887 research outputs found
Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization
The paper is concerned with patchy vector fields, a class of discontinuous,
piecewise smooth vector fields that were introduced in AB to study feedback
stabilization problems. We prove the stability of the corresponding solution
set w.r.t. a wide class of impulsive perturbations. These results yield the
robusteness of patchy feedback controls in the presence of measurement errors
and external disturbances.Comment: 22 page
Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation
Motivated by some recent results on the stabilization of homogeneous systems, we present a gain-scheduling approach for the stabilization of non-linear systems. Given
a one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show how the parameter can be rescaled as a function of the state to give a new
stabilizing controller. In the case of homogeneous systems, we obtain generalizations of some existing results. We show that this approach can also be applied to nonhomogeneous
systems. In particular, the main application considered in this paper is to the problem of stabilization with magnitude limitations. For this problem, we develop a design method for single-input controllable systems with eigenvalues in the left closed plane
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
On the stabilization problem for nonholonomic distributions
Let be a smooth connected and complete manifold of dimension , and
be a smooth nonholonomic distribution of rank on . We
prove that, if there exists a smooth Riemannian metric on for which no
nontrivial singular path is minimizing, then there exists a smooth repulsive
stabilizing section of on . Moreover, in dimension three, the
assumption of the absence of singular minimizing horizontal paths can be
dropped in the Martinet case. The proofs are based on the study, using specific
results of nonsmooth analysis, of an optimal control problem of Bolza type, for
which we prove that the corresponding value function is semiconcave and is a
viscosity solution of a Hamilton-Jacobi equation, and establish fine properties
of optimal trajectories.Comment: accept\'e pour publication dans J. Eur. Math. Soc. (2007), \`a
para\^itre, 29 page
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