A barrier Lyapunov-based fast adaptive robust control system for 6-DOF autonomous submersible vehicles

This paper proposes a novel fast adaptive back-stepping robust controller, based on thebarrier Lyapunov function ($\mathrm{BLF}$), to address the position and velocity constraints typically imposed in the design of Euler–Lagrange systems. The aim is to improve upon various aspects of conventional $L_1$ adaptive control and Model Reference Adaptive Control ($\mathrm{MRAC}$). The proposed controller reduces complexity by eliminating the low-pass filter from the design process in $L_1$ adaptive control, resulting in faster convergence and enhanced robustness against nonlinear uncertainties, external disturbances, and actuator dynamics, which are crucial in real-world applications. The performance of the proposed scheme is evaluated on two different Euler–Lagrange systems: a 6-degree-of-freedom (6-$\mathrm{DOF}$) remotely operated vehicle ($\mathrm{ROV}$) and a single-link robot manipulator. Key performance indicators such as settling time, overshoot percentage, control effort, and trajectory tracking error are used for assessment. The results confirm that the proposed controller outperforms both $L_1$ adaptive control and $\mathrm{MRAC}$ in terms of tracking accuracy and state estimation errors for both position and velocity outputs. Additionally, the proposed method demonstrates superior performance in handling actuator dynamics, mitigating matched nonlinear time-varying disturbances, and achieving precise trajectory tracking, even in the presence of input gain uncertainties. These improvements establish the proposed controller as a more robust and efficient alternative to traditional adaptive control methods.