, for instance, Lefebvre (2011) and the references therein. Kuhn (1985) and Makasu (2009) solved homing problems with a risk-sensitive cost criterion; see also Whittle (1990, p. 222). Recent papers written on homing problems include the ones published by Makasu Lefebvre (2012a, 2012b.…”

Section: Introductionmentioning

confidence: 98%

Analytical solutions to LQG homing problems in one dimension

Lefebvre

Zitouni

2014

Systems Science & Control Engineering

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The problem of optimally controlling one-dimensional diffusion processes until they leave a given interval is considered. By linearizing the Riccati differential equation satisfied by the derivative of the value function in the so-called linear quadratic Gaussian homing problem, we are able to obtain an exact expression for the solution to the general problem. Particular problems are solved explicitly.

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Section: Introductionmentioning

confidence: 98%

Analytical solutions to LQG homing problems in one dimension

Lefebvre

Zitouni

2014

Systems Science & Control Engineering

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“…In the general formulation, {X u (t), t ≥ 0} can be an n-dimensional controlled diffusion process, and all the functions can depend explicitly on t. The cost function 1 can also take the risk-sensitivity of the optimizer into account; see Whittle [9] or Kuhn [2] and Makasu [7]. Moreover, Lefebvre and Moutassim [6] considered the case when the uncontrolled process is a Wiener process with random parameters.…”

Section: Introductionmentioning

confidence: 99%

On the inverse LQG homing problem

Lefebvre

2022

Proceedings of NAS RA. Mathematics

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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.

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“…(ii) LQG homing problems have been considered extensively by the first author. Kuhn and Makasu have worked on risk‐sensitive versions of these problems. Recent papers on homing problems are the ones by Makasu and Lefebvre and Makasu , which presents an explicit solution to a two‐dimensional problem.…”

Section: Introductionmentioning

confidence: 99%