107 research outputs found
Global tracking for an underactuated ships with bounded feedback controllers
In this paper, we present a global state feedback tracking controller for
underactuated surface marine vessels. This controller is based on saturated
control inputs and, under an assumption on the reference trajectory, the
closed-loop system is globally asymptotically stable (GAS). It has been
designed using a 3 Degree of Freedom benchmark vessel model used in marine
engineering. The main feature of our controller is the boundedness of the
control inputs, which is an essential consideration in real life. In absence of
velocity measurements, the controller works and remains stable with observers
and can be used as an output feedback controller. Simulation results
demonstrate the effectiveness of this method
A Lyapunov approach to Robust and Adaptive Higher Order Sliding Mode
In this paper, we present Lyapunov-based robust and adaptive Higher Order Sliding Mode (HOSM) controllers for nonlinear SISO systems with bounded uncertainty. The proposed controllers can be designed for any arbitrary sliding mode order. The uncertainty bounds are known in the robust control problem whereas they are partially known in the adaptive control problem. Both these problems are formulated as the finite time stabilization of a chain of integrators with bounded uncertainty. The controllers are developed from a class of nonlinear controllers which guarantee finite time stabilization of pure integrator chains. The robust controller establishes ideal HOSM i.e. the sliding variable and its r−1 time derivatives converge exactly to the origin in finite time. The adaptive controller establishes real HOSM, which means that the sliding variable and its r - 1 time derivatives converge to a neighborhood of the origin. Saturation functions are used for gain adaptation, which do not let the states exit the neighborhood after convergence. The effectiveness of these controllers is illustrated through simulations
-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design
Consider the -th integrator , where
, , is the -th Jordan block and
. We provide easily implementable state
feedback laws which not only render the closed-loop system globally
asymptotically stable but also are finite-gain -stabilizing with
arbitrarily small gain. These -stabilizing state feedbacks are built from
homogeneous feedbacks appearing in finite-time stabilization of linear systems.
We also provide additional -stabilization results for the case of
both internal and external disturbances of the -th integrator, namely for
the perturbed system where
and
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