Distributed Lyapunov-Based Model Predictive Control for AUV Formation Systems with Multiple Constraints

This paper focuses on the formation tracking issue of autonomous underwater vehicles (AUVs) subject to multiple constraints in three-dimensional space. We developed a novel distributed Lyapunov-based model predictive controller (DLMPC) with a fast finite-time extended state observer (FFTESO). Initially, the external disturbances and internal uncertainties of each AUV were precisely compensated using the designed FFTESO. Subsequently, we proposed DLMPC-based position tracking and velocity tracking controllers, which solved an online optimization problem to determine optimal velocities and control forces. This hierarchical framework effectively managed system constraints, such as state constraints and actuator saturation. Additionally, the Lyapunov-based backstepping control law was applied to construct stability constraints in the distributed optimization problem, ensuring the recursive feasibility and closed-loop system stability of the proposed scheme. Sufficient conditions and attraction regions to ensure stability were explicitly provided. Finally, the simulation results demonstrated that the proposed method improved both the convergence speed and tracking accuracy by at least 30% compared to other methods.