Global uniform asymptotic stabilization and k-exponential trajectory tracking of underactuated surface ships with non-diagonal inertia/damping matrices

TL;DR

This paper develops new control strategies for underactuated surface ships with complex inertia and damping, ensuring global stability and accurate trajectory tracking through advanced nonlinear control techniques.

Contribution

It introduces novel state transformations and control methods that guarantee global uniform asymptotic stabilization and exponential trajectory tracking for ships with non-diagonal matrices.

Findings

Controllers achieve global convergence in simulations.

Effective handling of non-diagonal inertia and damping matrices.

Proven stability under mild persistent excitation conditions.

Abstract

In this work, we investigate the state stabilization and trajectory tracking problems of underactuated surface ships with full state model of having non-diagonal inertia and damping matrices. By combining the novel state transformations, the direct Lyapunov approach, and the nonlinear time-varying tools, the stabilization and the trajectory tracking controllers are developed respectively guaranteeing global uniform asymptotic convergence of the state to the desired set point and global exponential convergence to the desired reference trajectory via mild persistent exciting conditions. Simulation examples are given to illustrate the effectiveness of the proposed control schemes.