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Wave Equation With Cone-Bounded Control Laws.
- Source :
- IEEE Transactions on Automatic Control; Nov2016, Vol. 61 Issue 11, p3452-3463, 12p
- Publication Year :
- 2016
-
Abstract
- This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 61
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 119139486
- Full Text :
- https://doi.org/10.1109/TAC.2016.2519759