The optimal control problem with stopping for a discrete time linear stochastic system is investigated in this paper. Sometimes, in order to optimally realise the aim we need to know how long the system will be controlled. The traditional solutions with fixed terminal time are not enough to control the system optimally. The general aim of optimal control and stopping consists in minimization of a composite cost function. The paper presents two methods of solving this problem. A numerical example is included to illustrate the optimal control with stopping.
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Edward Kozłowski (2016) studied this question.
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