Hybrid combination controller of optimal control with backstepping method and PID backstepping for an underactuated X4-AUV

This paper presents comparative research of two hybrid nonlinear control strategies—Optimal Control with Backstepping Method for position and Backstepping PID for attitude (OBBPID), and Backstepping PID for position with Optimal Control and Backstepping for attitude (BPIDOB)—to stabilize an underactuated X4 Autonomous Underwater Vehicle (X4-AUV). Both controllers are created based on Lyapunov stability theory and tested in simulation. Results show that while both methods achieve stable tracking of desired positions and orientations, the OBBPID controller delivers faster settling times and lower overshoot. These findings demonstrate the effectiveness of hybrid backstepping-based control for robust underwater vehicle operation.