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We demonstrate the incoherent beam combining (BC) of four high-power single-mode fiber lasers. Adaptive fiber-optics collimators (AFOC) of 0.5 kW-level are developed to correct the tip/tilt-type phase errors among beamlets. The maximum deflection angle of the AFOC is about 0.29 mrad. A stochastic parallel gradient descent algorithm is employed as the tip/tilt control strategy. The tip/tilt control makes four separate laser beams overlap with each other in the far-field, and the average of normalized power-in-bucket increases from 0.171 in open loop to 0.798 in closed loop when 1.5-kW total output power is achieved. The precise tracking ability and control accuracy of this BC system are investigated. Experimental results expose that thermal-blooming effect disturbs BC seriously when the total output power is up to kW-level, which could be mitigated by inducing air flow near the laser output.