Soft robots are increasingly used in healthcare, especially for assistive care, due to their inherent safety and adaptability. Controlling soft robots is challenging due to their nonlinear dynamics and the presence of time delays, especially in applications like a soft robotic arm for patient care. This paper presents a learning-based approach to approximate the nonlinear state predictor (Smith Predictor), aiming to improve tracking performance in a two-module soft robot arm with a short inherent input delay. The method uses Kernel Recursive Least Squares Tracker (KRLST) for online learning of the system dynamics and a Legendre Delay Network (LDN) to compress past input history for efficient delay compensation. Experimental results demonstrate significant improvement in tracking performance compared to a baseline model-based non-linear controller. Statistical analysis confirms the significance of the improvements. The method is computationally efficient and adaptable online, making it suitable for real-world scenarios and highlighting its potential for enabling safer and more accurate control of soft robots in assistive care applications.