A key challenge in moving soft robots from the lab to unstructured real-world environments is achieving reliable closed-loop control, which requires integrating real-time sensing. To date, one of the most common ways to close a position feedback loop in soft robotics is vision-based tracking, due to its non-invasive nature. However, cameras often require bulky setups and can be highly sensitive to external conditions (e.g., lighting changes and environmental vibrations). This work addresses these limitations by proposing a sensorless perception and control architecture for dielectric elastomer (DE) soft robotic systems. DE actuators are an attractive alternative to traditional actuators employed in soft robotics thanks to their high compliance, large deformation, low weight, silent operation, energy efficiency, and intrinsic self-sensing capability. Building on prior work on sensorless proprioception for a DE-based soft robot [1], we integrate the estimation architecture in real time directly into the feedback loop. The proposed strategy relies solely on electrical measurements. In particular, by reading the voltages and currents it estimates the capacitance of the employed DEs. These estimates, together with the applied input voltage, are used as inputs to a learning-based architecture to estimate the configuration of the soft robot. This enables continuous state reconstruction without external sensors, remaining compatible with lightweight hardware and compact setups. To successfully regulate the robot configuration, we propose a robust control law that enables the DE soft robot to track multi-step reference signals by explicitly accounting for system nonlinearities and underactuation. The control law extends the approach proposed in [2] by guaranteeing that the same law ensures stability over a countable set of equilibrium points, thereby enabling tracking of multi-step reference signals. Finally, to validate the proposed approach, the control law is implemented on the real device using both the sensorless estimation and a feedback from a vision systems. The experimental results shows that the sensorless architecture achieves precision and tracking performance comparable to the camera-based feedback, indicating that reliable closed-loop control can be obtained without adding any external sensor on the robot. This result opens the door to integrating the proposed strategy into DE soft robots intended to operate in unstructured environments.