WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
Linear State Optimal Control Problem with a Stochastic Switching Time
Authors: ,
Abstract: In this paper, we analyse an optimal control problem over a finite horizon with a stochastic switching
time, assuming that the two optimal control problems present in its two stages have a particularly simple form
called linear state. It is well known that linear state optimal control problems can be solved easily using the HJB
equation approach and assuming that the value function is linear in the state. Unfortunately, this simplicity of
solution does not extend to the problem with stochastic switching time. We prove that a necessary and sufficient
condition for the problem to maintain a linear state structure is to assume that the hazard rate of the switching
time depends only on the temporal variable. Finally, assuming that the hazard rate is constant, we completely
characterise the solution of the obtained linear state optimal control problem.
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Pages: 608-613
DOI: 10.37394/23206.2024.23.64