In this paper, we continue the development of state feedback boundary control laws based on the backstepping methodology, for the stabilization of unstable, parabolic partial differential equations. We consider the linearized Ginzburg–Landau equation, which models, for instance, vortex shedding in bluff body flows. Asymptotic stabilization is achieved by means of boundary control via state feed...

Abstract. An explicit output-feedback boundary feedback law is introduced that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an n-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only measurements from the boundary. The backstepping method is used to design both the control law and a boundary observer. To apply backstepping the syste...

In this paper we present an abstract maximal Lp-regularity result up to T=∞, that is tuned capture (linear) Partial Differential Equations of parabolic type, defined on a bounded domain and subject finite dimensional, stabilizing, feedback controls acting (a portion of) the boundary. Illustrations include, beside more classical boundary example, two recent settings: (i) 3d-Navier-Stokes equatio...

Absorbing boundary conditions are generally associated to long-range memory behaviors. In the case of the Euler-Bernoulli beam, they are naturally based on Abel-Volterra operators of order 1/2. Diiusive real-izations of them are introduced and used for the construction of an original and eecient boundary dynamic feedback control.

Explicit boundary dissipative conditions are given for the exponential stability in L-norm of one-dimensional linear hyperbolic sytems of balance laws ∂tξ + Λ∂xξ −Mξ = 0 over a finite space interval, when the matrix M is marginally diagonally stable. The result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised Saint-Venant-Exner equ...

We develop an adaptive output-feedback controller for a wave PDE in one dimension with actuation on one boundary and with an unknown anti-damping term on the opposite boundary. This model is representative of a torsional stick–slip instability in drillstrings in deep oil drilling, as well as of various acoustic instabilities. The key feature of the proposed controller is that it requires only t...

This paper introduces an explicit output-feedback boundary feedback law that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an n-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only measurements from the boundary. The backstepping method is used to design both the control law and a boundary observer. To apply backstepping the system ...

Severe air pollution episodes have been frequent in China during the recent years. While high emissions are the primary reason for increasing pollutant concentrations, the ultimate cause for the most severe pollution episodes has remained unclear. Here we show that a high concentration of particulate matter (PM) will enhance the stability of an urban boundary layer, which in turn decreases the ...

Certain dynamical systems, such as the shift map and the logistic map, have an edge of chaos in their parameter spaces. On one side of this edge, the dynamics are chaotic for many parameter values, on the other side of the edge they are periodic. We find that discrete-time dynamical systems with wavelet filtered feedback from the dynamical variable to the parameters are attracted to a narrow pa...

The problem of absolute stability of a feedback loop of an abstract diierential system in Hilbert spaces is considered. Applications of Popov's type frequency domain criteria and of the Kalman-Yakubovich Lemma for the construction of Lyapunov functions are illustrated, in two situations pertaining distributed sytems. Finally, a new criterion for absolute stability of a class of parabolic system...