Abstract
In this work, we investigate the trajectory tracking and point stabilization problems of asymmetric underactuated surface ships with non-diagonal inertia and damping matrices. By combining the novel state and input transformations, the direct Lyapunov approach, and the nonlinear time-varying tools, the trajectory tracking controller is derived, guaranteeing global κ-exponential convergence of state trajectory to the reference one satisfying mild persistent exciting conditions. By properly designing the reference trajectory, the proposed tracking scheme is also generalized to achieve global uniform asymptotic point stabilization. Simulation examples are given to illustrate the effectiveness of the proposed control schemes.
Highlights
Based on the simplified assumption of the symmetric ship model with diagonal inertia and damping matrices, various control schemes have been developed for point stabilization [2,3,4,5,6,7,8], trajectory tracking [8,9,10,11,12,13], both point stabilization and trajectory tracking [14,15], and path following [16,17,18]
Realizing that such a simplifying model is unrealistic, recent research has aimed to deal with an asymmetric ship model with non-diagonal inertia and damping matrices [19,20,21,22,23,24,25,26]
For the full state trajectory tracking control of asymmetric ships, a controller is designed in [21] to force position and orientation to globally track their reference trajectories; the tracking errors are only guaranteed bounded, not convergent to zero, and the reference trajectory must satisfy some strict assumptions, excluding the reduced fixed-point trajectory and the one converging to a fixed-point
Summary
Control of surface ships is an active topic of research that continues to receive a considerable interest in the field of nonlinear control systems [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. Based on the simplified assumption of the symmetric ship model with diagonal inertia and damping matrices, various control schemes have been developed for point stabilization [2,3,4,5,6,7,8], trajectory tracking [8,9,10,11,12,13], both point stabilization and trajectory tracking [14,15], and path following [16,17,18]. The purpose of this work is to solve the asymptotic trajectory tracking and asymptotic point stabilization problems of asymmetric surface ships having non-zero off-diagonal terms presented in their inertia and damping matrices. By properly setting the reference trajectory, the obtained tracking controller can be used to achieve global uniform asymptotic point stabilization, and provides a unified frame to solve both the trajectory tracking and the point stabilization problems of the asymmetric ships with non-diagonal inertia/damping matrices. The control object for trajectory tracking can be stated as: find a feedback control law w1(·), w2(·) such that the origin of the closed-loop error model (19)-(20) is GKES
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