Model-based methods require an accurate dynamic model to design the controller. However, the hydraulic parameters of nonlinear systems, complex friction, or actuator dynamics make it challenging to obtain accurate models. In this case, using the input-output data of the system to learn a dynamic model is an alternative approach. Therefore, we propose a dynamic model based on the Gaussian process (GP) to construct systems with control constraints. Since GP provides a measure of model confidence, it can deal with uncertainty. Unfortunately, most GP-based literature considers model uncertainty but does not consider the effect of constraints on inputs in closed-loop systems. An auxiliary system is developed to deal with the influence of the saturation constraints of input. Meanwhile, we relax the nonsingular assumption of the control coefficients to construct the controller. Some numerical results verify the rationality of the proposed approach and compare it with similar methods.