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Robust global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters
Author(s) -
Xie Wenjing,
Ma Baoli
Publication year - 2013
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3129
Subject(s) - control theory (sociology) , underactuation , bounded function , lyapunov function , kinematics , exponential stability , uniform boundedness , controller (irrigation) , mathematics , stability theory , computer science , law , control (management) , nonlinear system , mathematical analysis , physics , classical mechanics , quantum mechanics , artificial intelligence , political science , agronomy , biology
Summary The full‐state stabilization scheme is proposed for the control of an underactuated surface vessel with unknown modeling parameters. By knowing only the upper/lower bounds of model parameters, the designed controller is the first one able to globally uniformly asymptotically stabilize all the states of the vessel to zero. The virtual surge velocity control law is first derived, which makes the Lyapunov function at the kinematic level non‐increasing, irrelevant to the yaw velocity, leaving a freedom for choosing the virtual yaw velocity control law to stabilize the other state variables. After finishing the design of virtual velocity law, the back‐stepping approach and the Lyapunov redesign technique are combined to obtain the actual force/torque control law despite parameter uncertainties. Simulation examples are given to illustrate the effectiveness of the proposed control law, showing that all the states and the control inputs are globally uniformly asymptotically convergent to zero under parameter uncertainties and are globally bounded under unknown external bounded disturbances. Copyright © 2013 John Wiley & Sons, Ltd.