Control with stochastic stopping time†

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Abstract
The usual (non-stochastic stopping) control problem is extended to the case of random terminal time. The more general model presented hero should be particularly useful when a system will change while being controlled. Systems which are otherwise deterministic, and systems with additive noise in the dynamic equation are considered. Results concerning the relevant aspects of reliability and Markov process theories are presented. We show that stochastically stopped control optimality conditions are simply extensions of the usual conditions and that the limits of the criteria and optimal control, as the variance of the stopping probability distribution approaches zero, are the corresponding quantities for the non-stochastic problem.

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