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In this paper, an incoherent control scheme for accomplishing the state control of a class of quantum systems which have wavefunction-controllable subspaces is proposed. This scheme includes the following two steps: projective measurement on the initial state and learning control in the wavefunction-controllable subspace. The first step probabilistically projects the initial state into the wavefunction-controllable subspace. The probability of success is sensitive to the initial state; however, it can be greatly improved through multiple experiments on several identical initial states even in the case with a small probability of success for an individual measurement. The second step finds a local optimal control sequence via quantum reinforcement learning and drives the controlled system to the objective state through a set of suitable controls. In this strategy, the initial states can be unknown identical states, the quantum measurement is used as an effective control, and the controlled system is not necessarily unitarily controllable. This incoherent control scheme provides an alternative quantum engineering strategy for locally controllable quantum systems.