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In this study, we propose a varying terminal time structure for the optimalcontrol problem under state constraints, in which the terminal time follows thevarying of the control via the constrained condition. Focusing on this newoptimal control problem, we investigate a novel stochastic maximum principle,which differs from the traditional optimal control problem under stateconstraints. The optimal pair of the optimal control model can be verified viathis new stochastic maximum principle.

A varying terminal time structure for stochastic optimal control under constrained condition