Safe and disturbance rejection optimal control of dielectric elastomer actuators via adaptive dynamic programming and control barrier functions

Dielectric elastomer actuators (DEAs) have attracted considerable attention due to their large strain, fast response, and broad application prospects in soft robotics and flexible electromechanical systems. However, their inherent hysteresis, quadratic nonlinearity, and sensitivity to external disturbances significantly complicate accurate control design. To address these challenges, this paper develops a comprehensive control method that combines hysteresis compensation, disturbance estimation, optimal control, and safety guarantees. An inverse Prandtl–Ishlinskii (PI) operator combined with a square-root transformation is employed to compensate for both hysteresis and quadratic nonlinearities, while an extended state observer (ESO) estimates unmeasurable states and lumped disturbances. On this basis, an adaptive dynamic programming (ADP) controller with an actor–critic structure approximates the optimal policy, and a control barrier function (CBF) guarantees output safety constraints. Lyapunov analysis proves uniform ultimate boundedness and forward invariance of the safe set. Simulation results demonstrate that the proposed method achieves accurate tracking, disturbance rejection, and safety assurance simultaneously.