The risk-sensitive homing problem

Abstract

The ‘homing' optimal control problem, described in Whittle and Gait (1970), is given a risk-sensitive formulation. It is shown that the reduction of an optimally controlled homing problem to the treatment of an uncontrolled process, demonstrated by Whittle and Gait, can be achieved in the risk-sensitive case. Two scalar problems are analyzed in detail.

Maximizing or minimizing survival time in the case of random parameters

“…We could further extend this work by considering a risk‐sensitive cost criterion, as in Kuhn 5 (see Whittle 9, p. 4 as well). We could also try to obtain the optimal control when only the parameter σ is random, and/or when σ and λ are both random variables.…”

“…for a positive scalar . Notice that in the scalar case, if B ≡ b = 0, N ≡ 2 > 0 and Q ≡ q > 0 are constants, then the above relation is always satisfied and yields the definition of given in (5).…”

“…LQG homing problems have been considered by the author in a series of papers (see, in particular, Lefebvre 4), by Kuhn 5, who gave them a risk‐sensitive formulation, and very recently by Makasu 6.…”

A dynamic game model of collective choice in multi-agent systems

“…, which is also computable by just knowing the exact initial conditions of all the agents. Once the agents agree on a λ, they start tracking the corresponding fixed point defined by (15). The fixed point vector λ describes the way the population splits between the destination points.…”

Exact and approximate solutions to LQG homing problems in one and two dimensions

“…(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.…”