IEEE transactions on automatic control, 2016-11, Vol.61 (11), p.3452-3463
2016
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- Autor(en) / Beteiligte
- Titel
- Wave Equation With Cone-Bounded Control Laws
- Ist Teil von
- IEEE transactions on automatic control, 2016-11, Vol.61 (11), p.3452-3463
- Ort / Verlag
- New York: IEEE
- Erscheinungsjahr
- 2016
- Quelle
- IEEE Xplore
- Beschreibungen/Notizen
- 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.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0018-9286eISSN: 1558-2523DOI: 10.1109/TAC.2016.2519759Titel-ID: cdi_hal_primary_oai_HAL_hal_01448483v1
- Format
- –
- Schlagworte
- Aerospace electronics, Asymptotic stability, Automatic, Boundary conditions, Closed loop systems, Control systems, Dynamics, Engineering Sciences, Infinite dimensional systems, Mathematical models, Nonlinear differential equations, nonlinear partial differential equations, Nonlinear programming, Nonlinearity, Partial differential equations, Propagation, saturated controls, Stability, Tuning, Wave equations