Constructive design of disturbance observer-based safe control for strict-feedback nonlinear systems with...

Existing safe backstepping control methods often rely on precise system models, which limits their robustness against external disturbances frequently encountered in real-world applications. To address the problem of safe control for strict-feedback nonlinear systems subject to unknown disturbances, this paper proposes a novel constructive control framework that integrates a disturbance observer, filtered backstepping, and control barrier functions (CBFs). A disturbance observer is first developed to estimate and compensate for unknown disturbances, providing a less conservative alternative to conventional robust methods that rely on "worst-case" assumptions. The estimated disturbance is then embedded into a recursive design framework that combines filtered backstepping with CBFs to construct smooth virtual and actual controllers. This unified approach mitigates the "explosion of complexity" typically associated with safe backstepping while avoiding the nonsmoothness inherent in optimization-based CBF controllers. Finally, the effectiveness of the proposed method is validated through numerical simulations and real-time experiments on a Franka Emika Panda robotic arm.