Smooth time-varying uniform asymptotic stabilization of underactuated surface vessels

Robust global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

“…To remove the term v in , we introduce a new state transformation , which is the same as Z 2 in or z 3 in . Differentiating yields .…”

“…In all these control problems, the full‐state stabilization is the most difficult one because the underactuated surface vessel system is neither linear controllable nor satisfying the Brokett's condition , and thus it cannot be asymptotically stabilized by classic linear stabilizing tools or by any time‐invariant continuous feedback. However, it is shown to be locally strongly accessible and small‐time locally controllable at any equilibrium, implying the existence of discontinuous time‐invariant feedback laws , smooth periodic time‐varying feedback laws and hybrid feedback laws . The less difficult control problem of underactuated vessels is the position stabilization because the system is still linear uncontrollable/unstabilizable, but satisfies the Brokett's condition , implying that the problem still cannot be solved by classic linear tools, but can be solved by a time‐invariant continuous feedback.…”

“…In the aforementioned papers on stabilizing the vessel, the model is assumed known exactly. Indeed, uncertainties exist in any realistic system because of modeling errors and environmental disturbances.…”

“…However, the inclusion of uncertainties introduces additional unknown or uncertain terms, which may destroy control performances originally fulfilled for exact model systems. Most of the existing schemes rely on converting the exact state model to a cascaded structure , which fail to work if the model parameters are unknown and appear in the expressions of control laws. A good control law should be robust against to model parameter uncertainties while guaranteeing a satisfactory behavior of the system, so it is desired to search control laws that globally uniformly asymptotically stabilize the vessel with parameter uncertainties.…”

Global Asymptotic Trajectory Tracking and Point Stabilization of Asymmetric Underactuated Ships with Non-Diagonal Inertia/Damping Matrices

“…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].…”