Approximate Nonovershooting Zeta-Backstepping Control With its Applications to Quad-Rotors

This article presents an approximate nonovershooting zeta-backstepping control method for a class of uncertain nonlinear systems. The proposed method ensures that the tracking error exhibits approximately nonovershooting characteristics by leveraging the zeta-backstepping approach to design the system with a critically damped ratio. A momentum gradient descent algorithm is employed for the neural network to estimate the effects of nonlinear uncertainty, thereby achieving faster and more robust convergence. By employing the second-order Lyapunov criterion within the zeta-backstepping framework, rigorous proofs are established for both the stability of the closed-loop system and the approximate nonovershooting performance. Finally, experimental results on a quad-rotor hover system demonstrate the effectiveness of the proposed control scheme.