arXiv subjects

S. Boulite

Publications and source records attributed to S. Boulite.

4 recordsLinked to original sources

arXiv2023

Null Controllability for Stochastic Parabolic Equations with convection terms

This paper addresses null controllability for both forward and backward linear stochastic parabolic equations by introducing convection terms on the drift parts with bounded coefficients. Moreover, the forward stochastic parabolic equation includes a convection term on the diffusion part. The null controllability results rely on novel Carleman estimates for both backward and forward stochastic parabolic equations, encompassing a divergence source term interpreted in the weak sense. These Carleman estimates are established through the application of the duality technique. In doing so, we resolve some previously unanswered questions (see Remarks 2.1-2.2 in [S. Tang, and X. Zhang, SIAM J. Control Optim., 48 (2009), p.p 2191-2216]). Additionally, we present a more accurate estimation of the null-control costs.

math.OC↗

arXiv2013

Stabilization of abstract thermo-elastic semigroup

In this paper we characterize the stabilization for some thermo-elastic type system with Cattaneo law and we prove that the exponential or polynomial stability of this system implies a polynomial stability of the correspond thermoelastic system with the Fourier law. The proof of the main results uses, respectively, the methodology introduced in Ammari and Tucsnak, where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system and a characterization, of the polynomial stability for C0-semigroup in Hilbert space by a polynomial estimation of the associated resolvante of the generator of this semigroup, obtained by Borichev-Tomilov.

math.AP↗

arXiv2012

Sufficient and Necessary Conditions for the Solvability of the State Feedback Regulation Problem

In this paper, we discuss the state feedback output regulation problem (SFRP) for infinite-dimensional linear control systems with infinite-dimensional exosystems. Under the polynomial stabilizability assumption, sufficient and necessary conditions are given for the solvability of the SFRP. The solvability of this problem is characterized in terms of the solvability of a pair of linear regulator equations. An application of the solvability of the SFRP for polynomial stable SISO system is given.

math.OC↗

arXiv2010

Stabilization of coupled second order systems with delay

In this paper we characterize the output feedback stabilization of some coupled systems with delay. The proof of the main result uses the method introduced in Ammari and Tucsnak \cite{at} where the exponential stability for the closed loop system is reduced to an observability estimate for the corresponding conservative adjoint system, under a boundedness condition of the transfer function of the associated open loop system.

math.AP↗