Regularity of an Euler–bernoulli Equation with Neumann Control and Collocated Observation
نویسنده
چکیده
This paper studies the regularity of an Euler–Bernoulli plate equation on a bounded domain of Rn, n ≥ 2, with partial Neumann control and collocated observation. It is shown that the system is not only well posed in the sense of D. Salamon but also regular in the sense of G. Weiss. It is also shown that the corresponding feedthrough operator is zero.
منابع مشابه
Well-posedness and regularity for an Euler-Bernoulli plate with variable coefficients and boundary control and observation
The open loop system of an Euler–Bernoulli plate with variable coefficients and partial boundary Neumann control and collocated observation is considered. Using the geometric multiplier method on Riemannian manifolds, we show that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. Moreover, we determine that the feedthrough operator of this system is zero....
متن کاملWell-posedness and regularity of Euler–Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation
Two types of open-loop systems of an Euler–Bernoulli equation with variable coefficient and Dirichlet boundary control and collocated observation are considered. The uncontrolled boundary is either hinged or clamped. It is shown, with the help of multiplier method on Riemannian manifold, that in both cases, systems are well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. ...
متن کاملOn Well-posedness, Regularity and Exact Controllability for Problems of Transmission of Plate Equation with Variable Coefficients
A system of transmission of Euler-Bernoulli plate equation with variable coefficients under Neumann control and collocated observation is studied. Using the multiplier method on a Riemannian manifold, it is shown that the system is well-posed in the sense of D. Salamon. This establishes the equivalence between the exact controllability of an open-loop system and the exponential stability of a c...
متن کاملDynamic stabilization of an Euler-Bernoulli beam under boundary control and non-collocated observation
We study the dynamic stabilization of an Euler–Bernoulli beam system using boundary force control at the free end and bending strain observation at the clamped end. We construct an infinite-dimensional observer to track the state exponentially. A proportional output feedback control based on the estimated state is designed. The closed-loop system is shown to be non-dissipative but admits a set ...
متن کاملControllability and stability of a second-order hyperbolic system with collocated sensor/actuator
A second-order hyperbolic system with collocated sensor=actuator is considered. The semigroup generation is shown for the closed-loop system under the feedback of a generic unbounded observation operator. The equivalence between the exponential stability of the closed-loop system and exact controllability of the open-loop system is established in the general framework of well-posed linear syste...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006