In industrial applications, hydraulic presses maintain workloads by controlling the hydraulic cylinder to extend and retract, ensuring optimum tracking performance in terms of position and force. Dealing with nonlinear and multinode systems, such as hydraulic systems, often requires an advanced approach that frequently includes machine learning and artificial intelligence methods. Introducing an adaptive control system to significantly improve the response of hydraulic presses is a challenge. Therefore, a polynomial regression model predictive control (PR-MPC) mechanism is proposed in this paper to compensate for external disturbances such as the forming processes and friction dynamics. Using polynomial regression modeling and least squares optimization, the approach produces highly accurate data-driven models with an R2 value of 0.948 to 0.999. The simplicity of polynomial regression facilitates the integration of smart algorithms into an expert system with additional decision-making rules. Remote adaptive control integrated within a 5G network is based on I 4.0 distributed system guidelines that provide insights into the behavior of the hydraulic press. The results of real-time experiments have shown that the PR-MPC mechanism integrated into the expert system reduces the absolute response error of the hydraulic press by up to 98.7% compared to the initial control system with a PID regulation.