Variable displacement hydraulic pumps are widely used for energy efficiency, and they often have a mechanical feedback mechanism to ensure target tracking control performance and stability of tilt angle control. Furthermore, there are many examples which add electronic control to realize higher tracking control performance. However, in such cases, the control performance is significantly affected by the dynamic characteristics of the mechanical feedback mechanism, and this problem prevent its widespread use. Additionally, tilt angle control is susceptible to changes in dynamic characteristics and load pressure depending on the operating point, and there are constraints on the tilt angle. Hence, high control performance cannot be obtained without considering these nonlinearities. In this study, the variable displacement pump without mechanical feedback mechanism is focused on, and the objective of this study is to design a displacement control system for a hydraulic pump based on a model predictive control (MPC) that can consider various constraints on the design step. An adaptive system, which handles changes in dynamic characteristics and the effects of load pressure, is introduced. Additionally, the control performance of adaptive MPC is compared to adaptive model matching-based MPC with inverse optimization that can optimally design the weight matrices of the evaluation function without trial and error. Furthermore, in order to improve the transient response, a variable control input constraints are added in these two control systems. Experimental results of control performance have shown that the proposed method achieved a high tracking performance and short settling time, which confirmed the effectiveness of the variable control input constraints.