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In this paper, we develop an adaptive output trajectory tracking control (AOTTC) method for a class of affine nonlinear discrete-time systems. The controller designed by this AOTTC method can make real-system output track the given expected trajectory asymptotically. Our method has some advantages: 1) it requires relatively few assumptions about the system model; 2) it can simplify the control problem by dynamically linearizing the system model and designing and adjusting the feedback gain matrix to adaptively stabilize the system online; and 3) it can estimate the system parameters by using an optimization scheme without using vast amounts of sampled data. This designing and adjusting procedure of the feedback gain matrix has a clear physical meaning and is easily applied. We also give out the convergence condition of the AOTTC method. Then, a voltage-controllable permanent magnet linear motor system is employed for computer simulation, whose results demonstrate the feasibility of our control method. [ABSTRACT FROM PUBLISHER]