We propose a hybrid feedback-feedforward control scheme for output current tracking in a solenoid, based on an integrate-and-reset paradigm. The feedback, based on a First-Order Reset Element, produces stabilizing inputs comprising diverging exponentials, inducing an aggressive feedback correction. The feedforward uses a hybrid recursive leastsquares method with directional forgetting. The hybrid nature of the control loop allows using non-exponentially stable filters, which preserve the past information, as opposed to the stable filters typically used in the adaptive control literature. We prove stability of both the estimation and the tracking error, also using a novel result on forward invariance of a desirable set where the information matrix evolves. Experimental results confirm the effectiveness of the proposed hybrid control scheme.